Resources Efficiency Optimisation in a Job ShopScheduling Problem

Joao Pedro Filipe Nunes

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisors: Prof. Carlos Baptista CardeiraProf. Paulo Miguel Nogueira Pecas

Examination Committee

Chairperson: Prof. Paulo Jorge Coelho Ramalho Oliveira

Supervisor: Prof. Paulo Miguel Nogueira Pecas

Members of the Committee: Prof. Elsa Maria Pires Henriques

Prof.Duarte Pedro Mata de Oliveira Valerio

June 2017

Acknowledgments

I would like to thank to my supervisors, Prof. Paulo Pecas and Prof. Carlos Cardeira, for their support,guidance and motivation during the development of this work. I am also very grateful to Prof. InesRibeiro, for sharing her knowledge and experience.

I would like to thank to my office colleagues for their companionship and support along these months,for their advices and enlightenment, which helped me to get to know more.

I am very grateful to all my friends whose support and motivation were essential along this academicjourney. To David, Rafael, Tiago, Diogo and Filipe or their companionship during these last months andlunch hours. An many others that are not listed, but had an enormous input in my academic journey.

To my parents and sister I’d like to thank for all support and have always believed in me during thisjourney, even when I didn’t, for all patience, attention and encouragement.

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Abstract

The need to optimise the utilisation of resources in the manufacturing process is a demand, not onlyexternal but also in the companies itself.

In the course of scheduling the production plan, exists the request to assure the maximum effective-ness of the machines. For that exists the need to create algorithms that can achieve a good solution ina short period.

Accordingly, optimise the resources in planning process proves to be a difficult task in the manufactur-ing industry, which leads to the use of optimisation techniques as support. In this thesis, the optimisationwas performed with the use of meta-heuristics.

Towards exploring the impact that the energy consumption and cost of the machines have on theresource utilisation, taking as case study the mould production industry, genetic algorithms were imple-mented, to compare and relate the two factors were performed several tests for different scenarios.

The existence of rework in the manufacturing process is a factor that companies try to reduce on adaily basis. A study to minimise the effect of parts with defects was conducted, for that, a simulationof the process for an overproduction situation was performed, considering the flow of the process forseveral machine configurations.

The obtained results were positive. The proposed optimised planning methods presented solutionsthat can prove helpful in the support to the decision.

In the simulation for the several machine configurations, the results allow the understanding flow ofthe process and the best choice for the different levels of quality.

Keywords: Resource Efficiency, Optimisation, Planning, Meta-heuristics, Mould Manufacturing

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Resumo

A necessidade de optimizar a utilizacao de recursos no processo de fabrico e um requesito, nao apenasexterno, mas tambem nas proprias empresas.

No decorrer dao planeamento de producao a necessidade garantir a maxima eficacia das maquinas.Para isso existe sao criados algoritmos que consigam uma boa solucao num curto perıodo.

Consequentemente, o autilizacao correcta dos recursosno planeamento revela-se uma tarefa difıcilna industria, o que conduz ao uso de tecnicas de optimizacao como suporte. Nesta dissertacao, aotimizacao foi realizada com o uso de metaheurısticas.

Para explorar o impacto que o consumo de energia eo custo das maquinas tem sobre a utilizacaode recursos, e tendo como estudo de caso a industria de producao de moldes, algoritmos geneticosforam implementados, para comparar e para relacionar os dois fatores foram realizados varios testespara diferentes cenarios.

A existencia de retrabalho no processo de fabrico e um fator que as empresas tentam reduzir diaria-mente. Foi realizado um estudo para minimizar o efeito de pecas com defeitos, para isso, foi realizadauma simulacao do processo para uma situacao de sobreproducao, considerando o fluxo do processopara sendo a simulacao para varias configuracoes de maquina.

Os resultados obtidos foram positivos. Os metodos de planeamento propostos, apos otimizadosapresentaram solucoes que podem ser uteis no suporte a decisao. Na simulacao para as variasconfiguracoes da maquina, os resultados permitem entender o fluxo do processo e a melhor escolhapara os diferentes nıveis de qualidade.

Keywords: Eficiecia de recursos, Optimizacao, Planieamento, Meta-Heuristicas, Producao de Moldes

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Contents

List of Tables viii

List of Figures x

Acronyms xiii

1 Introduction 11.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Dissertation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Efficiency in Production Systems 52.1 Efficiency of the Production System, a Global Trend . . . . . . . . . . . . . . . . . . . . . 52.2 Eco-Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Eco-efficiency Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Eco-efficiency in the industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Lean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 key Performance Indicator (KPI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Engineering of the Job Shop Problem and Optimisation Technics 133.1 Introduction to Job Shop Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Flexibility in a manufacturing system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3 Flexible Job Shop scheduling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.1 Total Flexibility vs Partial Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4 Review on previous studies on PF-JSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.5 Optimisation Technics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5.1 Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.5.2 Meta-heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Effect of Energy consumption in the Process Plan 214.1 Process Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1.1 Problem Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.1 Guide lines for formulating the scheduling problem . . . . . . . . . . . . . . . . . . 264.2.2 Position Based MILP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Algorithm Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.1 Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3.2 Crossover Percentage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3.3 Elite Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4.1 Time-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4.2 Cost-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4.3 Energy-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.4.4 Energy-Cost-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.6 Operationalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5 Simulation of a System in Over Production 515.1 Model of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2 Sensitivity Analysis on the Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . 545.3 Production Systems Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3.1 Production System with Non-Dedicated Machines with FIFO Queues . . . . . . . 565.3.2 Production System with Non-Dedicated Machines with Priority Queues . . . . . . 585.3.3 Production System with a Partially Dedicated Machine . . . . . . . . . . . . . . . . 595.3.4 Production System with a Dedicated Machine . . . . . . . . . . . . . . . . . . . . . 61

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6 Conclusion 656.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Bibliography 67

viii

List of Tables

2.1 General Eco-efficiency Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 Previous studies on PF-JSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Common Dispatching Rules Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Times of Process Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Characteristics of the Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3 Time-based Method - Results Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.4 Cost-based method - CNC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.5 Cost-based method - Lathe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.6 Cost-based method - Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.7 Cost-based method - Wire EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.8 Cost-based method - Drill EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.9 Cost-based method - Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.10 Cost-based method - Results Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.11 Energy-based method - CNC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.12 Energy-based method - Lathe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.13 Energy-based method - Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.14 Energy-based method - Wire EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.15 Energy-based method - Drill EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.16 Energy-based method - Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.17 Energy-based method - Results Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.18 Energy-Cost-Based Method - CNC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.19 Energy-Cost-Based Method - Lathe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.20 Energy-Cost-Based Method - Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.21 Energy-Cost-Based Method - Wire EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.22 Energy-Cost-Based Method - Drill EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.23 Energy-Cost-Based Method - Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.24 Energy-Cost-Based Method - Results Aggregation . . . . . . . . . . . . . . . . . . . . . . 42

4.25 Comparison % occupation machines - CNC . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.26 Comparison % occupation machines - Lathe . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.27 Comparison % occupation machines - Milling . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.28 Comparison % occupation machines - Wire EDM . . . . . . . . . . . . . . . . . . . . . . . 45

4.29 Comparison % occupation machines - Drill EDM . . . . . . . . . . . . . . . . . . . . . . . 46

4.30 Comparison % occupation machines - Rectification . . . . . . . . . . . . . . . . . . . . . . 46

4.31 Results Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.32 Normalized Overall Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

ix

5.1 Average Throughput Time Non-Dedicated FIFO System . . . . . . . . . . . . . . . . . . . 565.2 Throughput time [Hours] in a Non-Dedicated system with FIFO Queue to the mold A . . . 575.3 Average Throughput Time Non-Dedicated Priority System . . . . . . . . . . . . . . . . . . 585.4 Throughput time [Hours] in a Non-Dedicated system with Priority Queue to the mold A . . 595.5 Average Throughput Time Partially Dedicated Priority System . . . . . . . . . . . . . . . . 605.6 Throughput time [Hours] in a Partially Dedicated system to the mold A . . . . . . . . . . . 615.7 Average Throughput Time Dedicated Priority System . . . . . . . . . . . . . . . . . . . . . 625.8 Throughput time [Hours] in a Dedicated system to the mold A . . . . . . . . . . . . . . . . 635.9 Comparison Between Average Throughput Time of the Systems . . . . . . . . . . . . . . 64

x

List of Figures

2.1 PDCA Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 KPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Representation of TF-JSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Representation of PF-JSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1 Population Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 % Crossover Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Elite Group Average Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 Elite Group Standard Deviation Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5 Elite Group Iteration Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.6 Comparison between the different methods applied . . . . . . . . . . . . . . . . . . . . . . 48

5.1 Flowchart of CNC Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Evolution on CNC Queue with a Quality Level of 100% . . . . . . . . . . . . . . . . . . . . 535.3 Effect of the simulation time on the throughput time . . . . . . . . . . . . . . . . . . . . . . 545.4 Flowchart of CNC Production with a Dedicated Machine . . . . . . . . . . . . . . . . . . . 555.5 Flowchart of CNC Production with a Partially Dedicated Machine . . . . . . . . . . . . . . 555.6 Throughput time in a FIFO system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.7 Throughput time in a FIFO system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.8 Throughput time in a Non-dedicated Priority System . . . . . . . . . . . . . . . . . . . . . 585.9 Throughput time in a Non-dedicated Priority System . . . . . . . . . . . . . . . . . . . . . 595.10 Throughput time in a Partially Dedicated Priority system . . . . . . . . . . . . . . . . . . . 605.11 Throughput time in a Partially Dedicated Priority system - Mould A . . . . . . . . . . . . . 615.12 Throughput time in a Dedicated system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.13 Throughput time in a Dedicated system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

xi

Acronyms

DMAIC Define-Measure-Analyze-Improve-Check.

EDM Electrical discharge machining.

F-JSSP Flexible Job Shop Scheduling Problem.

GA Genetic Algorithm.

JSSP Job Shop Scheduling Problem.

KEPI key Environmental Performance Indicator.

KPI key Performance Indicator.

MILP Mixed Integer Linear Programing.

OEE Overall Equipment Effectiveness.

OR Operation Research.

PDCA Plan-Do-Check-Act.

PF-JSSP Partial Flexible Job Shop Scheduling Problem.

PSO Particle Swarm Optimization.

Tc Cycle time.

TF-JSSP Total Flexible Job Shop Scheduling Problem.

TPS Toyota Production System.

WBCSD World Business Council for Sustainable Development.

WIP Work in Progress.

xiii

Chapter 1

Introduction

In this new age, companies want to stay competitive while reducing the environmental impact of pro-cesses and products, which has been reflected in the increase of environmental demands from govern-mental bodies and also from the costumers, who stress the importance of the environmental perform-ance of companies and demand for more environmentally-friendly products.

The need for sustainability emerged, and three main pillars have to be taken into account: economicgrowth, environmental protection and social equality. In need of practical actions, two of those threepillars were put at stake by hands of Eco-efficiency, and this management philosophy has emergedand became the principal evaluation and decision tools for process focused on resource efficiency. Itis mandatory that these processes become more and more efficient in order to be sustainable and toguarantee the desired competitiveness level.

Evidence suggests that Lean, Six Sigma and Green approaches make a positive contribution to theeconomic, social and environmental performance of organisations. However, evidence also suggeststhat organisations have found their integration and implementation challenging[1]. The increase of re-source (energy and material) efficiency by eliminating unnecessary consumption represents the logicalcontinuation from lean manufacturing to lean and green manufacturing. However, economic efficiencyremains the primary decision criterion for the implementation of the corresponding strategies[2].

Manufacturing must accept responsibilities for placing pressure on the environment. Indeed, it isbecoming increasingly apparent that manufacturers play a critical, multi-faceted role in dictating thematerial and energy resources in modern society. The processes designed and employed directly bymanufacturers have a sizable environmental impact, the control of the energy and resource intensiveproduction of materials and the energy and resources consumed by products across their life cycle [3].

This scenario led studies to be carried out towards an improvement of the environmental essen-tials within the manufacturing industrial activities, thus uncovering the elements and factors that mostlyinfluence it.

Currently exists a European Research project, MAESTRI, funded by the European Union’s Horizon2020 research and innovation program, that ”aims to advance the sustainability of European manufac-turing and process industries...to encourage a culture of continuous improvement within manufacturingand process industries. It supports informed decision making processes and strategies for continu-ous performance improvement. Furthermore, the proposed framework accounts simultaneously for theenvironmental and economic performance, helping to define priorities and estimate impacts.”[4].

1

To introduce Eco-efficiency within the strategies and policies of companies and organisations, prac-tical measures are required, though economic/value and environmental scopes are vast which lead todifferent interpretations. From there comes the necessity of developing general and proper metrics toenable designers, engineers and managers to orientate their decision processes, from the factory plan-ning, to operations, management and control [5].

Resorting to Operation Research (OR) techniques while considering the inherent complexity of theproblem and the need for efficient solutions, appeals for the so-called meta-heuristics, a family of ap-proximate optimization techniques that gained a lot of popularity in the past two decades, being amongstthe most promising and successful optimization techniques. This significant growth of interest in meta-heuristic domain is due to the fact that meta-heuristics provide “acceptable” solutions in a reasonabletime for solving hard and complex problems in science and engineering [6].

1.1 Contributions

The flexibility of the mould production system results in a significant diversity of the machines types.For this production system, the complexity of the scheduling can is increased with the addition of theenvironmental impacts and with the search for a more sustainable production. Since manufacturingcompanies need to maintain the competitiveness, the creation and development of tools to supportthe decision makers are essential to evaluate the current state of the companies and assure a betterunderstanding of the path to take in search for continuous improvement.

In this thesis was presented a study on the effect that the energy consumption has on the production,and the possible alternatives to the production planning. A penalization based optimisation was used toachieve the best energy consumption and the best cost per hour of the machines. The main contributionof this work comprehends the application of optimisation methods to support the decision making in theplanning phase. By applying the meta-heuristic Genetic Algorithm (GA) to improve the relation betweenthe energy consumption and the cost per hour of the machines in the duration of the project, while stillprocessing the job in the shortest period of time.

The other contribution was the tests of several methodologies to machine formations, applied to thecritical section, to improve the process flow reducing the effect of the existent Work in Progress (WIP)and minimising the permanence time of the parts in the process.

With these tests, it was possible to demonstrate the effects of choosing the different machine form-ations. For the several levels of quality of the system, the time of completion of the parts changes fromconfiguration to configuration, with some configurations having a better performance for higher levels ofquality and others achieving the best performance when the quality of the system decreases.

1.2 Dissertation Overview

A brief overview of the developed work is presented in the following points. Initially, some researchwas made in the fields of Resource Efficiency and in the understanding of the Job shop schedulingproblem and the optimisation techniques such as the heuristics and meta-heuristics. After making theassessment of the problem, a test to the effects of the energy consumption in the planning was made.It was also developed a methodology to deal with systems that present some degree of rework. Alongwith the application of both studies, follows the methodology, results and conclusions.

