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7/29/2019 Pertemuan 1 (OR, an interesting field).pptx
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Operations Research and
Optimization: an interesting fieldRuhul A Sarker
School of Engineering and ITUNSW Canberra, Australia
Presented with a little modification by:
Samsul Amar
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Background
PhD (IE/OR) 1991, Daltech, DalhousieUniveristy, Canada
M.Engg (IPE) 1984 & B.Sc. Eng. (ME)1982
Deputy Head of School (Research),School of Engineering & IT, University ofNew South Wales, Australia
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OR in the News (Sept. 2009):J apanese PM has PhD in OR
On August 31, when the Democratic Party ofJapan defeated the long-ruling LiberalDemocrats, the party leader, Yukio Hatoyama,became the presumptive prime minister.
Dr. Yukio Hatoyama earned his PhD inOperations Research at Stanford University inthe 1970s. His PhD advisor was the late GeraldLieberman.
His fellow operations researchers at INFORMS(INstitute ForOperations Research andManagement Science) wish him luck andsuccess as he applies his analytical expertise tosolving his country's economic challenges.
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John Malone, chairman of Liberty Media, cablemagnate, and number 488 on Forbesmagazinesbillionaires listing (with $2 billion). Got his Ph.D. from
Johns Hopkins. His paper with Manny Bellmore on thetraveling salesman problem continues to bereferenced a lot.
Bill Gates of Microsoft, coauthored a paper with
Christos Papadimitriou on a sorting algorithm, thoughhe did not receive a Ph.D. (not counting his fourhonorary ones).
Virgil Carter, quarterback for the NFLs CincinattiBengals, wrote papers on football and OR forOperations Research and Management Science in the1970s (but did not get a Ph.D.: he is an MBA from
Northwestern).
http://en.wikipedia.org/wiki/John_Malonehttp://www.forbes.com/lists/2007/10/07billionaires_John-Malone_ZP8G.htmlhttp://scholar.google.com/scholar?q=bellmore+malone&hl=en&lr=&btnG=Searchhttp://en.wikipedia.org/wiki/Bill_Gateshttp://www.cs.berkeley.edu/~christos/papers/Bounds%20For%20Sorting%20By%20Prefix%20Reversal.pdfhttp://www.cs.berkeley.edu/~christos/papers/Bounds%20For%20Sorting%20By%20Prefix%20Reversal.pdfhttp://www.bengalszone.com/article.php?sid=541http://links.jstor.org/sici?sici=0030-364X(197103/04)19:2%3C541:OROF%3E2.0.CO;2-Ehttp://links.jstor.org/sici?sici=0025-1909(197812)24:16%3C1758:OSOFD%3E2.0.CO;2-Mhttp://links.jstor.org/sici?sici=0025-1909(197812)24:16%3C1758:OSOFD%3E2.0.CO;2-Mhttp://links.jstor.org/sici?sici=0030-364X(197103/04)19:2%3C541:OROF%3E2.0.CO;2-Ehttp://www.bengalszone.com/article.php?sid=541http://www.cs.berkeley.edu/~christos/papers/Bounds%20For%20Sorting%20By%20Prefix%20Reversal.pdfhttp://www.cs.berkeley.edu/~christos/papers/Bounds%20For%20Sorting%20By%20Prefix%20Reversal.pdfhttp://en.wikipedia.org/wiki/Bill_Gateshttp://scholar.google.com/scholar?q=bellmore+malone&hl=en&lr=&btnG=Searchhttp://www.forbes.com/lists/2007/10/07billionaires_John-Malone_ZP8G.htmlhttp://en.wikipedia.org/wiki/John_Malone7/29/2019 Pertemuan 1 (OR, an interesting field).pptx
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Hedy Lamarr, actress and famous beauty, invented amethod for hopping frequencies in wirelesscommunication.
Dan Gimaldi, actor who played the twin Parisi brotherson the Sopranos, has a masters in OR and a Ph.D. indata processing. He has a position in the Departmentof Mathematics and Computer Science at
Kingsborough Community College. Anyone know whathe works on?
Gomory himself is a good example: terrific OR
credentials but even better known as President of theSloan Foundation.
http://en.wikipedia.org/wiki/Hedy_Lamarrhttp://en.wikipedia.org/wiki/Dan_Grimaldihttp://www.kingsborough.edu/academicDepartments/math/index.htmlhttp://www.kingsborough.edu/academicDepartments/math/index.htmlhttp://en.wikipedia.org/wiki/Ralph_Gomoryhttp://scholar.google.com/scholar?q=gomory&hl=en&lr=&btnG=Searchhttp://scholar.google.com/scholar?q=gomory&hl=en&lr=&btnG=Searchhttp://scholar.google.com/scholar?q=gomory&hl=en&lr=&btnG=Searchhttp://scholar.google.com/scholar?q=gomory&hl=en&lr=&btnG=Searchhttp://en.wikipedia.org/wiki/Ralph_Gomoryhttp://www.kingsborough.edu/academicDepartments/math/index.htmlhttp://www.kingsborough.edu/academicDepartments/math/index.htmlhttp://en.wikipedia.org/wiki/Dan_Grimaldihttp://en.wikipedia.org/wiki/Dan_Grimaldihttp://en.wikipedia.org/wiki/Hedy_Lamarrhttp://en.wikipedia.org/wiki/Hedy_Lamarrhttp://en.wikipedia.org/wiki/Hedy_Lamarr7/29/2019 Pertemuan 1 (OR, an interesting field).pptx
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Carlos Slim (The richest man on the world):
Do you think your engineering training has helped
you to evaluate business opportunities and risk?
Carlos Slim: Well, I think talking about curiosity...When you love life, you want to know more about life. I thinkengineering is important to give you the tools. And in business, toanalyze, it's important to simplify, to have the essential points, theessential issues, the fundamentals, the basics, and take outeverything that is secondary, to have less variables to study or tolook at. Because when you have a lot of variables, and you don'tmake a distinction between the ones that are essential and thesecondary ones and parameters, you have confusion. I will say
that engineering is important, but also when I was finishing my(academic) career, I make my thesis about linear programming.That's operational research. That's to optimize functions, optimizeresults of things, and the study ofmodels that take you to the
optimization of the solutions.
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Have you carried out that theory of optimizing
solutions throughout your business ventures?
Carlos Slim: I think so. When I was studying that 45years ago, the parametric linear programming was veryinteresting, because the problems in the models werethe parameters. That's very difficult to define precisely.
The parametrics give you the difference between whichsolution is optimal. One teacher said that an engineer issomeone who makes with one dollar what others thatare not engineers make with two dollars.
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Outline
An opening storey
Introduction to OR
Our research in OR
Traditional OR
Evolutionary Optimisation
Discussions
8 9 10 11 12 13 14 15 16 17 18
11
14
17
175000
185000
195000
205000
215000
225000
Totalcos
Value ofn
Valueofm
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An Opening StoryTortoise vs Hare: Who is faster?
Once upon a time a tortoise and a hare had anargument about who was faster.
Settle the argument with a race.
Agreed on a route and started off the race.
The hare was ahead.
The hare sat under the tree and soon fell asleep.
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Tortoise vs Hare: Who is faster?
The tortoise plodding on overtook him and soonfinished the race, emerging as the undisputedchamp.
The hare woke up and realized that hed lost therace.
The moral - Slow and steady wins the race.
A story that weve all grown up with.
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Tortoise vs Hare: Who is faster?
Who is really faster Hare or Tortoise?
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Tortoise vs Hare:The Storey Goes on (1)
The hare was disappointed at losing the race.
He lost the race only because he had been
overconfident, careless and lax. If he had not taken things for granted, theres no
way the tortoise could have beaten him.
So he challenged the tortoise to another race. The tortoise agreed.
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Tortoise vs Hare:The Storey Goes on (1)
This time, the hare went all out and ran withoutstopping from start to finish.