2

Chapter 1 - Introduction. In this chapter, a text presents an incorporation and utilisation of the ResourceEfficiency technics and the need to incorporate the simulation in the process of planning and scheduling.It also includes the motivation, contributions and an overview of this dissertation.Chapter 2 - Efficiency in Production Systems. I this chapter is shown the efforts in the industry toachieve a greener way of production. And the presentation of two established philosophies, the Eco-efficiency, where the metric for this assessment is shown and the development and use of this philosophyin the industry. The second philosophy is the Lean production system, a structural way of reducing thewaste in the different systems.Chapter 3 - Engineering of the Job Shop Problem. The job shop scheduling problem is a subjectof constant discussion in the literature due to the growth in complexity and diversity in the production,and in this chapter is discussed its complexity, mathematical formulation and the optimisation methodsto solve it, like the meta-heuristics like GA, Particle Swarm Optimization (PSO) among others.Chapter 4 - Effect of Energy consumption in the process plan. A study on the effects that consid-ering the energy consumption, and the machine cost in the work schedule have in the duration of theproject and for the machine percentage of usage.Chapter 5 - Simulation of a system in overload In this chapter a closer analysis in the manufactur-ing process was taken and were done tests in the configuration and in the queue of the machines tocomprehend how each one would handle the existence of rework when the system is overflowed withrequested parts.Chapter 6 - Conclusion. A final statement regarding the development of the proposed solution andtheir outcomes.

3

4

Chapter 2

Efficiency in Production Systems

This chapter is divided into three sections and is focused on the research of resources efficiency in themanufacturing process, being this the environmental resources, primarily the energy consumption usedto solve the problem in this dissertation, and the time wasting resources.

The first section has the intend to demonstrate the growth in the environmental friend industry, mainlythe energy consumption, and policies, and the efforts taken to achieve the goal of sustainability.

The second chapter is a study on the eco-efficiency, a methodology that is focused in two of the threepillars of the sustainability, the economic pillar and the environmental pillar. And how this methodologyis used to assure a correct use of the resources in an eco-friendly form balancing a trade-off with theeconomic factors.

The third chapter is the explanation of the Lean philosophy, this philosophy has the goal of reducingthe waste in the production process, maximising the added value of the process, using fewer resourcesand minimising the inefficiencies.

2.1 Efficiency of the Production System, a Global Trend

In the era of climate awareness, not only organisations but also customers, companies and governmentshave directed their attention towards the environment. Through the exposure of the media, global warm-ing and depletion of natural resources, resultant from human activities, put companies on a greener pathof development [7].

According to [8, 9] companies have the responsibility to contribute to a sustainable development,improving the resource efficiency of their operations, where reducing their environmental implicationsis gaining importance from an economic perspective as well, not neglecting its profit orientation whenstriving for an improved environmental sustainability. Its goal thus has to be to improve both in theenvironmental and in the economic performance simultaneously[10].

As a consequence, manufacturers are realising the financial and environmental benefits of practisingsustainable manufacturing, not only because of improvements in energy but also in another resource.Sustainable Manufacturing can be defined as the creation of products or services through economicprocesses that minimise the environmental impacts while conserving energy and natural resources [11].

5

The lack of industrial applications to reduce the waste of energy, due to the lack of information onhow to do it and the benefits that would result from that reduction. Also the uncertainty of obtainingsuccessful results and the potentially negative effects has held back the efforts on its improvement.[12]

Sustainable machine tools consume less energy and have low costs during their life cycle. With theincrease in energy prices, the energy consumption of machine tools is a very important factor regardingecological and economic targets. ISO 20140 ”Environmental and energy efficiency evaluation methodfor manufacturing system”, ISO 22400 ”Key performance indicators for manufacturing operations man-agement” and ISO 14955 ”Environmental evaluation of machine tools” are being developed with theobjective of reducing energy consumption and maintain performance and cost-effectiveness [13].

2.2 Eco-Efficiency

The sustainability improvement effort must achieve benefits in, all three elemental pillars, environmental,economical and social[14].

The concept of Eco-efficiency emerged from the need of rapid and useful answers, whose ”prac-tical and theoretical importance lies in its ability to combine performance along two of three pillars ofsustainable development, environment and economics”[15].

In 1990 for the first time, the term Eco-efficiency was discussed for by two researchers, Schalteggerand Sturm, being this concept adopted for the first time by the World Business Council for SustainableDevelopment (WBCSD) and presented in 1991. Eco-efficiency is has been turning more and morecommon and widely used for different purposes, shifting from specific for larger systems, achievingeconomic and environmental improvements[15].

The WBCSD defines eco-efficiency as being “achieved by the delivery of competitively priced goodsand services that satisfy human needs and bring the quality of life, while progressively reducing ecolo-gical impacts and resource intensity throughout the life-cycle, to a level at least in line with the Earth’sestimated carrying capacity.”[16]

The two most common goals of eco-efficiency determined by the WBCSD are (i) measuring progressand (ii) internal and external communication of economic and environmental performance. For that theWBCSD identified seven elements, called the eco-efficiency principles:

1. Reduce material intensity

2. Reduce energy intensity

3. Reduce dispersion of toxic substances

4. Enhance recyclability

5. Maximize use of renewable resources

6. Extend product durability

7. Increase services intensity

A measurement framework for Eco-efficiency was proposed by the WBCSD, where the relationshipbetween economic growth and environmental pressure is expressed by the ratio represented by theequation 2.1.

6

Eco´ efficiency “ProductionorserviceV alue

EnvironmentalInfluence(2.1)

2.2.1 Eco-efficiency Indicators

To measure the level of eco-efficiency the industry uses the equation 2.1, and thekey EnvironmentalPerformance Indicator (KEPI) are the environmental influence, the denominator, used to monitor productperformance, as they can indicate improvement opportunities to prevent environmental damage[17]. Foran organisation KEPI or Green Performance indicators provide a way to measure and quantify theirenvironmental performance[18].

In the ”Environmental Key Performance Indicators - Reporting Guidelines for UK Business” [10] wereproposed guidelines to give clear guidance to companies on how to report their environmental andeconomical performance, defining which key Performance Indicator (KPI) are the most relevant by sectorand to set business rationale for managing companies performances.

The KEPI are represented by four sectors, Emission to air, fossil fuel consumption in transport-ation and total air emissions, Emissions to water, polluted liquid waste volume, Emissions to Land,reusable parts, rate of defective products and number of components, and Resource Use, product dens-ity, useful lifetime, degree of utilization, number of hazardous materials and packing mass fraction[17].

Eco-efficiency indicators rose from the need to measure and quantify Eco-efficiency in order to provideimportant qualitative and quantitative information for decision making. They can be defined as a para-meter or a reference value of a parameter, and are used worldwide as a management tool to assess acompany’s progress based on a certain requirement [5].

The eco-efficiency indicators are based on 8 principles that ensure that they are not only accurate anduseful for all kinds of businesses but also are scientifically supportable and environmentally relevant. TheWBCSD suggests that the eco-efficiency indicator should follow the following principles[19].

1. Be relevant and meaningful with respect to protecting the environment and human health and/orimproving the quality of life

2. Inform decision making to improve the performance of the organization

3. Recognize the inherent diversity of business

4. Support benchmarking and monitoring over time

5. Be clearly defined, measurable, transparent and verifiable

6. Be understandable and meaningful to identified stakeholders

7. Be based on an overall evaluation of a company’s operations, products and services, especiallyfocusing on all those areas that are of direct management control

8. Recognize relevant and meaningful issues related to upstream (e.g. suppliers) and downstream(e.g. product use) aspects of a company’s activities

The classification of the indicators of eco-efficiency can be done as seen in the table 2.1, used byany business, relating to a global concern or business value, with measuring methods accepted globally,using available metrics for impact measurement, or Business specific indicators which are defined fromone business, to another, not being necessarily less important than the first group. For the Business.

7

Specific indicators the use of the ISO 14031 standard (ISO 2013)is recommended as a guide for theselection of relevant indicators[5].

Table 2.1: General Eco-efficiency Indicators[19]

Indicators Units

Product/ Service value

Quantity of goods/servicesproduced or provided

Number or mass (Kg, ton, etc.)

Net sale e ,$,$, etc.

Environmental Influence inproduct/service creation

Energy Consumption GJ, KW.h, etc.

Material Consumption Kg, ton, etc.

Water Consumption m3

Greenhouse gas emissions CFC11 equivalent/ton

Ozone depletins substanceemissions

CO2/ton

2.2.2 Eco-efficiency in the industry

The Manufacturing sector has a high environmental impact associated. Consuming both renewableand non-renewable materials as well as large amounts of energy, causing an enormous stress for theenvironment. Manufacturing also releases solid, liquid, and gaseous waste streams that can result indamage to the environment[3].

Manufacturers, when faced with this situation, are externally pressured to assure an increase in theirenergy efficiency and reduce their environmental footprint[20].

The manufacturing process transforms inputs such as materials, personnel and energy into products,these finished products often originate undesirable outputs like different forms of waste and other emis-sions. Within the last two centuries, industrial revolutions lead to manufacturing in factories with highermanufacturing volumes and productivity. With the economic aspects in focus, factories are associatedwith diverse negative environmental and social impacts[5]

The governments have changed the “end-of-pipe” environmental laws to more comprehensive ones,in the hope of change, broadening the responsibility of producers towards a “cradle-to-grave” perspective[17]. According to the National Research Council of the United States of America, 70% or more of finalproduct costs is determined in the initial design stages. The design is, therefore, a critical determinantnot only of competitiveness but also of the consequences to the environment[21].

8

2.3 Lean

The concept of Lean was developed in 1990 by Womack, Jones and Roos that was based on themethodology used by Toyota, Toyota Production System (TPS), created by Taiichi Ohno.

The main ideology of the TPS was that to maintain quality, efficiency and flow trough the system.Where a total view of the systems in the manufacturing process is Key factor[22].

While The goal with the Lean Thinking is to achieve zero waste by maximising the value added ofthe product in each stage of the process, for that every process has to compel four factors known asV.A.C.A[23].

• Valuable

The stage need to aggregate value to the costumer, if it doesn’t then it should be eliminated.But if the stage is necessary and can’t be eliminated, it must be the simplest possible.

• Adequate

The stage should be done with the appropriate resources and the correct way, reducing wastesrelated with rework and/or movement.

• Capable

Capability of a stage is measured by the stability presented, and can be characterized by a lowstandardization. Where stages or processes with a low level of capability generate WIP, reworkand movement.

• Available

A stage with that is unavailable or has long Cycle time (Tc), will generate WIP , overproductionand movement. Being characterized by processes with unbalanced work flow.

The main goal of the Lean philosophy is to eliminate wastes, improving quality while reducing theproduction time and costs.

When the value added time is equal to the total lead time, creating a perfect process with zero waste.For that is necessary to optimize the flux of products.

According to Taiichi Ohno wastes are all the activities in the processes that don’t add value to theproduct, the authors consider the existence of the 7+1 Wastes of Lean, where the 8th waste is thewaste of the workers talent [24].

1. Overproduction - Producing work or providing services that were not required or requested, over-producing same type of work encompasses other wastes.

2. Waiting - Reducing this waste is considered the most easily achievable, often people don’t thinkas product sitting in a station as a waste, considered also the excessive number of times an objectis ”touched”.

3. Motion - The movement of people, papers, etc. that doesn’t add value is waste. It can be createdby an deficient access to the supplies, poor plant layout or ineffective office equipment.

4. Transport - Is an important waste and affects the delivery of any work.

5. Over-processing - Doing more work or effort than required in the work by internal or externalcostumers is a waste, since time and resources are being wasted with no added value.

9

6. Inventory - Excessive supplies, Work piles are waste, since they require space or time that shouldbe used in improving the process.

7. Defects - The existence of defects generates additional work to repair the defect or the productionof additional units, increasing costs and processing time, this waste can be reduced by reducingthe velocity of the task, working correctly.

8. People - The under-utilizing of people is a result of not placing the right worker in the right stage,where they will not use their full potential and knowledge.

The 5’S, was created as a methodology to help identify and eliminate the wastes, they are the fivesteps of a workplace organization and were developed through intensive work in manufacturing context.Kaizen, continuous improvement, at any company should start with three activities, standardization, 5’Sand muda, waste, elimination[25].

1. Seiri - Sort - Separating the necessary from the unnecessary , and discard them later.

2. Seiton - Straighten - Arrange all the items remaining in orderly manner.

3. Seiso - Scrub - Keep the machines and working environments clean.

4. Seiketsu - Systematize - Extend the concept of cleanliness to oneself, and continuously practicethe preceding three steps.

5. Shitsuke - Standardize - Build a self-discipline and make a habit of engaging in 5’S by establishingstandards.

A Lean system to ensure the continuous improvement and the elimination of wastes is the Plan-Do-Check-Act (PDCA) cycle, represented in the figure 2.1, a well known project model that precededother model like the Define-Measure-Analyze-Improve-Check (DMAIC). It is used in the maintenance,improvement of products and process, as in the innovation process[26].This cycle is a method that promotes the Kaizen Philosophy and is applied in four distinct steps[25].

• Plan - Recognize an opportunity, and plan the change.

• Do - Test the change.

• Check - Review the test, analyze the results, and identify key learning

• Act - Take action based on what is learned in the check step.

Figure 2.1: PDCA Cycle[26]

10

2.3.1 key Performance Indicator (KPI)

In any organization its possible to find gaps between he wanted performance and the real performanceof the organization, and the KPI allows to attribute a value to that gap, showing where the organizationshould act in order to improve the overall performance[27][28].

KPI gives to the organization a way to define strategies to achieve predefined goals, they are usedin great part to evaluate the organization status and predict the benefits of changes in the process. KPIare represented by quantified values, where their selection is based in critical factor for the organization.[29][30].

Figure 2.2: KPI[31]

To develop a system based on KPI, this indicator have to be chosen previously, and the choice mustbe SMART, ( Specific, Measurable, Achievable, Realistic and Time based)[32]. Some rules should beconsidered for selection of these indicators.[31]

• Focus on critical factors, shouldn’t be used to many indicators so the measures can do real impactin the process. If to many indicators are used the confusion degree will be higher with no addedvalue.

• Ensure the KPI represent the strategy of the organization, as seen before each organization hasits own strategy, and the chosen KPI must be the ones that are critical to that strategy.

• KPI relatable through all the organization, the KPI shouldn’t be made by sector, instead they mustrelate the sectors with each other, so every member can understand the metrics and be proactivechecking for possible problems and solution, and also analyze the status of the organization.

• Validate the data for the KPI, before any measure is implemented all the data acquired should bevalidated to check for its repeatability and reproducibility, then just there the standardization of thesystem is proved.

• Check if KPI are controllable, for the chosen indicators the operators must be able to control theeffects of any improvement to the system, and that this improvements are related with the goals.

The most common Indicators used by different organization accordion to a large number of researchpapers an corroborated in publications like [33].

• Production - It is the KPI the demonstrates the amount of product created, can be quantified byshift of production, week or monthly levels of production. This indicator is used to compare valuesbetween shifts or different operators to find the points where the production capacity is lost.

11

• Quality - Represents the amount of wast produced. The goal of the corporations is to reduce thislevel of wast allowing a reduction in the production costs, by using this indicator the organizationcan control this ratio in acceptable levels.

Quality “ApprovedProducts´RejectedProducts

ApprovedProducts(2.2)

• Rate - Measures the speed of production, if the level of production is too fast the quality of theproduct is compromise, and if the production is to slow the organization will not be able to completethe orders on time. So this indicator is used to keep the levels of production at a certain point. Thevalue of this indicator is inversely proportional to the Tc. Tc is the time that takes to finish theslowest task, this value can’t be higher than the Takt Time.

Rate “1

Tc(2.3)

• Target - This indicator is used to set specific goals to the levels of production and overall quality ofthe process, the goals are set individually to each operator, and for the organization as a whole toimprove the productive process.

• Takt Time - maximum time allowed between two consecutive operations or finalized products. Thisindicator allows to check where are the bottlenecks of the process.

Takttime “AvailableT ime

Demand(2.4)

• Downtime - Considered one of the most essential indicators, representing a larger cost to theorganization. Where the main goal is to reduce this value in order to minimize the productivelosses.

• WIP - Is the number of partial finish products waiting in queues or buffers to completion.

WIP “ Throughputˆ Tc (2.5)

Throughput time is the time that a products take from the start to the end of production.

• Overall Equipment Effectiveness (OEE) - It measures the efficiency in the usage of the equip-ments, resources and men power, the goal is to get an higher value, taking the best advantagepossible of the resources available.

OEE “ RatioˆQuality ˆAvailability (2.6)

12

Chapter 3

Engineering of the Job Shop Problemand Optimisation Technics

In this chapter, the concept of Job shop is presented, and the flexibility of this concept is demonstrated.To complement the optimisation technics, heuristics and meta-heuristics, are presented and comparedin its utility to solve this type of problems.

This chapter is divided into five sections, in the first three sections consider the problem environment,its formulation constraints and particularities in the mathematical possibilities, the fourth section is areview on previous works developed for this problem type, and in the fifth section are presented andcompared optimisation technics to solve this problem type.

The importance of scheduling in manufacturing systems has increased in recent years due to thegrowth in customer demand for variety, reduced product life cycles, changing markets with global com-petition, and rapid development of new processes and technologies [34].

With the constant change in the economy and the markets, the industry is in constant pressure tominimise the inventory while maintaining customer satisfaction. While reducing the production costsand the delivery deadlines. This requires efficient, effective and accurate scheduling.

3.1 Introduction to Job Shop Scheduling

To outline the problem studied in this thesis is required to address some definitions. The main productionconfiguration Job Shop is first addressed, and then a generalisation of the main problem is created.Hence, this chapter is commenced with the definition of JSSP and its mechanics.

A Job Shop Scheduling Problem (JSSP) has a set of n jobs pj1...jnq to be processed by a set of mpm1...mmq machines .

Each job is processed on the machines by a given order, and with a given processing time, and eachmachine can process only one job at a time.

The scheduler’s objective is to find an optimal ordering of all the jobs with respect to their variedrouteing requirements through the machines. Each job must visit the machine in a sequence[35].

13

The classical JSSP, the process plan of a part consists of the sequence of the machines the part mustvisit: there is an a priori assignment of operations to machines. Therefore, the process plan is fixed, andno process plan flexibility is associated[36].

To explain how F-JSSP works, all sources of flexibilities in manufacturing systems are reviewed. Andthe related flexibility is addressed, with the details of F-JSSP being given.

3.2 Flexibility in a manufacturing system

In the literature different types of flexibilities in manufacturing systems were identified and classifiedby ElMaraghy (2005)[37], in a way that promotes a better comprehension in the relations between thevarious types of flexibility.

• Machine Flexibility - Different number of operations performed without requiring a set-up change

• Material handling flexibility - Number of used paths or total number of possible paths betweenall machines.

• Operation Flexibility - Number of different processing plans available for part fabrication.

• Process Flexibility - Set of parts with similarities that can be produced without major set-upchanges.

• Product Flexibility - Ease (time and cost) of introduction products into an existing product mix.Contributing to the production agility.

• Routing Flexibility - Number of feasible routes of all types/number of part types.

• Volume flexibility - the ability to vary production volume profitably within production capacity.

• Expansion flexibility - Ease (effort and cost) of augmenting the capacity and/or the capability,when needed, through physical changes in the system.

• Control Program Flexibility - The ability of a system to run virtually uninterrupted due to theavailability of intelligent machines and systems control software.

• Production Flexibility - Number of all part types that can be produced without adding majorcapital equipment.

Taking into account the before-cited sources of flexibility, the considered problem is transformed fromclassical JSSP to F-JSSP, explored in the next section.

3.3 Flexible Job Shop scheduling Problem

The increase of flexibility in the JSSP makes scheduling the resources extremely challenging, due to theexpanding machine tools capabilities and increased product variety[36].

With the creation of multi-purpose machinery manufacturers were with provided competitive capab-ilities, on the other hand, managing changes in products and markets requires adaptation at two levels,developing enablers of change, reconfigurable machines and systems, and logical enablers includingadaptable controls, process and production planning and scheduling[38].

Scheduling is responsible for planning detail the resource assignments and sequences. Schedulingthe production in real industrial environment presents additional challenges of size, which is normallylarger than the capabilities of most existing algorithms[39].

14

According to Kacem [40], flexibility in job shop, refers to a machine flexibility, and it may be partialor total. Partial Flexible Job Shop Scheduling Problem (PF-JSSP) is a sub-case of Flexible Job ShopScheduling Problem (F-JSSP) where the preference of using some machines for a certain operationarise.

With certain numbers of multi-purpose machines distributed throughout the facility, the versatility andflexibility of which is not identical. This feature enables a certain part to be processed by at least one ma-chine out of the available, feasible machines, the routeing flexibility of parts allows the re-assignment ofparts to other available machines in case of facing any event in the shop floor like machine breakdowns,order cancellation or arrival.

For PF-JSSP, exists m machines in the system and n jobs to be processed, each of this jobs j

requires a nj precedence or constrained operations to be done, and each one of this operations Oj,l canbe processed on a number of machines, based on their characteristics. This results in multiple routeingfor the jobs, and due to this problem Brandimarte [41], defined two distinctive decisions to be made inthe routeing assignment.

• Assign Operation to Machines, operations are assigned to their respective feasible machines.In Total Flexible Job Shop Scheduling Problem (TF-JSSP), random assignment of operations toavailable machines is feasible as all the machines in the shop floor possess the same operationalcapabilities. But, in the PF-JSSP, that is not the case due to the fact that the different machinesdo not possess identical characteristics.

• Sequencing of Operations, sequencing decision is made for those operations whose processingroute share the same machine, operations that are not assigned to the same machine are notconsidered for sequencing with respect to each other on that particular machine. Therefore, se-quencing decision is made for those operations that share the same subset of machines.

3.3.1 Total Flexibility vs Partial Flexibility

The TF-JSSP, presented in the figure 3.1, where three jobs are assign to three multi-purpose machines.For these case all jobs have total routing flexibility to be assign to any machine in the shop floor, thisevent is possible if all machines have identical operational capabilities[36].

Figure 3.1: Representation of TF-JSSP[36]

When not all the jobs have total routing flexibility to be processed by any available machine in theshop floor, the problem is considered a PF-JSSP. As illustrated in figure 3.2, the assignment of three jobs

15

to three multi-purpose machines, and the machines are not identical, presenting different functionalitiesand versatilities[36].

Figure 3.2: Representation of PF-JSSP[36]

3.4 Review on previous studies on PF-JSSP

In order to verify the relevance of this dissertation, a review on previews works had be done. This reviewwas not only to see the objective and the type of problems addressed in the previous works, but also theverification of the most common algorithms used and their performance.

Since a work of Wagner [42] in modeling production scheduling trough a mathematical solution,researchers have applied various objective functions, assumptions, and solution algorithms to formulateand solve production scheduling problems.

Table 3.1: Previous studies on PF-JSSP

ObjectiveProblem

AddressedAlgorithm Reference

Makespan F-JSSP GA [43]

Makespan, critical machine workloadand total workload of machines

F-JSSPBiogegraphy-based

Optimization[44]

Makespan and total operation costs PF-JSSP GA [45]

Earliness and tardiness costs F-JSSP GA and PSO [46]

Makespan F-JSSP GA [47]

Tardiness F-JSSP GA [48]

Makespan TF-JSSP GA [49]

Makespan JSSP GA [50]

Makespan JSSP GA [51]

Makespan JSSP Adaptive annealing GA [52]

Makespan, total machine idle timeand total tardiness

PF-JSSP GA [53]

16

3.5 Optimisation Technics

In Job-shop scheduling problems, the problem is considered NP-complete due to the large search spacein possible combinations of goals and resources. With this complexity that is not a single strategy tosolve this problem. The typical optimisation methods can only give an optimal solution to a reasonablesize problem, therefore a recourse to Meta-heuristic is necessary to achieve solutions that can solve theproblem, in a reasonable amount of time [54].

Programming formulation of a Job-shop problem where the main objective is to minimize the makespanCmax, considering that exist n jobs and m machines with each job being processed by a number of ma-chines in a giving order. The variable yij denote the starting time of the operation (i,j), with an operationtime pij , with N as the set all operations (i,j), and a set A of all routing constraints pi, jq Ñ ph, jq witchrequire job j to be processed on machine i before being processed on machine h. The following math-ematical program minimises the makespan [55].

minimize Cmax (3.1)

subject to

yhj ´ yij ě pij , for all pi, jq Ñ ph, jq P A

Cmax ´ yij ě pij , for all pi, jq P N

yij ´ yik ě pik or yik ´ yij ě pij , for all pi, kqandpi, jq, i “ 1, ...,m

yij ě 0, for allpi, jq P N

In the formulation of the equation 3.5 the first set of constrains ensures that consecutive operationscannot start without the first one finishes, the third constrain ensures the order among operations ofdifferent jobs that have to be processed on the same machine.

3.5.1 Heuristics

Heuristic is method that provides a very good and feasible solution, it can solve local problems but areinefficient in complex problems due to the lack of knowledge or human experience [54], being extremelyuseful as guidelines, solving problems in real time producing good solutions, but it does not guaranteethe optimal solution[56].

Dispatching Rules are rules that prioritise the jobs that are waiting to be processed on a machine. Theprioritizing rules take in account the attributes of the jobs , the machines attributes and the current time,these rules can be classified in various ways, they can be Static or Dynamic, static rules only dependon the jobs and machine date, on other hand dynamic are time dependent, implying that in some pointin the process the priorities of jobs change related to the due date and processing time. Local that onlyuses information regarding the queue where the job is waiting or Global when the information related toother operation queues are taken in account, as the route and the processing time[55].In table 3.2 arerepresented some of the most common and used Dispatching Rules heuristics.This different types of dispatching rules are of limited use when a complex objective has to be minimisedthis rules performance may not be effective.

17

Table 3.2: Common Dispatching Rules HeuristicsDispatching Rule Description

Shortest Processing TimeThe Job with the shortest time on the machines is

selected.

Longest Processing TimeThe job with longest processing time on machine is

selected.

Minimum Due DateThe job with the earliest due date is processed

first.RANDOM Selects the next job to be processed at random.

Minimum Slack Time Per OperationTime remaining until the due date - processing

time remaining

Minimum Energy ConsumptionThe next Job is attributed to the machine with the

lowest energy consumption.

Minimum Cost HourThe next Job is attributed to the machine with the

lowest cost per hour.

First in first outSelects the next job to be processed by arriving

time.

By PrioritySelects the next job to be processed by attributed

weight.

3.5.2 Meta-heuristics

Meta-heuristics are optimisation algorithms that find a solution to a given problem by efficiently exploringthe universe of possible solutions, where the key feature of the methods is the ability to not getting stuckin a local optimum. Thus allowing to solve large-sized problems, by obtaining good satisfactory solutionsin a reasonable time span. Their algorithms are used to find solutions to problems where the look of theoptimal solution is unknown [57].

They are a general solution methods that can provide good structure and guidelines for developing aheuristic method to solve a specific problem[56]. With a vast field of application, being present in severalareas of research, engineering, economics, social, medical and others.

” A meta-heuristic is a general kind of solution method that orchestrates the interaction between localimprovement procedures and higher level strategies to create a process that is capable of escaping fromlocal optima and performing a robust search of a feasible region.” [56]

The meta-heuristic can be characterised by different aspects concerning the search path and howmemory is exploited, the main differences between them are the balance between the exploitation ofthe search space to identify regions with high-quality solutions and the exploitation of the accumulatedsearch experience[58].

18

Some ways to classify the types of meta-heuristics according to [58, 56] .

• trajectory methods vs discontinuous methods, if they Follow one single search trajectory cor-responding to a close walk in the neighbourhood, like simulated annealing and tabu search, orlarger jumps in the neighbourhood, like GA and the ant colony.

• Population based vs single point based, this characteristic is related to the distinction betweentrajectory methods and discontinuous walk methods, where one single solution is manipulated,tabu search and simulated annealing, or a population of individuals used, ant colony and GA.

• Memory usage vs memoryless methods, short term memory is used to forbid revisiting foundsolution and avoid cycles, tabu search, while long term memory is used for diversification andintensification of selected features GA and ant colony, on other hand simulated annealing andgrasp do not use memory functions to influence the future search.

• One vs single neighborhood structures, most local search algorithms are based on one singleneighborhood that defines the type of moves, like simulated annealing and tabu search, when inthe search neighborhood a local optimum is reached is applied a kick-move to catapult the searchto another point, in GA the mutation operator corresponds to this kick-move and crossover hasbeen interpreted as moves in hyper-neighborhoods, on other side ant colony and grasp are notbased on a specific neighborhood structure.

• Dynamic vs static objective function, some algorithms modify the evaluation of the single searchstates during the run of the algorithm, tabu search, but most of the known methods use staticobjective functions, GA, ant colony, etc.

In this thesis, a Genetic Algorithm is used to solve the TF-JSSP. This meta-heuristic can be classifiedas being an evolutionary algorithm since it mimics Darwin’s law of natural selection. GA use randombased criteria to search for a satisfactory solution from a population. The main procedures for a GAare the creation of the initial population, the selection of the parents, crossover, mutation and elitism,and finally testing the stopping criteria. These procedures, as well as the interactions among them. Adetailed explanation about GA can be found in the next section.