He won by several miles. The moral - Fast and consistent will alwaysbeat the slow and steady.
Its good to be slow and steady; but its better
to be fast and reliable.
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Tortoise vs Hare:The Storey Goes on (2)
There is no way the tortoise can beat the hare ina race the way it was currently formatted.
The tortoise challenged the hare to another
race, but on a slightly different route. The hare agreed.
They started off.
In keeping with his self-made commitment to beconsistently fast, the hare took off and ran at topspeed until he came to a broad river.
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Tortoise vs Hare:The Storey Goes on (2)
The finishing line was a couple of kilometres onthe other side of the river.
The hare sat there wondering what to do.
In the meantime the tortoise trundled along, gotinto the river, swam to the opposite bank,continued walking and finished the race.
The moral - First identify your corecompetency and then change the playingfield to suit your core competency.
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Tortoise vs Hare:The Storey Goes on (3)
The hare and the tortoise, by this time, hadbecome pretty good friends.
Both realised that the last race could have been
run much better. So they decided to do the last race again, but to
run as a team this time.
They started off, and this time the hare carried
the tortoise till the riverbank. There, the tortoise took over and swam across
with the hare on his back.
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Tortoise vs Hare:The Storey Goes on (3)
On the opposite bank, the hare again carried thetortoise and they reached the finishing linetogether.
They both felt a greater sense of satisfactionthan theyd felt earlier.
The moral - Its good to be individually brilliant andto have strong core competencies; but unless youre
able to work in a team and harness each others corecompetencies, youll always perform below parbecause there will always be situations at whichyoull do poorly and someone else does well.
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Tortoise vs Hare:Who is the Winner?
Our core question:
Faster or Winner?
Who is the winner & why? How can we make sure that the faster will be the
winner?
Performance measures
Environments /constraints
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Operations Research
The science of better and responsiblemanagement
Interdisciplinary: Mathematics, Statistics,Computing, Business/Management, EngineeringManagement
Useful for all levels of decision making Operations Research (OR)
Hard OR: Quantitative Soft OR: Qualitative
Operations Research (OR) Optimisation Simulation
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Operations Research:Problem Solving Cycle
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Decision Problem & Mathematical Model:A Simplified Example
Blue Ridge Hot Tubs produces two types of hottubs: Aqua-Spas & Hydro-Luxes.
There are 200 pumps, 1566 hours of labor,and 2880 feet of tubing available.
Aqua-Spa Hydro-Lux
Pumps 1 1Labor 9 hours 6 hours
Tubing 12 feet 16 feetUnit Profit $350 $300
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Model for Blue Ridge Hot Tubs
Decision Variables:X1=number of Aqua-Spas to produceX2=number of Hydro-Luxes to produce
MAX: 350X1 + 300X2S.T.: 1X1 + 1X2
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Optimisation Problem Classification
Differentiable
orNon-differentiable
Convex
or
Non-convex
Linear
or
Nonlinear
Level 1: General
problem
Level 3: Problem
classification
Level 4: Variable
classification
Level 5: Function
classification
Problem
Unconstrained Constrained
Continuous Integer/Discrete
Single Objective Multiple Objectives
Mixed
Level 2:
Objective
classification
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Our Research
Applied Operations research
Defining decision situations as OR problems
Modelling
Solution approaches
Evolutionary Optimisation
Development of algorithms
Solving practical problems
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Applications(1)
Agriculture Crop planning
Mining Coal mining: Planning & Scheduling
Oil mining: Production planning Manufacturing
Production planning Job-shop scheduling
Machine layout & job scheduling Climate change
Planned human relocation
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Applications(2) Logistics and Supply Chain
Inventory management Transportation Defence logistics Joint maintenance-inventory systems Joint production-inventory systems
Supply chain modelling & analysis Supply chain under disruption
Rostering Doctors in Hospital Maintenance crews for Airlines
Other Forex exchange Rate Prediction Share market forecast Sales/demand forecast
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Crop Planning(1)
National or regional problem
n crops (usually 100+)
Limited land
Different soil characteristics
Different type: single-, double-, or triple-crop
Combination of crops
Certain regions /sub-regions suitable for certain crops
Different input requirements
Different yield rates
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Crop Planning(2)
Local demand must be fulfilled
Import/export restrictions
Budget limitation
Manpower & other resource limitation Decision problem:
Determine the areas of land to be used for differentcrops
Maximise return or profit not violating the constraints Can be formulated as a single or multiobjective
LP or NLP model.