Genetic Algorithm

The GA was developed by John Holland and his collaborators between 1960 and 1970, this method isbased Darwin’s theory of natural selection, using crossover and recombination, mutation and selectionin the study of adaptive and artificial systems [59].

Instead of processing one a single trial solution, GA works with an entire population of trial solutions.The feasible solution corresponds to members of a particular species, where the fitness of each memberis measured by the value of the objective function [56]. The algorithm 1 provides a pseudocode of GAfor minimizing a cost function[60], Where for each iteration, generation, the current population consistsof a set of trial solutions, some of the members of this generation become parents of the children ofthe next generation who share some features of the parents, with the possibility of occurring mutationshelping the algorithm explore new solutions.[56]

19

Evaluation of the Population determines the fitness value for each individual, and this value isrelated to the objective function value of an individual, the fitness of the individual, FIT(i) ca be describedas

FIT piq “

$

&

%

F ´ FipSiq, if FipSiq ă F

0, otherwise(3.2)

where FipSiq is the value of the schedule Si resulting from the individual i and F is the objectivefunction value of the solution[61].

Algorithm 1 Pseudocode for Genetic Algorithm[60]1: InputPopulationsize, P roblemsize, Pcrossover, Pmutation

2: Output Sbest

3: procedure4: Population Ð Initialize Population (Populationsize, P roblemsize)5: Evaluate Population (Population)6: Sbest Ð Get Best Solution (Population)7: while Stop Condition () do8: Parents Ð Select Parents (Population, , Populationsize)9: Children ÐH

10: for Parent1, Parent2 P Parents do11: Child1, Child2 Ð Crossover (Parent1, Parent2, Pcrossover)12: Children Ð Mutate (Child1, Pmutation

13: Children Ð Mutate (Child2, Pmutation

14: end for15: Evaluate Population (Children)16: Sbest Ð Get Best Solution (Children)17: Population Ð Replace (Population, Children)18: end while19: Return Sbest

20: end procedure

20

Chapter 4

Effect of Energy consumption in theProcess Plan

In this chapter, a methodology to support the planning decision is proposed. To achieve all the results ina sustained manner, this chapter is divided into six sections.

The model of the process was characterised in the first section, this was achieved using real dataacquired from a mould factory.

In the second section, the mathematical formulation of the problem was achieved, this was done bydetermining the constraints of the problem and the algorithm to use.

The third section was the main step in the solving of the problem, in there the algorithm was tested,and the optimal parameters to obtain the optimal solution were determined.

In the fourth and fifth sections the algorithm and four methods were tested, the time-based method,the cost-based method, the energy-based method and the energy-plus-cost-based method. In the fourthsection, a comparison of the total values of cost and energy was made by working section for eachmethod. And in the fifth section a comparison between the methods was performed, this comparisonwas done not only by section, but was also done a comparison to the overall process.

The sixth section is an explanation of how to apply the algorithm and analyse the results obtained.

In this thesis, the developed scheduling optimisation methodologies are applied to an industrial prob-lem, to demonstrate the effect that energy consumption can have in the planning of the productionsystem. The energy input of a manufacturing process might be very high in some cases and are closelyconnected to energy costs, and environmental consequences, an accurate forecasting of energy con-sumption is critical.

21

4.1 Process Model

In this section, a characterization of the production system utilised and its modelling is done, for that allthe working section are explored and explained, and the problem data was collected and exposed.

The model of the production system utilised in this thesis is based on a real production system of amould production company.

Since the number of moulds available, to study is low, compared with the real production level ofthe company, a scale on the real model was made, eliminating the machines with the same costs andenergetic consumption. This step was possible because in this study only the times and operationsequences of the parts were taken into account, that fact allows that all the machines in a section canperform the operation required.

The Model incorporates 6 independent workstations, composed by the correspondent machines, themachines are considered to have the same work capacity with the processing time attributed off-line tothe part not to the machine, each machine can only operate a part at a time and the setup time were nottaken in account in the resolution of this problem.

• CNC - Is the automation of the machining process using a CAD project. This section contains 6independent machines, from [1 - 6].

• Lathe - is a tool that uses the rotation of the object over is axis to remove the material. This sectioncontains 2 independent machines, from [7 - 8].

• Milling - is a machining process that requires the rotational movement of the cutters to removematerial to the part. This section contains 2 independent machines, from [9 - 10]

• Wire Electrical discharge machining (EDM) - uses thin single-strand metal wire, fed through theworkpiece, submerged in a tank of dielectric fluid. This section contains 4 independent machines,from [11 - 14].

• Drill EDM or Sinker EDM - this process consists of an electrode and workpiece submerged in aninsulating liquid. The electrode and part are connected to a suitable power supply. The power sup-ply generates an electrical potential between the two parts. This section contains 5 independentmachines, from [15 - 19].

• Rectification - Is the process of abrasive cutting and polishing the parts. This section contains 6independent machines, from [20 - 25].

22

4.1.1 Problem Data

The problem data was, made available by a mould company, and gathered and analysed with the useof the PHC tool. In the table4.1, is represented the processing times and sequence of operation of theseveral parts.

For this analysis, the setup and transportation times were not taken into account. Also, the effect ofthe rework in the planning was not taken into consideration, but were addressed in chapter 5 .

Table 4.1: Times of Process Operations

Mold Part CNC Lathe Milling Wire EDM Drill EDM Rectification Operation Order

A1 50 20 38 24 134 63 3,6,1,4,2,5

2 181 - - - - - 1

B

3 106 - - - - 61 1,6

4 10 - - - - - 1

5 70 - - 22 101 41 6,1,5,4

6 2 - 1 - - - 1,3

7 6 - 3 - - - 1,3

8 13 - 5 - 40 27 6,5,3,1

9 56 - - - - - 1

C

10 125 25 14 - 38 33 1,2,6,3,5

11 10 3 - - - 6 1,2,6

12 6 - - - - - 1

13 108 - 9 - 75 16 1,6,3,5

14 58 55 - 11 106 - 2,1,5,4

15 5 1 - - - - 2,1

16 5 - - - - - 1

17 5 23 - - - - 2,1

18 3 2 - - - - 1,2

19 1 - - - - - 1

20 66 - - - - - 1

D

21 10 - 47 41 61 30 3,1,6,4,5

22 180 - 11 126 18 48 3,1,5,4,6

23 15 - - 5 11 17 1,6,5,4

24 15 - - - 3 11 1,6,5

The values of energy consumption of the machines and their cost per hour were also acquired froma mould company.

In order to achieve a valid solution, and since the values of energy consumption and the cost perhour of the machines have for several cases a great discrepancy, it wouldn’t be scientifically correct to

23

mix both in the formulation, for that reason the values were normalised by section, allowing an evenpenalisation among the process, table 4.2.

Table 4.2: Characteristics of the Machines

Section MachineTrue Values Normalized Values

Energy Consumption[KW/h] Cost [e/h] Energy Consumption Cost

CNC

1 12,5 8,68 1,25 1,21

2 10 19,53 1,00 2,73

3 25 13,02 2,50 1,82

4 28 15,19 2,80 2,12

5 32,28 7,16 3,23 1,00

6 12,91 10,85 1,29 1,52

Lathe7 1,36 0,65 1,11 1,00

8 1,22 0,87 1,00 1,34

Milling9 5,74 0,39 1,00 1,00

10 7,5 1,74 1,31 4,46

Wire EDM

11 6,45 5,42 1,00 1,25

12 9,18 4,34 1,42 1,00

13 7,2 5,21 1,12 1,20

14 6,8 6,07 1,05 1,40

Drill EDM

15 2,86 1,21 1,00 1,00

16 6,88 6,51 2,41 5,38

17 6,64 8,89 2,32 7,35

18 5,95 8,24 2,08 6,81

19 3,44 7,16 1,20 5,92

Rectification

20 7,45 3,56 8,01 11,87

21 4 0,48 4,30 1,60

22 5,05 1,82 5,43 6,07

23 0,93 0,3 1,00 1,00

24 7,5 1,08 8,06 3,60

25 14,3 5,64 15,38 18,80

24

4.2 Mathematical Formulation

In this section, the assumptions to solve the problem are analysed, and a guide to formulate the TF-JSSPis reviewed, and based on this assumptions, the mathematical formulation is presented.

The Mixed Integer Linear Programing (MILP) used in this thesis adopt the modelling paradigm ofWagner [42] and Manne [62], commonly referred to as position-based and sequence-based respect-ively. These two modelling paradigms have proven to generate fewer numbers of decision variables andconstraints.

In the resolution of this problem, the following assumptions were used for all formulation.

• Operations can be processed on more than one machine, there exists routing flexibility.

• Jobs are independent and no priorities are assigned.

• Preemption or cancellation of jobs were not considered.

• A machine can only process one job at a time.

• No defective parts are considered

• The jobs were available at time zero.

• Breakdowns were not considered.

This thesis uses two complementary solution methodologies to meet the scheduling requirements ofthe problem. The meta-heuristic algorithm will run with the mathematical model to obtain the optimalsolution.

• Mathematical modelling The MILP presented in this work follow both the integrated and hierarch-ical approaches to solve the problem.

• Meta-heuristic, the use of the GA results from a extensive review of previous approaches, and itsgood performance proved in the literature.

For the realisation of this work, two new Parameters were taken into account, Ci, the normalisedcost of placing a part in a specific machine of a section, and Ei, the normalised energy consumption ofplacing a part in a specific machine of a section, introduce in the equation 4.10.

The program to implement this work was acquired from a free source site [63], it was developed in C#and chosen due to its easy comprehension and applicability. After the verification of the mathematicalformulation, this program was tested with several literature problems and the solutions compared withthe optimal results.

With the integration of the meta-heuristic in the mathematical model, an analysis on the sensitivity ofthe algorithm parameters must be done to assure that the optimal solution is achieved.

25

4.2.1 Guide lines for formulating the scheduling problem

Some Researchers do not follow a proper guideline to formulate their problems [64]. If following con-straints are properly defined, the model is constructed easier.

• Constraints for assigning and sequencing of operations to available processing positions

• Constraints for machine capability utilization.

• Machine eligibility constraints.

• Technical/logical precedence constraints among operations of a part.

• Machine non-interference constraints.

• Constraints for relating processing positions to operations.

• Constraints for capturing the value of objective function.

• Constraints demonstrating the nature of decision variables.

4.2.2 Position Based MILP

The position based MILP -1 was developed [64], becoming the first position based MILP presented inthe literature. For this Dissertation it was used the MILP - 2, a variation of the previous, in this case onlyone binary decision variable is used to handle the routing and sequencing sub-problems, where for theMILP-1 were utilised two distinct binary variables.

Parameters and decision variables

j Subscript for jobs where 1 ď j ď n

i Subscript for machines where 1 ď j ď m

l Subscript for operations on job where 1 ď j ď nf

Oj,l l - th operation of job jej,l,i Parameter that takes value 1 if machine i is able to process Oj,l an 0 otherwise.pj,l,i Processing time of operation Oj,l on machine iCi Normalised Cost of processing the operation Oj,l on machine iEi Normalised Energy Consumption of processing the operation Oj,l on machine ifi Subscript for processing positions of machine i where 1 ď f ď fipfi “

ř

j

ř

l ej,l,iq

M A large positive numberXj,l,i,f Binary decision variable taking value 1 if Oj,l is processed on the f-th position of machine iYj,l,i Binary decision variable taking value 1 if machine i is selected to process operation Oj,l

Cj,l Continuous variable for the completion time of operation Oj,l

Sj,l Continuous variable for the starting time of operation Oj,l

Bi,f Continuous variable for the beginning time of each processing position Oj,l

26

minimize Cmax

subject to (4.1)i“1ÿ

m

f“1ÿ

fi

Xj,l,i,f “ 1 @j,l (4.2)

j“1ÿ

n

l“1ÿ

nj

Xj,l,i,f ď 1 @i,f (4.3)

f“1ÿ

fi

Xj,l,i,f ď ej,l,i @i,f (4.4)

Sj,l`1 ě Sj,l `

i“1ÿ

m

f“1ÿ

fi

Xj,l,i,f ˆ pj,l,i @j,lănj (4.5)

Bi,f`1 ě Bi,f `

j“1ÿ

n

f“1ÿ

nj

Xj,l,i,f ˆ pj,l,i @i,făfi (4.6)

Bi,f ď Sj,l `Mp1´Xj,l,i,f q @i,f ,@j,l (4.7)

Bi,f ď Sj,l ´Mp1´Xj,l,i,f q @i,f ,@j,l (4.8)

Cmax ě Sj,nj `

i“1ÿ

m

f“1ÿ

fi

Xj,l,i,f ˆ pj,nj ,i ˆ Ci ˆ Ei @j (4.9)

Bi,fSj,l ě 0 @i,f ,@j,l (4.10)

Xj,l,i,f ε0, 1 @j,l,i,f (4.11)

4.3 Algorithm Sensitivity Analysis

In this section an analyse on the algorithm performance is made, this is a fundamental step in theoptimisation process, here all the parameters are tested, and the combinations that guarantee the bestsolution are selected.

In order to optimise the algorithm to solve the problem, an analyse on the effect that the differentparameters have in the final solution of the problem was made.

For this algorithm, three parameters were optimised, the Population, Crossover Percentage andthe size of the Elite Group. The processing time of the algorithm is directly proportional to the numberof the population, so it was not optimised from a specific standpoint.

The formulation used included both of the new machine parameters, the normalised cost per hourand energy consumption.

The optimisation of the parameters was done sequential; first, the population parameter was optim-ised, next was the crossover percentage and for last the size of the elite group.

To test the different interactions, the optimal value achieved for the population size was used tooptimise the other two parameters, and the optimal values for the crossover percentage was used todetermine the optimal value for the size of the elite group.

For each value tested for the parameters, were done thirty runs in the algorithm, and were used forthe evaluation the average and standard deviation values.

27

4.3.1 Population

To determine the optimal value for the population, were done tests to a range of values from 10000 to700. For the optimal score of the algorithm, 14505, it achieved with zero deviation with a population of10000. In the next iteration the test was done with a population size of 5000 and an average score of14526, which represented an increase of 0.14% from the previous value. To a population size of 3000the score is 14537, representing an increase of 0.22% from the optimal value, and when the populationsize is set a value of 1000 the score value is 15668, which is an increase of 8% related to the optimal.

The value of the population size chosen for the realisation of the project was 3000. Since the presen-ted error is lower than 5%, and all the tests for a lower values of population presented a higher differencethan 5% from the optimal value, as seen in the figure 4.6.