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Crop Planning(3)
New way of solving crop planning problem
Better solution than existing practices
Key Publications:
Sarker, R. and Ray, T. (2009) An Improved Evolutionary Algorithmfor Solving Multi-objective Crop Planning Models, Computers andElectronics in Agriculture, 68, pp191-199. (ISI Impact factor 1.273).
Sarker, R. and Quaddus, M. (2002) Modelling a Nationwide CropPlanning Problem Using a Multiple Criteria Decision Making Tool,
Int. J. of Computers and Industrial Engineering, 42/2-4, pp541-553.
(ISI Impact Factor 1.057) Sarker, R., Talukder, S. and Haque, A. (1997) Determination of
Optimum Crop-Mix for Crop Cultivation in Bangladesh,AppliedMathematical Modelling, 21, pp621-632. (ISI Impact Factor 0.931)
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Fleet Mix Problem(DSTO/Army)
MISG 2002
Presentation in Canberra
Future fleet-mix: spend billions Seed funding from 2002-2003
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Optimisation Problem
Minimising the number of vehicles
Subject to
Performing all (or given % of) the tasks on time
Mobility criteria Material type & mix
Vehicle type & capacity
Weight & volume
Driving hours & rest/break
Passengers & others
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Difficulties
Timeliness is a crucial factor
Unmanageable problem size in terms of the
number of variables and constraints
Impossible to solve using the existingoptimisation techniques and current computing
resources
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Heuristic Approach
To find workable solutions within areasonable computational effort
Our approach: Minimise the number of vehicles required by
maximising the capacity utilisation ofindividual vehicle and overall vehicle
effectiveness while satisfying all theconstraints
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Planned HumanRelocation(1)
Due to climate change or surface mining A number of regions to be evacuated
Fully .. not suitable for living
Partially .. new opportunity Relocated to a number of other regions Basis of relocation
Job/business opportunity in new locations
Individual & family preference Logistics for relocations Resources available for settlement
Budget limitation
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Planned HumanRelocation(2)
Approach Integrated AHP & GP
Key Publications Zahir, Z. and Sarker, R. (2008) Optimizing Multi-Objective
Decisions for Planned Relocation of People in Surface Miningfor a Densely Populated Environment, 2008 Conference of the
Administrative Sciences Association of Canada(ASAC2008),Halifax, Canada, Received Best Paper Award.
Zahir, S. and Sarker, R. (2009) An Interactive DSS forImplementing Sustainable Relocation Strategies for
Adaptation to Climate Change: A Multi-Objective OptimizationApproach, International Journal of Mathematics in OperationsResearch, 1(3), pp326-350.