Figure 4.1: Population Score

4.3.2 Crossover Percentage

To determine the optimal value for the percentage of crossover were done tests to a range of values of1%, 5% and 10%. For the optimal score of the algorithm, 14505, it achieved with zero deviation witha crossover percentage of 5%, in the next iteration the test was done with crossover percentage of 1%with an average score of 14537, which represented an increase of 0.22% from the previous value, to apercentage of crossover of 10% the score is 14515, representing an increase of 0.07% from the optimalvalue.

The percentage of crossover chosen was 5% guaranteeing a value that corresponds to the optimalvalue, as seen in the figure 4.2.

28

Figure 4.2: % Crossover Score

4.3.3 Elite Group

To determine the optimal value for the size of the elite group were done tests to a range of values from5 to 20. For the optimal score of the algorithm, 14505, it achieved with a group size of 5, 10 and 20, forthe group size of 15 the score values is 14515, as seen in the figure 4.3, excluding this value from thevalid, and with three possible values for the optimal values, further tests were required.

Figure 4.3: Elite Group Average Score

An analysis to the standard deviation presented in runs was determined to find the optimal size ofthe elite group for the solution of the problem.

The results achieved from this analysis, came only to prove the point taken above, that the optimalsolution would result with group sizes of 5, 10 and 20, as seen in figure 4.4, something that was alreadyexpected since the average score achieved with this parameters was the optimal solution. Once againa deeper analysis was needed.

29

Figure 4.4: Elite Group Standard Deviation Score

For the closest look in the analysis of the results acquired with the different values for the size ofthe elite group, of 5, 10 and 20, the results are close between all of them, as seen in figure 4.5. For agroup size of 5 the algorithm needs in average 14477 iterations to reach the optimal solution, for a groupsize of 10 the algorithm needs in average 14367 iterations to reach the optimal solution, and for a groupsize of 20, the algorithm needs in average 14533 iterations to reach the optimal solution. Then for theparameter of the group size, it was chosen the value of 10.

Figure 4.5: Elite Group Iteration Test

In summary the parameters determined to find the optimal solution for this problem were, populationof 3000 individuals, the crossover percentage is 5%, and for the size of the elite group the value is 10.

Having achieved the optimal parameters, it is now possible to compare the several methods pro-posed.

30

4.4 Results

In this section, the four proposed methods were tested, and their results analysed, with the goal ofverifying the effect that the developed parameters have in the planning process.

The resolution of this problem resided in using or not the combination of the parameters Ci, a cost ofusing a certain machine during one hour, and Ei, the value of energy consumption of a certain machineduring one hour.

The four methods used were, reducing the project time alone, reduce the project time and the energyconsumption, reduce the project time and the machine cost, and reduce the project time, the energyconsumption and the machine cost.

The resulting analysis for the different methods was done, section by section, comparing the energyconsumption, the cost per hour and the idle time of the several machines. To compare the differentmethods was used the average values for the energy consumption, the cost per hour and the totalduration of the project, the makespan. For a more detail look was checked the occupations of themachines.

4.4.1 Time-Based Method

The method where the objective is to reduce the duration of the project does not take into account thenew developed parameters.

In this case, all of the machines in a section have the same characteristics, so the algorithm onlyconcern is to reproduce an optimal path for all of the parts reducing the time of completion, and withoutcaring in which machine the job is done.

The analysis for the method will be an overall, as seen in table 4.3, analysis instead of a section bysection, as it was done for the other three methods, due to the fact that there is no distinguish on howand why the machines are selected to perform the operations.

This Method was the base of comparison for all of the three methods proposed since in the industrythis is the main methodology used, to achieve the project in the least time possible, without taking intoaccount the machines cost and the machine energy consumption.

As expected this method takes the optimum time to process the project, with a makespan of 383hours. But as explained above it does not take into account the two new variables proposed to solve theproblem, so the values of total cost and total energy consumption are completely arbitrary.

Table 4.3: Time-based Method - Results Aggregation

Makespan [Hours] Idle Time [Hours] Cost [e] Energy Consumption [KW]

Total 383 7043 18777.56 31455.14

31

4.4.2 Cost-Based Method

The Cost-based method, the objective is to reduce the duration and the total cost of the project, it takesinto account the new developed parameter Ci.

In this case, all of the machines of each section have different penalties in their utilisation based ontheir cost per hour. The value of energy consumption is not taken is account and the time of processinga specific part in a section is the same for any machine in that section.

Considering the CNC section we can verify in the table 4.4, that the algorithm gave the most amountof work to the machine number five, 299 hours, the one with the lowest cost per hour, resulting in a costof 2140.84e, close as the same amount of the machine three, but this one with only 162 working hours.On the other hand the values for energy consumption achieve high numbers since the machine numberfive, the most used, is the one with the higher penalization in terms of energy wise.

Table 4.4: Cost-based method - CNC

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

CNC

1 J20-1; J2-1 247 210 2143.96 3087.5

2 J3-1 106 351 2070,18 1060

3J7-1; J10-1; J24-1; J4-1;

J12-1162 295 2109,24 4050

4J14-2; J11-1; J21-2;J23-1; J15-2; J16-1

103 354 1564,57 2884

5 J22-2; J1-3; J9-1; J8-4 299 158 2140,84 9651,72

6J5-2; J13-1; J18-1;J17-2; J19-1; J6-1

189 268 2050.65 2439.99

In the Lathe section, table 4.5, the normalised values of cost per hour of the machines change from1 in the machine number seven to 1.34 in the machine eight, that results on the machine seven workingalmost the double of the time of the machine eight but only with an increase of 29% on the total cost.

Considering the energy consumption, the normalised values are similar and in that way the totalenergy consumption followed the same pattern as the working time, being almost the double on machineseven.

Table 4.5: Cost-based method - Lathe

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Lathe7

J14-1; J15-1; J11-2;J17-1; J18-2

84 373 54,6 114,24

8 J10-2; J1-5; 45 412 39,15 54,9

32

The Milling section presents a great difference in terms of energy consumption between both of themachines, with the machine number ten presenting a penalty value 4.46 times higher than the machinenumber nine.

Considering the big difference on penalty values between the two machines, and as seen in the table4.6, the machine number nine processed 110 more hours than the machine ten, with that resulting onlyin a total cost of 3 times greater. When considered the energy consumption and with such a differencein the working hours, the total energy consumption of the machine nine is 10 times greater than themachine ten.

Table 4.6: Cost-based method - Milling

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Milling9

J22-1; J1-1; J21-1;J10-4; J13-3

119 338 46,41 683,06

10 J7-2; J8-3; J6-2 9 448 15,66 67,5

The section of the wire EDM, the table 4.7 presents the first case where one of the machines isnot utilised, the machine fourteen, the one with the highest cost per hour. The algorithm optimises thissection maximising the usage of the machine twelve with more 97 hours than the machine eleven and52 hours than the machine thirteen.

In this section, the penalty of only considering the reduction of the cost and the duration of the projectis seen by an elevated energy consumption, since the machine that has the second lowest cost is theone with highest energy consumption.

Table 4.7: Cost-based method - Wire EDM

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Wire EDM

11 J1-4; J23-4 29 428 157,18 187,05

12 J22-4 126 331 546,84 1156,68

13 J21-4; J14-4; J5-4 74 383 385,54 532,8

14 - - 457 0 0

In the Drill EDM Section, as seen in the table 4.8, occurs the same event as the one in the Wire EDMsection, a machine that does not have any job attributed, the machine number seventeen.

For this section, the penalty values between the machine that has the lowest cost per hour, themachine fifteen, and the rest are very different. If a closer look is taken into the two machines with thelowest cost, is possible to see that the difference of working hours between them is 9 hours, but themachine sixteen has a total cost 1176.31e superior to the machine fifteen.

33

Table 4.8: Cost-based method - Drill EDM

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Drill EDM

15 J21-5; J1-6; J10-5 233 224 281,93 666,38

16 J14-3; J8-2; J24-3; J13-4 224 233 1458,24 1541,12

17 - 457 0 0

18 J22-3; J23-3 29 428 238,96 172,55

19 J5-3 101 356 723,16 347,44

The Rectification section has a greater difference in the penalties of the machines, with the machinestwenty-three and twenty-one having the lowest ones, in the other side the machine twenty-five has apenalty value 18,80 times superior to the lowest one, that is not utilised in this case.

The existence of such discrepancy in penalty values origins that most of the work is processed bythe machine twenty-one with 109 hours, with a difference of 76 hours for the next one, and the machinetwenty-three with 177 hours, but the values of the total cost of the machines have a maximum differenceof 17.64e, as seen in the table 4.9.

Table 4.9: Cost-based method - Rectification

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Rectification

20 J24-2 11 446 39,16 81,95

21 J1-2; J21-3; J13-2 109 348 52,32 436

22 J23-2; J11-3 28 429 50,96 141,4

23 J5-1; J8-1; J22-5; J3-2 177 280 53,1 164,61

24 J10-3 33 424 35,64 247,5

25 - 457 0 0

When summarized the results of the cost-based method, presented on the table 4.10, and comparingthem to the time based method, it was possible to verify that the project took more 74 hours than theoptimal value but, it achieved one of the main goals that was too reduce the total cost, a reduction of2519.3e.

34

The machines with lower cost tend to be the ones with highest energy consumption, but in the CNCsection, that is the bottleneck, originating most of the working hours, the ranking of the machines in thepenalty is the same, only with the change of the machine two, the one with lowest energy consumption,but with the highest cost and the machine five with the lowest cost but highest energy consumption,resulting in a decrease of 1686.7KW.

Table 4.10: Cost-based method - Results Aggregation

Makespan [Hours] Idle Time [Hours] Cost [e] Energy Consumption [KW]

Total 457 8888 16258.29 29768.39

4.4.3 Energy-Based Method

In the energy-Based method, the objective is to reduce the duration and the total energy consumptionof the project, it takes into account the new developed parameter Ei.

In this case, all of the machines of each section have different penalties in their utilisation, based ontheir energy consumption per hour. The value of the cost per hour is not taken is account and the timeof processing a specific part in a section is the same for any machine in that section.

Considering the CNC section, in the table 4.11, we can verify that the algorithm gave the most amountof work to the machine number two, 296 hours, the one with the lowest energy consumption. Thefollowing machines with the most use are the machine one with 252 hours, and the machine six, with249 hours, since they have similar penalty values.

When compared with the cost-based method, we can see that with the change of the optimisationobjective, the machines two and five change position originating an elevated total cost for the process.

Table 4.11: Energy-based method - CNC

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

CNC

1 J22-2; J12-1; J11-1; J9-1 252 166 2187,36 3150

2J10-1; J14-2 ;J13-1;

J17-2296 122 5780,88 2960

3J5-2; J21-2; J7-1; J24-1;

J15-2; J4-1; J16-1121 297 1575,42 3025

4 J3-1; J18-1; J19-1 110 308 1670,9 3080

5 J23-1; J8-4; J1-3 78 340 558.48 2517.84

6 J6-1; J20-1; J2-1 249 169 2701,65 3214,59

35

In the Lathe section, in the table 4.12, the normalised values of cost per hour of the machineschange from 1 in the machine number eight to 1.11 in the machine seven, that results on the machineeight working more 33 hours than the machine seven, producing a difference of 33.54 KW in the totalenergy consumption.

Considering the cost per hour, the total cost of the machine eight is more than the double of themachine seven.

Table 4.12: Energy-based method - Lathe

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Lathe7 J10-2; J15-1; J1-5; J18-2 48 370 31,2 65,28

8 J14-1; J17-1; J11-2 81 337 70,47 98,82

The Milling section presents a difference in terms of penalty value for the energy consumptionbetween both of the machines of 0.31, resulting in a difference of 6.5 in the energy consumption whenthe difference in working hours is 18 hours.

Considering the big difference on the penalty in cost per hour values between the two machines, themachine number nine processed 18 more hours than the machine ten, with that resulting in a total costof 2.4 times higher, as seen in the table 4.13.

Table 4.13: Energy-based method - Milling

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Milling9

J6-2; J22-1; J1-1; J10-4;J13-3

73 345 28,47 419,02

10 J21-1; J8-3; J7-2 55 363 95,7 412,5

For the Wire EDM section using the energy-based optimisation, we can see the first big change fromthe cost-based optimisation since all the machines are utilised, even though the machine with the higherpenalty value, the machine twelve, has a higher difference to the least penalised than in the cost-basedoptimisation.

In this case we see an increase in the total cost since the machine that has the lowest cost per houris also the one with the highest energy consumption. For the penalisation on the energy-based method,the three best machines with the lowest consumption have a maximum difference of 0.12 points betweenthem, contrasting with the cost-base method where the two best machines, with the lowest cost have adifference of 0.20 points, as seen in the table 4.14.

36

Table 4.14: Energy-based method - Wire EDM

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Wire EDM

11 J1-4; J22-4 150 268 813 967,5

12 J23-4; J14-4 16 402 69,44 146,88

13 J5-4 22 396 114,62 158,4

14 J21-4 41 377 248,87 278,8

In the Drill EDM Section occurs the same event as the one in the Wire EDM section, related to thecost-based method, all of the machines have a job attributed.

For this section, the penalty values between the machine that has the lowest energy consumption isthe same that has the lowest cost per hour, the machine fifteen, with that it is possible to also reduce theeffect of the machine cost.

With such difference in the penalty values, is possible to verify that the machine with the highestworking time is the one with the lowest total cost. And when the total energy consumption of the ma-chines is analysed is possible to verify that the difference of consumption of the best machine and theworst three machines is at maximum 244.18 KW to a difference of 166 hours, as seen in the table 4.15.

Table 4.15: Energy-based method - Drill EDM

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Drill EDM

15 J22-3; J1-6; J13-4 227 191 274,67 649,22

16 J8-2; J10-5 78 340 507,78 536,64

17 J21-5 61 357 542,29 405,04

18 J14-3 106 312 873,44 630,7

19 J23-3; J5-3; J24-3 115 303 823,4 395,6

The Rectification section has a great difference in the penalties of the machines, with the machinetwenty-three being the lowest one, and in the other side the machine twenty-five has a penalty value15.38 times superior than the lowest one. For these method three of the machines are not utilised.

The existence of such discrepancy in penalty values origins that most of the work is processed bythe machines twenty-three, with 248 hours, a difference of 190 hours to the machine that has the mostused after this one. And with such a difference in machine consumption, the machine twenty-three stillends up with the lowest total energy consumption in the section, as seen in the table 4.16.

37

Table 4.16: Energy-based method - Rectification

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Rectification

20 - - 418 0 0

21 J5-1; J23-2; 58 360 27,84 232

22 J21-3; J24-2; J11-3 47 371 85,54 237,35

23J8-1; J1-2; J10-3; J3-2;

J13-2; J22-5248 170 74,4 230,64

24 - - 418 0 0

25 - - 418 0 0

Analysing the overall results of the energy-based method, table 4.17, and comparing them with bothmethods performed before, we can clearly verify a great change in the results by applying a penalisationaccording to the energy consumption of the machines.

When looking at the time expended to complete the project the energy-based method takes more 35hours than the time-based method, but less 39 hours than the cost-based method, this last occurs dueto the greater difference in the penalization between machines in the same section.

In terms of the total cost of project, as expected, this method is more expensive than the cost-basemethod by 2897.5e, and when compared with the time-based method the cost difference is 378.2e, thisfact is related to most of the machines that have lower cost per hour also have lower energy consumption.

For the energetic consumption this method has the best results, comparing with the cost-basemethod we have a decrease in consumption by 5957 KW, and an even great decrease compared withthe time-based method by 7643.7 KW, this fact occurs due to most of the machines that have lowercosts per hour also have lower energy consumptions.

Table 4.17: Energy-based method - Results Aggregation

Makespan [Hours] Idle Time [Hours] Cost [e] Energy Consumption [KW]

Total 418 7918 19155,82 23811.82

38

4.4.4 Energy-Cost-Based Method

In the energy-cost-Based method, the objective is to reduce the duration, the total cost of the projectand the total energy consumption of the project, taking into account the new developed parameters Ci

and Ei.In this case, all of the machines of each section have different penalties in their utilisation based on

their cost per hour, and for the value of energy consumption. The time of processing a specific part in asection is the same for any machine in that section.

For the CNC section the machine with more working hours, 361 hours, is the machine one, that hasthe lowest combined penalisation (ranking second in both categories), all of the other machines havecloser values in the working time, table 4.18. The normalised values for the penalisations for the energyhave a larger difference, because of that the machine with higher energy consumption, machine five ismore penalised than the machine with the highest cost per hour, the machine two.

Table 4.18: Energy-Cost-Based Method - CNC

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

CNC

1 J22-2; J2-1 361 22 3133,48 4512,5

2J11-1; J4-1; J10-1;J16-1; J8-4; J15-2

168 215 3281,04 1680

3J19-1; J9-1; J21-2; J1-3;J23-1; J6-1; J17-2; J12-1

145 238 1887,9 3625

4 J13-1; J18-1 111 272 1686,09 3108

5 J5-2; J14-2 128 255 916,48 4131,84

6 J24-1; J3-1; J7-1; J20-1 193 190 2094,05 2491,63

In the Lathe section the normalised values of the penalizations are similar, and with one machinehaving the lowest cost per hour and the highest energy consumption, the algorithm attributed moreworking hours to the machine that has the lowest combined penalization value, by 0.23, with privilege tothe cost per hour.

Considering the cost per hour, the total cost of the machine seven is more 15,45e, and when con-sidered the energy consumption, the machine seven has a consumption 59.34 KW superior, as seen inthe table 4.19.

Table 4.19: Energy-Cost-Based Method - Lathe

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Lathe7

J11-2; J14-1; J10-2;J15-1

84 299 54,6 114,24

8 J17-1; J1-5; J18-2 45 338 39,15 54,9

39

The Milling section presents, as seen in the table 4.20, differences regarding the penalty value forthe energy consumption between both of the machines of 0.31, and of 3.46 for the cost per hour. Thismakes the algorithm choose the machine nine, the better in both of the categories, with a difference of52 hours of working time.

Considering the difference on penalty values between the two machines, the machine number nineprocessed 52 more hours than the machine ten, with that resulting in a total cost of 1.88 times higher,and an energy consumption 1.81 times greater.

Table 4.20: Energy-Cost-Based Method - Milling

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Milling9

J22-1; J7-2; J13-3; J6-2;J10-4

90 293 35.1 516.6

10 J1-1; J21-1; J8-3 38 345 66.12 285

For the Wire EDM section, optimising the energy and the cost simultaneously, we can see the firstchange from the energy-based optimization, and a similar one with the cost-based method, since oneof the machines is not utilized, the machine number fourteen, that has the highest cost per hour but hasthe second lowest energy consumption, and combining the two penalizations it is the machine with thehighest score, as seen in the table 4.21.

In this case we see an increase in the total energy consumption related to the energy-based method,since the machine with second lowest consumption is not utilised, the machine fourteen, but related tothe same method it was possible to achieve a better total cost.

For the cost-based method this section, with the machine fourteen not operating we have the samemachines working in both section, but with an increase in the total cost due to the fact that the machineeleven has the lowest combined penalization, but has the highest cost per hour of the three workingmachines.

Table 4.21: Energy-Cost-Based Method - Wire EDM

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Wire EDM

11 J22-4; J14-4 137 246 742,54 883,65

12 J5-4; J23-4 27 356 117,18 247,86

13 J1-4; J21-4 65 318 338,65 468

14 - - 383 0 0

40

In the Drill EDM Section all of the machines are utilised, the same as in the energy-based method,and contrary to the cost-based method, due to a more balanced penalization with the simultaneousintroduction of both parameters.

For this section, the penalty values between the machine that has the lowest energy consumptionare the same that has the lowest cost per hour, the machine fifteen, with that it is possible to also reducethe effect of the machine cost.

With such difference in the penalty values, between the machine five and the others, is possible toverify that the machine with the highest working time is the one with the lowest total cost and also withthe lowest energy consumption, table 4.22. And if a closer look is taken in the total cost, it is possible toverify that even working more hours, it has the lowest total cost and a lower total energy consumptionthan the second most utilised machine.

Table 4.22: Energy-Cost-Based Method - Drill EDM

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Drill EDM

15 J5-3;J13-4 176 207 212,96 503,36

16 J22-3; J14-3 124 259 807,24 853,12

17 J21-5; J23-3 72 311 640,08 478,08

18 J24-3; J8-2; J10-5 81 302 667,44 481,95

19 J1-6 134 249 959,44 460,96

The Rectification section has a great difference in the penalties of the machines, with the machinetwenty-three being the lowest one in both cases, energy consumption and cost per hour, in the otherside the machine twenty-five has a penalty value 15.38 times superior than the lowest one for the energyconsumption and 18.8 times superior than the lowest one for the cost per hour. For these case two ofthe machines are not utilised, the machine twenty-five that has the highest penalization combined andthe machine twenty with the second highest penalisation Combined, as seen in the table 4.23.

The two machines that have the lowest cost per hour are the same that have the lowest energyconsumption, that fact makes the algorithm choose to make most of the operating time in the machinetwenty-three, 172 hours, and in the machine twenty-one, 90 hours. The values of the penalisation areso different that even with the machine twenty-three working more 82 hours than the machine twenty-one the total value of the energy consumption is 200 Kw lower and the total cost is only 8.4e, and canachieve less 83e than the third most used machine, machine twenty-two that works during 74 hours,less 98 hours than the machine twenty-three.

41

Table 4.23: Energy-Cost-Based Method - Rectification

Section Machines OperationsWorking

Time[Hours]

IdleTime

[Hours]

Cost [e]Energy

Consumption[KW]

Rectification

20 - 383 0 0

21 J1-2;J8-1 90 293 43,2 360

22 J24-2;J21-3:J10-3 74 309 134,68 373,7

23J5-1J;J11-3;J13-2;J3-

2;J22-5172 211 51,6 159,96

24 J23-2 17 366 18,36 127,5

25 - 383 0 0

Analysing the overall results of the energy-cost-based method, table 4.24, and comparing them withthe methods performed before, we can clearly verify a change in the results by applying a penalisationaccording to the energy consumption and cost per hour of the machines.

When looking at time expend to complete the project this method takes the same time, 383 hoursthan the time-based method, less 74 hours than the cost-based method, and less 35 hours than theenergy-based method. This effect results due to the balance between the machines, since for the mostpart the ones with the highest consumption have the lowest cost, and the ones with the highest costhave the lowest consumption.

In terms of the total cost of the project, this method is more expensive than the cost-base methodby 2020,49e, when compared with the time-based method the cost difference is 498,81e, and whencompared with the energy-based method the total cost is less 877,01e.

For the energy consumption this method have better results comparing with the cost-base model,with a decrease in consumption off 3384,17 KW, and an even greater decrease compared with the time-based method by 5070,87 KW, but when compared with the energy-based method that is an increaseof energy consumption of 2572,83e.

Table 4.24: Energy-Cost-Based Method - Results Aggregation

Makespan [Hours] Idle Time [Hours] Cost [e] Energy Consumption [KW]

Total 383 7043 18278,79 26384,23

42

4.5 Overview

In this section it was made the comparison between the four different methods in study, this comparisonwas made by section, analysing the occupation rates of the machines in the different the section, byevaluating the total costs, total energy consumption, and relative impact of the developed methods inthe cost, energy consumption and duration of the project.

Analysing the occupancy rate of every section, it is possible to see the waste of productive timeinstead of the costs and energy consumptions. The average of the occupancy rate is directly related tothe duration of the project, that is why the energy-cost-based method with has the same occupancy rateof the time-based method.

In the CNC section, for the time-based method, the occupancy of every machine is stable, as themachine selection is randomly attributed, there are no penalisations, so the selection is only made bythe production time that is the same in every machine.

For the cost-based method, the highest occupation rate is 70,8% on the machine two, and thismethod is the least efficient in this section with a greater waste of productive time of 3,8% in relation tothe energy-based method and 7,8% to the most efficient methods.

For the energy-based method the machine with the highest occupation rate is the machine five witha rate of 65,4%, this method has an higher efficiency that the cost based method, situating is efficiencybetween the worst method, 3,8%, and the most efficient methods, 4%.

This section is the one with highest average occupation rate, but even with that factor, the averageoccupation rate never reaches the 50%, as seen in the table 4.25.

Table 4.25: Comparison % occupation machines - CNC

Section Machine% of Occupancy

Energy Cost Energy-Cost Time

CNC

1 60,3 54 94,3 33,2

2 70,8 23,2 43,9 52,5

3 28,9 35,4 37,9 18,5

4 26,3 22,5 29,0 47,3

5 18,7 65,4 33,4 79,9

6 59,6 41,4 50,4 57,4

Average 44,1 40,3 48,1 48,1

The lathe section is composed of two machines, and comparing the two methods that privileged thetotal cost, the cost-based method and the cost-energy-based method, due to the total duration of theproject is possible to see that both of the machines have greater occupation rate in the energy pluscost-based method, with an average increase of 2,7%, as seen in the table 4.26.

The energy-based method, as seen in the section above, utilised the machine eight the most, thismachines as the lowest energy penalization but the highest aggregated penalization.

The time-based method is the most balanced method, with the less discrepancy in the occupationrates on the machines, a difference of 3,4%.

43

Table 4.26: Comparison % occupation machines - Lathe

Section Machine% of Occupancy

Energy Cost Energy-Cost Time

Lathe7 11,5 18,4 21,9 15,1

8 19,4 9,8 11,7 18,5

Average 15,4 14,1 16,8 16,8

The Milling section, in the table 4.27, like the Lathe section, is composed of two machines, butcontrary to the lathe section, in this section the machine with the lowest cost is also the one with thelowest energy consumption, so for the methods that utilized the penalisation parameters the machinewith the highest occupation rate is the machine seven. For the cost-based method, the machine numberten only has a 2% occupation.

The energy-based method, as seen above, utilised the machine nine the most, this machines havethe lowest energy penalisation but with the penalisation being similar, with a difference of 0.11, theoccupation rate is more balanced.

The time-based method is the one that utilised the machine ten for the most of working process, withan occupation rate of 27,3% and the machine seven with an occupation of 6,3%.

Table 4.27: Comparison % occupation machines - Milling

Section Machine% of Occupancy

Energy Cost Energy-Cost Time

Milling9 17,5 26,0 23,5 6,3

10 13,2 2,0 9,9 27,2

Average 15,3 14,0 16,7 16,7

The Wire EDM section is composed of four machines and is the first section that presents a machinewith no time allocated, this event occurs in the cost based method and in the energy-cost-based method.

In the energy-based method the occupancy rate of the machine one is 1,9 times superior than theoccupancy of all the other machines combined.

For the cost-based method, the work was divided by the machine twelve with 27,6%, and the machinethirteen with 16,2%, and the machine eleven with a lesser percentage with 6,3%.

The energy-cost-based method behaves in the same manner as the cost-based method, with two ofthe machines doing most of the work, in this case, are the machine eleven with 35,8% of the occupationrate and the machine thirteen with 17% of the occupation rate, the machine twelve has a residualoccupation rate of 7%.

The time-based method utilises every machine in the planning but one of the machines, the machinetwelve, has attributed 39,2% of the work, and with the machine eleven with 2,9%, and the machinethirteen with 5,7%, makes this section one the most unbalanced for this method.

This section is the first in the project that the number of machines in one section is not the most ad-equate, since that for two separated methods there was a machine that is not utilised, and the existenceof other with reduced occupancy rates, as seen in the table 4.28.

44

Table 4.28: Comparison % occupation machines - Wire EDM

Section Machine% of Occupancy

Energy Cost Energy-Cost Time

Wire EDM

11 35,9 6,3 35,8 2,9

12 3,8 27,6 7 39,2

13 5,3 16,2 17,0 5,7

14 9,8 0,0 0 12,0

Average 13,7 12,5 14,9 14,9

The Drill EDM section has the second highest average occupation rate after the CNC section, in thissection for the cost-based method the event that happened in the previous section also exists in thisone, there is a machine with no work attributed. All of the other methods have all the machines withwork attributed.

The energy-based method uses all of the machines available, has in the machine fifteen the one withhighest occupation rate 54,3%, the machine with the lowest penalisation. The other four machines havethe occupation rates stabilised with a maximum difference of 13% between the machine nineteen andthe machine seventeen.

The cost-based method is the one in this section that has a machine with no work attributed, themachine seventeen, and a machine with a low occupation rate, the machine eighteen with 6,3%, thiseffect occurs because of the high value on the penalisations. With this great difference in the penal-isations, most of the work is situated in the machine fifteen, 51%, and the machine sixteen also has ahigher occupation, 49%, due to the fact that the algorithm also has to reduce the project time in all of themethods.

For the energy-cost-based method most of the work is done in the machine fifteen since it is the onewith the lowest penalisation in both the parameters, and since the penalisation order of the parameterchange, the highest ones in energy consumption tend to be the lowest ones in the cost per hour, theoccupation rates of the machines are grouped, the machine sixteen and nineteen are similar and themachine seventeen and eighteen are similar.

The time-based method uses all the machines with the machine sixteen having the highest occupa-tion rate, 51,4%, and the machine eighteen has the lowest occupation, 2,9%.

In this section, the same event that happened in the previous occurs also in this one, but the differ-ence this time is that with higher occupation rates it can penalise the duration of the project by not takingadvantage of the equipment available, as seen in the table 4.29.

45

Table 4.29: Comparison % occupation machines - Drill EDM

Section Machine% of Occupancy

Energy Cost Energy-Cost Time

Drill EDM

15 54,3 51,0 46,0 43,6

16 18,7 49,0 32,4 51,4

17 14,6 0,0 18,8 19,6

18 25,4 6,3 21,1 2,9

19 27,5 22,1 35,0 35,8

Average 28,1 25,7 30,7 30,7

In the rectification section, there are three methods with machines that have no work assign; only thetime-based method has all the machines assigned.

The energy-base method uses three of the six machines available, with most of the work being donein the machine twenty-three, with 59,33% of occupation, the other two machines used have lower oc-cupation rates, twenty-one, with 13,88% and the twenty-two, with 11,24%. In the cost-based methodonly the machine twenty-five, the one with the highest penalisation does not get used. The values ofthe occupation rates are more balanced with two machines having most of the work instead of one, themachine twenty-three, 38,73% and twenty-one, 23,85%, the other three machines have lower occupa-tion rates since their penalisation values get considerably higher than the previous two machines. Theenergy-cost-based method has two machines that have no work assign, the machine twenty-five andthe machine twenty, this are the ones with the highest penalisation combined. The machine that hasthe higher level of occupancy is the machine twenty-three, 44,91%, the machine twenty-four as residualwork assigned with only 4,44% of occupancy. For the time-based method all the machines have workassigned, with the maximum occupation rate being achieved with the machine twenty-five at 24,3%, withthe machines twenty-four and twenty-two having residual occupancy values.

This section being the one with the lowest average occupation rates and the biggest difference inpenalisation amongst the several machines, it is possible to say that the number of machines in thesystem is superior to the required, as seen in the table 4.30.

Table 4.30: Comparison % occupation machines - Rectification

Section Machine% of Occupancy

Energy Cost Energy-Cost Time

Rectification

20 0,00 2,41 0,00 17,8

21 13,88 23,85 23,50 21,1

22 11,24 6,13 19,32 5,7

23 59,33 38,73 44,91 20,4

24 0,00 7,22 4,44 2,9

25 0,00 0,00 0,00 24,3

Average 14,1 13,1 15,4 15,4

46

Analysing and comparing the overall performance of the three methods developed,4.31, energy-based, cost-based and energy-cost-based, with the existing time-based method, it is possible to directlyverify the impacts of using the developed parameters in the planning.

Comparing the Makespan, duration of the project, the optimal duration is 383 hours, this duration isachieved using the time-based method and the energy-cost-based method, this happens because thismethod tends to balance the total values, since the machines that cost more tend to be the ones thathave less energy consumption. The energy-based method takes more 35 hours than the optimal value,in here starts to see the effect that higher penalisations values on certain machines have on the durationof the project. The cost-base method, with a duration of 457 hours, is the method that takes longer tofinalise taking more 74 hours than the optimal value, this method is the one with more discrepanciesbetween the penalty values among the machines in the different sections resulting in heavier work loadsto specific machines.

For the total energy consumption the method that has the best result is the energy-based method,with a total energy consumption of 23811,4 KW, this is a great decrease in consumption taking in consid-eration the total energy consumption on the time-based method, the one with the highest consumption,of 31455,1 KW, a difference of 7643,7 KW. the cost-based method with a energy consumption of 29768,4KW, presents an increase of 5957 KW related with the energy-based method. When analysing the effectof only considering the energy penalization instead of considering both, energy and cost penalisations,there is an increase of 2664,4 KW when considered both penalisations.

The method with the lowest total cost is the cost-based method with a total cost of 16258,3e, adecrease in the total cost of 2519,5e comparing with the time-based method. The energy-based methodhas a total cost of 19155,8e, which is an increase of 2897,3e compared with the cost-based method.The energy-cost-based method is the one who achieves a closer result to the cost-based method, havinga difference of 2090,4e.

Table 4.31: Results Comparison

Method Makespan [Hours] Energy [KW] Cost [e]

Time 383 31455,1 18777,6

Cost 457 29768,4 16258,3

Energy Consumption 418 23811,4 19155,8

Energy + Cost 383 26475,8 18348,9

In the figure 4.6 is represented graphically the results studied and shown by the table 4.31. The valueof total energy consumption is represented on the x-axis, with the total cost represented in the y-axis,the makespan is represented by the size of circles of each method.

Represented in red is the energy-based method, in grey is the energy-cost-based method, in blue isthe cost-based method and in yellow is the time-based method.

Analysing the figure 4.6 is possible to verify that the differences between the methods is greater forthe energy consumption than for the total cost, and if only those two factors are taken into account thebest method of planning is the energy-based method.

47

Figure 4.6: Comparison between the different methods applied

To achieve a better understanding of the obtained results, it was created a criteria based on thenormalised values for the total cost, total energy consumption and total duration of the project.

This normalization was performed, dividing the value lowest value obtained in the different outputsby the values of each method for that output, i.e. for the makespan the reference value were the onesfrom the time-based and energy-cost based methods, this value was taken and divides by the values onthe other methods, with the cost-based method obtaining 0.84 and the energy-based method 0.92.

As seen in the figure 4.6 where the methods present greater differences is in the total energy con-sumption, and the factor that has less effect on the overall score is makespan, the duration of the project.

The overall score is obtained by multiplying the normalised factors, and with that in account the bestmethod is the energy-cost-based method, with a score of 80%, the second best method is the energy-based method, with a score of 78%. If the duration of the project was not taken in account for thisanalysis the best method would be th energy-based method.

Table 4.32: Normalized Overall Score

MethodNormalized

Overall ScoreMakespan Energy Cost

Cost 0,84 0,80 1,00 0,67

Energy 0,92 1,00 0,85 0,78

Energy-Cost 1,00 0,90 0,89 0,80

Time 1,00 0,76 0,87 0,66

48

4.6 Operationalisation

In this section, a methodology for the application of the decision support method is constructed.

The applicability of this method is appropriated for control and learn of the process to help in theplanning decision, and not as toll to produce the companies production plans. With the analysis of theprocess being made from data of already processed parts.

To achieve the best results, this method must be applied in a systematic and regular platform.

For a more structural and understandable application is possible to divide the method in four phases,Phase 1, where the goal of the project is defined, Phase 2, the method is applied, Phase 3, the resultsare analysed, and in Phase 4 application of the results achieved, and study to future optimisations.

Phase 1In this phase the foundation for the study is assured, completing several points to systematise the

goals and the control factors.

• The goal of the study

• Study of the system, determination of the current state

• Variables need to control and optimise

• Period of the study, a longer period of data collection assures a better representation of the process

This correct formulation of this points allows a better definition of the next phase, with a correct choiceof what to study, and which parameters are needed to collect and control.

Phase 2This phase is the main part, and is the one produced in the current chapter. Here the following steps

are produced, (1)the data is collected and analysed with the parameters normalised, (2) the parametersin the algorithm are optimised, and (3) the collect of the different solutions.

Step 1 - Data Gathering

With the definition of the project concluded in the Phase 1, the required data must be collected in astandardise form for all the machines in the several sections, for this part is crucial that the informationmust be collected in the most precise way, to assure a correct study of the process.

• The processing time of the parts in a specific machine

• Which machine in a section can process the part

• The operations needed to complete a part and their sequence

After gathering the information, the data must be checked to verify if it is conforming. With theverification done, a normalisation by working section of the process parameters must be realised, thisnormalisation allows a more balanced perform by the algorithm.

49

Step 2 - Algorithm Sensitivity AnalysesWith the process parameters normalised and introduced, the fine-tunning of the algorithm paramet-

ers are a vital part of the optimisation process.The fine-tunning is made trough an iteration system. For each of the optimisation parameters, Pop-

ulation, Crossover Percentage and size of the Elite Group, there are tested several values and verifiedthe best combination among them, combination that should achieve the optimal solution.

Every test must be run at least 20 times, then the average and standard deviation values are takenas an evaluation metrics.

Step 3 - Collect of SolutionsHaving the optimal parameters for the algorithm, the next step is to proceed with the several tests.

This tests must be done with all the combinations possible between the process parameters.For all the combination a large number of runs should be performed, since there are several possib-

ilities to perform the planning, is possible to achieve different values for the outputs in study.

Phase 3In this phase an analyse to the solutions gathered in the previous step is required, not only to de-

termine the best approach in the future but also to study special conditions in the system.

With a large number of possible schedules, there is a chance of finding schedules as the onesachieved in this thesis, where one or more machines in a section have no work attributed.

For those cases, the step 3 of the Phase 2 must be repeated without the presence of those machines.After the new results are determined, the effect of reducing the number of machines the section in causeshould be analyse not only in overall terms but also results in the specific section.

The solution determined, and studied by the algorithm are only a mean to compare the current plan-ning system with the possible best solutions and help in the decision maker in future planning projects.And not seen as a definitive decision making tool for the company.

Phase 4With all the analyses made and the different solution taken into account a new planning bust be

conceptualised based in the conclusion.After this project is concluded a new one must start to produce in the company a continuous im-

provement movement, and the further the projects reach the time between them should be smaller withthe intent of making this type of project as close from the actual reality of the company as possible.

50

Chapter 5

Simulation of a System in OverProduction

In this chapter a production system is put in over production, this means that it is introduced in the systema greater number of parts than it is capable of processing. It was also added the existence of rejectedparts, parts that do not meet the quality requirements. To reduce this effect, various methodologies wereapplied to improve this production process, with the goal of minimising the delays.

As seen in the chapter 4, the bottleneck of the process is the CNC section, so the performance testswere applied in this section.

The optimisation of the queue process is done through the implementation of a selection of Dispatch-ing Rules Heuristics, FIFO or Priority based, described in Chapter 3, and three different methodologiesfor the configuration of the machines.

There were tested different machines configurations, None-dedicated, Partially dedicated and Ded-icated, as the queue system, FIFO or Priority, considering the throughput time and the occupancy ofthe machines, for several levels of quality, the different level of quality tested change between 100% and50%, to assure the best OEE. To compare and consider which of the formation and Heuristics assurea better flow in the process, the KPI’s taken as measures of the effectiveness of the system were thethroughput time and the level of quality.

For this simulation, the system was forced to work in overload which means that the machines willbe at full capacity all the time, so the values of energy consumption and cost per hour of the machinesare not taken into account since the overall level of occupation on the machines are stabilised in similarvalues.

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5.1 Model of the system

The simulation schematics used to interpret the behaviour of a mould factory were done resorting toa toolbox in SIMULINK called SimEvents, a toolbox that recreates systems based on Discrete EventSimulation. The model is composed of four sectors, the order generator, where the parts of the differentmoulds are generated, the routing system, where the program counts the steps that the parts has alreadytaken and the next step to do, all the different workstations, contain several machines and a block servesas a sink to the parts.

The simulation was conducted for 10000 hours in order to get a reasonable number of all mouldscompleted, for the quality level of 50%, to assure a good representation and achieving a valid statisticalbase in the result.

The Model incorporates 6 independent workstations, composed by the correspondent machines, themachines are considered to have the same work capacity with the processing time attributed off-line tothe part, not to the machine, each machine can only operate a part at a time and the setup time werenot taken in account in the resolution of this problem. Also, it was considered that for every time a partis marked as rejected the time of the rework is the same time as initially attributed for its production.

• CNC - Contains 6 independent machines

• Lathe - Contains 2 independent machines

• Milling - Contains 2 independent machines

• Wire EDM - Contains 4 independent machines

• Drill EDM - Contains 5 independent machines

• Rectification - Contains 6 independent machines

In the figure 5.1 is exemplified the functioning of the CNC workstation with none dedicated machines.The parts arrive and are place in a queue, that can be ordered by FIFO or by Priority, then a distributordefines the attribution of work by checking which machine is available, starting with machine 1 andfinishing in 6, and selecting the first that is free. When the part has finished processing it passes to thenext stage, the control stage, to check if the part meet the requirements to advance to the next process.

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Figure 5.1: Flowchart of CNC Production

With the access to the production time log, as seen in chapter 4 the theoretical average throughputtime of production is 104.79 hours, this time is the time acquired from the company logs and correspondsto the real production time of the parts. When the simulation is done and the quality defined is 100%, theaverage throughput is 470.4 hours, which corresponds to a waiting time of 365.61 hours, and as shownin the figure 5.2 it’s in the queues that is wasted most of the processing time.

In the figure 5.2 are represented 13 cycles of production, for the 4 moulds required and with 100%quality, the process can produce 52 moulds in 10000 hours. For the first cycle, the maximum numberof parts in the queue is 3, this occurs because the system is empty and can absorb the work, after thatpoint, it is entirely visible the cycles with the number of parts in the queue reaching the 18 units at a time.

Figure 5.2: Evolution on CNC Queue with a Quality Level of 100%

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5.2 Sensitivity Analysis on the Simulation Model

In this section, an analysis to the effect of the simulation time on the output of the system was made toassure reliability of the simulation program.

To verify the necessary simulation time, were processed tests for three different times, 10000 hours,20000 hours and 30000 hours. These tests were conducted for values of quality of 100%, 99%, 95%and 90%. Previous studies on production systems of this type determined that the level of overall qualityof the process is 95%, so for this tests, the quality level was only decreased up to 90%.

Comparing the test with 100000 hours with the other two tests, as seen in figure 5.3, the values ofthe error is, for a quality level of 100%, is 1.46% for 20000 hours and 1.89% for 30000 hours. Whenconsidered the operation level of 95%, the difference is 3.71% for 20000 hours and 3.28% for 30000hours.

With the maximum value of error not surpassing the 10% of error and behaviour similar betweentests, the value of 10000 hours was selected for the simulation time of the project ahead.

Figure 5.3: Effect of the simulation time on the throughput time

5.3 Production Systems Selection

In this section were tested three different methodologies for the production, two systems with non-dedicated machine, a system with a partially dedicated machine, and a system with a dedicated ma-chine, existing two subcategories in the non-dedicated production system, in which two different queuesystems were tested, a FIFO system and a Priority system. For this different Heuristics, the reworkmust then be ordered according and attributed to a machine by the process exemplified previously in thefigure 5.1.

The second production system consists in incorporating the rework as a separate system, where amachine is allocated to do all the rework necessary, figure 5.4, allowing for the other machines to keepthe predetermined schedule, maintaining a good production flow.

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Figure 5.4: Flowchart of CNC Production with a Dedicated Machine

For the third and the last system it was tested a variant of the dedicated system represented in thefigure 5.4, this system consists in partial allocating a single machine to treat all the rework, figure 5.5,being this system a mix of the previous ones, it works as a non-dedicated system if there is no rework tobe done but if any rejected part is generated a machine is allocated to solve it, as the level of quality inthe production declines this system becomes similar to the one with a machine dedicated to the rework.

Figure 5.5: Flowchart of CNC Production with a Partially Dedicated Machine

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5.3.1 Production System with Non-Dedicated Machines with FIFO Queues

For this case, it was tested a system where the queue is ordered by arrival position, and the exit of thequeue is based on that position. The FIFO philosophy is applied to the system.

In higher levels of quality, up to 90%, the system behaves in a way that allows to achieve a level ofzero units in the queue, with the maximum value of 22 units for the simulation time. When the qualityof the production system is decreased it is incapable of suppressing all the demand required, with thevalues of items increasing in the queue up to 142 for the quality level of 50%.

Table 5.1: Average Throughput Time Non-Dedicated FIFO SystemQuality Level

100% 99% 95% 90% 80% 70% 60% 50%Average Throughput time [Hours] 470.4 472.6 499.5 534.7 838.8 1239.5 1587.4 2072.9Max units in Queue 18 18 20 22 41 70 102 142

It is possible to see in the table 5.1, and the figure 5.6, that the system maintains a regularity in theoverall process, showing an increase of 64.3 hours in the production time from 470.4 hours at 100% to534.7 hours at 90%. And beyond that point it is able to see an increase of 304.1 hours, decreasing thequality level by 10%.

With the simulations, it was possible to determinate for the different levels of production quality theaverage throughput time and the maximum value in the queue. For this case is possible to verify thatafter the quality drops 20% or more, the system is incapable of suppressing the demand. The numberof parts in the queue does not reach zero or stabilises in a fixed value, with the average throughputincreasing at higher rates than up to that point.

Figure 5.6: Throughput time in a FIFO system

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For a better overview, the mould A was selected for a closer analysis, and for both parts, the evolutionof the throughput time behaves as the average of the process. From the table 5.2 it is possible to verifya waste of 417.8 hours for part 1 and 334.8 hours for part 2 considering the real time of production andthe time needed for this system to process the parts.

Table 5.2: Throughput time [Hours] in a Non-Dedicated system with FIFO Queue to the mold A

Mold Part Real Production timeThroughput Time [Hours] for various Quality levels

100% 99% 95% 90% 80% 70% 60% 50%

A1 330 747,8 747,8 802,3 840 1181 1383 1629 2122

2 182 516,8 516,8 544,8 546,3 918,9 1187 1233 1274

In the figure 5.7 is possible to see a slow increase in both parts from the 100% to 90%, and anexponential growth form that point forward for part 1 and a higher increase when the quality level dropsto 80%, almost doubling the time required, and a linear growth from that point forward.

Figure 5.7: Throughput time in a FIFO system

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5.3.2 Production System with Non-Dedicated Machines with Priority Queues

For this case was tested a system were the queue is ordered by priority level, where for the parts to bereworked it was attributed a high value of priority, and the order of the queue is based on that position, thehigher the value the fastest the part is processed in the queue, a system where the Priority philosophyis applied, figure 5.9.

For higher levels of quality, up to 90%, the system behaves in a way that allows to achieving a level ofzero units in the queue, with the maximum value of 18 units for the simulation time, table 5.3. When therates of rejected parts are increased, the system is incapable of suppressing all the demand required,with the values of items increasing in the queue up to 141 for the quality level of 50%.

Figure 5.8: Throughput time in a Non-dedicated Priority System

For this case is possible to verify that after the quality level decreases pass the point of 80%, thesystem is incapable of suppressing the demand with the average throughput increasing at higher ratesthen up to that point.

Comparing with the previous system it is possible to say that this production system gives a betterflow of process and reduces the time of the parts in the process.

Table 5.3: Average Throughput Time Non-Dedicated Priority SystemQuality Level

100% 99% 95% 90% 80% 70% 60% 50%Average Throughput time [Hours] 470.4 472.6 499.5 534.7 788.1 952 1006.6 1162.8Max units in Queue 18 18 20 22 38 69 102 141

Looking closely at Mould A, we are able to see that for the part 2 there is a decreasing in theproduction time when the level of quality is lowered form 60% to 50%,figure 5.9, the case for that effectis the selection of the parts that require reworking, being this selection made by random attribution,so there is the case where fewer parts of a mold fail the quality check for a lower quality level in theproduction system.

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Figure 5.9: Throughput time in a Non-dedicated Priority System

If the growth in the time of part 1 is taken for a closer analysis it is possible to verify that it behavesas expected, same behaviour as in the previous methodology, it has a better overall performance, notonly is more stable in its growth but also the value of the throughput time decreased, table 5.4.

Table 5.4: Throughput time [Hours] in a Non-Dedicated system with Priority Queue to the mold A

Mold Part Real Production timeThroughput Time [Hours] for various Quality levels)

100% 99% 95% 90% 80% 70% 60% 50%

A1 330 747,8 747,8 802,3 840 1155 1459 1689 1986

2 182 516,8 516,8 544,8 546,3 791,8 1176 1412 1128

5.3.3 Production System with a Partially Dedicated Machine

For this case was tested a system with a partially dedicated machine, all the rejected parts are done onthis specific machine leaving the rest of machines available to do the planned work with no interruptionson the schedule, maximising the flow.

If there is no rework to be done in the partially dedicated machine this production system worksas a non-dedicated machine, like the ones represented previously. The change for the system abovehappens if there is some part that does not meet the quality requirements, then a machine is allocatedto do all the rework. The queue is ordered by priority level, the parts that came to be reworked takepriority over the ones that were already planned.

For higher levels of quality, up to 90%, the system behaves in a way that allows achieving a level ofzero units in the queue, with the maximum value of 18 units for the simulation time. When the level ofquality of the system is decreased it is incapable of suppressing all the demand required, with the valuesof items increasing in the queue up to 114 for levels of quality of 50%.

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Figure 5.10: Throughput time in a Partially Dedicated Priority system

With the simulations, it was possible to determine the different rates of rejected parts, the averagethroughput time and the maximum value in the queue. For this case is possible to verify that afterthe quality drops 20% or more, the system is incapable of suppressing the demand with the averagethroughput increasing at higher rates than up to that point.

In this system the main difference is having two independent queues, the general queue stabilises at35 units never going over this value, which guarantees a continuous flow and a control of the productionplan. In another hand the rework queue reaches a point, at 80%, that it can no longer manage therequested work, table 5.5.

Table 5.5: Average Throughput Time Partially Dedicated Priority SystemQuality Level

100% 99% 95% 90% 80% 70% 60% 50%Average Throughput time [Hours] 470.4 473.3 495.1 544.7 837.5 989.2 1095.2 1158.5Max units in General Queue 18 18 19 22 34 34 34 35Max units in Rework Queue 0 1 2 3 11 39 72 114

For this method and analysing once again the mould A, figure 5.11, it is verifiable that the behaviourfor the different parts changed, with the part 1 showing a slow growth on the process time and evendecreasing past the level of 80% quality. The case for the part 2 is the reverse, it grows exponential pastthe point of 80%.

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Figure 5.11: Throughput time in a Partially Dedicated Priority system - Mould A

From the table 5.5, and table 5.6, we can assume that this method achieves results as the methodof a non-dedicated machine with a priority queue. With the main difference being the continuous flow inthe process plan, not needing to stop and reschedule due to the existence of a part with defects.

Table 5.6: Throughput time [Hours] in a Partially Dedicated system to the mold A

Mold Part Real Production timeThroughput Time for various Quality levels

100% 99% 95% 90% 80% 70% 60% 50%

A1 330 747,8 762,9 862 918,6 1107 1527 1226 1403

2 182 516,8 516,8 531,9 578,1 814,6 1366 1394 1942

5.3.4 Production System with a Dedicated Machine

To study this case, it was also tested a system with a dedicated machine, all the rejected parts aredone in this specific machine leaving the rest of machines available to do the planned work with nointerruptions on the schedule. The rework queues are ordered by priority level, where the parts attributedwith an higher value take priority to be processed, for this case study it was attributed the same prioritylevel for all the rejected parts, and the exit of the queue is based on that position, a system where thePriority philosophy is applied.

For higher levels of quality, up to 90%, the system behaves in a way that allows achieving a levelof zero units in the general queue and in the rework machine queue, with the maximum value of 35units in the income queue and 2 in the rework queue for the simulation time. When the rates of rejectedparts are increased, the system is incapable of suppress all the demand required, with the values ofitems increasing in the rework queue up to 112 units, maintaining the value of 35 units in the incomemachine. In these case the number of parts in the queue never drops to zero but maintains a stablecyclic development, for the levels of quality of 50%.

With the simulations, it was possible to determine for the different levels of quality the averagethroughput time and the maximum value in the queue. For this case is possible to verify that afterthe quality drops 20% or more, the system is incapable of suppressing the demand with the averagethroughput increasing at higher rates than up to that point.

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From the table 5.7, it is possible to see that since the number of available machines is now five insteadof six the average time of processing is higher right from the first test, quality at 100%. But in anotherhand is assured a more stable system with a variation of 419 hours, and after the system is no longercapable of solving all the demand it behaves like the two systems above.

Table 5.7: Average Throughput Time Dedicated Priority SystemQuality Level

100% 99% 95% 90% 80% 70% 60% 50%Average Throughput time [Hours] 753.6 754.3 762.1 773.8 882.4 1023.1 1096.3 1172.9Max units in General Queue 35 35 35 35 35 35 35 35Max units in Rework Queue 0 1 1 2 10 38 72 112

In the figure 5.12, it is confirmed what was explained above, the system is stable, even though thereis shown an existence of peaks mainly for lower levels of quality. Focusing on the overall time spendin the process, it confirms that this methodology presents the worst results until the point, where thesystem can no longer meet the requirements, and from that point forward the capacity of the process issimilar to the ones above.

Figure 5.12: Throughput time in a Dedicated system

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Taking a closer look, in the figure 5.13, and the table 5.8, at the mould A, is possible to see a levelof stability, being the variation of the throughput time of the parts 1 and 2, 216 hours and 255.8 hoursrespectively.

This means that even testing this type of methodology for a level of quality of 100%, the time spent toprocess the parts is similar to the ones that it is possible achieve for lower levels of quality in the previousmethodologies.

Table 5.8: Throughput time [Hours] in a Dedicated system to the mold A

Mold Part Real Production timeThroughput Time [Hours] for various Quality levels

100% 99% 95% 90% 80% 70% 60% 50%

A1 330 1125 1125 1125 1158 1341 1103 1329 1153

2 182 843,2 843,2 858,3 843,2 843,2 1088 828 1099

Figure 5.13: Throughput time in a Dedicated system

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5.4 Results

Comparing the four methodologies, table 5.9, it is possible to verify that the system that achieves the bestoverall result is the one with non-dedicated machines with the priority rule applied in the queue. If thequality levels are higher than 80%, the system with non-dedicated machine with FIFO methodology inthe queue can achieve the same result as the previous, or even the partially dedicated system machinethat presents similar results.

Considering that the time difference between the system with non-machine dedicated with the priorityrule applied in the queue, and the system with partially dedicated machine is small. The choice of whichsystem to use is based on how fluid the whole production system must be, in that case the partiallydedicated machine system guarantees this fluidity, allowing the new parts to be processed on time,maximizing the usage of the machines, and controlling the level of rework.

Table 5.9: Comparison Between Average Throughput Time of the SystemsQuality Level

100% 99% 95% 90% 80% 70% 60% 50%Non-Dedicated FIFO [Hours] 470.4 472.6 499.5 534.7 838.8 1239.5 1587.4 2072.9Non-Dedicated Priority [Hours] 470.4 472.6 499.5 534.7 788.1 952 1006.6 1162.8Partially Dedicated [Hours] 470.4 473.3 495.1 544.7 837.5 989.2 1095.2 1158.5Dedicated [Hours] 753.6 754.3 762.1 773.8 882.4 1023.1 1096.3 1172.9

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Chapter 6

Conclusion

In this thesis was proposed to assess the impact of the energy consumption in the process planning,through the use of meta-heuristics, has support to the management in the decision making.

The definition of the process to study was made taking into account the advantage of using previousstudies undertaken within the IST investigation group, allowing the gather of the data and validation ofthe system in an initial phase.

After modelling the system to be optimised in a mathematical form, containing continuous and binaryvariables, therefore categorised as a MILP model, the meta-heuristic had to be integrated, with the newdeveloped parameters introduced in the formulation of the problem.

The GA needs a fine-tunning to optimise their parameters in order to achieve the optimal result. Thisprocess is mandatory to the problem since it allows to apply the meta-heuristic in different scenarios,while varying the parameters of model maintaining the goal of achieving the optimal solution.

With the four proposed methods optimised, an analyse on the performance was made, consideringthe total values of the performance indicators, the total cost, the total energy consumption and themakespan. Considering all of the factors the method that had a better performance was the energy-cost-based method. If only the total cost and the total energy consumption are taken into account, thebest method is the energy-based method, this happens due to the fact that the energy values are higherthan the other two originating a greater disparity between the values.

A methodology to help as a support for the decision maker was proposed. For the project studiedthere were special cases in the achieved solutions, in some cases the solution presented machineswith no work attributed, this effect could mean that the machine is not needed and can be allocated toperform other jobs. In the specific cases that needs a deeper analysis of the system, the decision makerwould need to run the algorithm without the presence of those machines and analyse the new results.

This method can not be used as a planning tool, but as a learning one. Since it requires past dataand does not take into account the actual state of the production system. Having the most effect inunderstanding the past choices in the planning to adjust for future projects.

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In a second stage of the dissertation a test on various machine configuration and queue systemswas done, to find the best form to handle the existence of defect parts, These tests were made to thesection that was determined as the bottleneck of the system, the CNC section.

For this part of the dissertation, for all of the configurations proposed, system with no dedicatedmachine with a FIFO queue, a system with no dedicated machine with a Priority based queue, systemwith a Partial dedicated machine with a Priority based queue, and a system with a dedicated machinewith a Priority based queue, were run tests at various levels of quality, from 100% to 50%.

With all the tests evaluated, it was possible to verify an evolution in the behavior of the system, forhigh levels of quality the best system is the system with no dedicated machine with a Priority basedqueue, but with the decrease of quality the system a Partial dedicated machine with a Priority basedqueue achieves the best results. For when the system reaches levels of quality too low for it to handlethe rework required, the systems with priority queues tend to the same results.

6.1 Future Work

Towards a propagation of Resources Efficiency within manufacturing industries, the application of meta-heuristics is proposed to be applied in other manufacturing processes.Where more scenarios with dif-ferent constraints and cost functions can also be defined.

In this thesis, it was possible to verify the effect of the different parameters chosen to optimise, theenergy and the cost, in the planning process. It is proposed as the future work the introduction newparameters related to the environmental impact of the process.

It is also proposed an integration of the planning with the simulation process, this would guarantee abetter overview of the process. And allow the introduction of new factors to the optimisation, factors asthe existence of the rework, different systems for the buffers and the stochasticity of the human factor inthe process.

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