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Planned HumanRelocation(3)
Media Coverage Wall Street Journal
Science Daily
United Press International (UPI)
COP15: UN Climate Change Conference, 2009 Times of the Internet
TerraDaily
MarketWatch
EcoEarth
Eurocean Softpedia
Oneindia
ScienceBlog
Planned Human
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Planned HumanRelocation(4)
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Coal Mining (1)
A number of operating mines with differentproduction capacity
Quality of coals varies - mine to mine & period toperiod
Customer demands and contract specifications Price of coal is a function of quality parameters Raw coal quality can be upgraded through
mechanical process and blending with better
quality coal Upgradation capacity Environmental factor for supplied coals
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Coal Mining (2)
Decision Problem Determine the yearly production plan by
maximising the total revenue
Subject to Production capacity
Quality specification
Demand fulfilment
Environmental condition Employment level
Resource limitation
Wash-plant
Mi 1
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Coal Mining (3)
Developed algorithms /heuristics Better than current practices Key Publications:
Sarker, R. (2009) Alternative Mathematical Programming Models: ACase for Coal Blending Decision Process, Optimization: Structure andApplications, Springer Series in Optimization and its Application,
Volume 32, pp383-399. Sarker, R. and Gunn, E. (1997) A Simple SLP Algorithm for Solving a
Class of Nonlinear Programs, European Journal of OperationalResearch, 101/1, pp140-154. (ISI Impact Factor 1.627)
Sarker, R. and Gunn, E. (1995) Determination of a Coal PreparationStrategy Using a Computer Based Enumeration Method, IndianJournal of Engineering and Material Sciences, 2, pp150-156. (ISIImpact Factor 0.197)
Sarker, R. and Gunn, E. (1994) Coal Bank Scheduling Using aMathematical Programming Model,Applied Mathematical Modelling,18, pp672-678. (ISI Impact Factor 0.931)
BlendingProcess
Mine-1
Mine-2
Period-1
BlendingProcess
Mine-1
Mine-2
Period-2
BlendingProcess
Wash-plant
Mine-1
Mine-2
Period-3
Wash-plant
Mine-n
Washedcoal inv.
Washedcoal inv.
Washedcoal inv.
Pileor
Customer
Mine-n
Mine-n
Pileor
Customer
PileorCustomer
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Supply Chain &Inventory Management (1)
Inventory is usually optimised for individual sub-systems
The solution is sub-optimal
Our research: Two stage production-inventory system underdifferent conditions
Joint maintenance-spare inventory plan Multi-stage inventory system under transportation
restriction Material flow analysis in supply chain Supply chain design & redesign
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Supply Chain &Inventory Management (2)
Better solutions than single system approach Better solutions than existing practices Key publications:
Zahir, S. and Sarker, R. (2010) Optimizing Multi-Objective LocationDecisions in a Supply Chain using an AHP-Enhanced Goal
Programming Model, International Journal of Logistics Systems andManagement, Accepted, publication scheduled for 2010. Sarker, R. and Zahir, S. (2008) Supply Chain Expansion using AHP,
ILP and Scenario-Planning,The Journal of American Academy ofBusiness, 12 (3), pp21-29.
Khan, L. and Sarker, R. (2002) An Optimal Batch Size for a JITManufacturing System, International Journal of Computers and
Industrial Engineering, 42/2-4, pp127-136. (ISI Impact Factor 1.057) Sarker, R. and Khan, L. (2001) Optimum Batch Size under Periodic
Delivery Policy, International Journal of Systems Sciences, 32(9),pp1089 1099. (ISI Impact Factor 0.634)
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Supply Chain &Inventory Management (3)
Sarker, R., Runarsson, T. and Newton (2001) A Constrained Multiple RawMaterials Manufacturing Batch Sizing Problem,International Transaction inOperational Research, 8(2), pp121-138.
Sarker, R. and Haque, A. (2000) Optimization of Maintenance and SpareProvisioning Policy Using Simulation,Applied Mathematical Modelling, 24(10),pp751-760. (ISI Impact Factor 0.931)
Sarker, R., (2000) A Note on Production Capacity Planning and Control in Multi-
Stage Manufacturing, Journal of the Operational Research Society, 51(5), pp639-640. (ISI Impact Factor 0.839) Sarker, R. and Khan, L. (1999) An Optimal Batch Size for a Production System
Operating under a Periodic Delivery Policy, Computers and Industrial Engineering:An International Journal, 37(4), pp711-730. (ISI Impact Factor 1.057)
Sarker, R., Karim, M. and Haque, A. (1995) An Optimum Batch Size for aProduction System Operating under a Continuous Supply/Demand, InternationalJournal of Industrial Engineering- Theory, Applications and Practice, 2(3), pp189-
198. Zahir, S. and Sarker, R. (1991) Joint Economic Ordering Policies of Multiple
Wholesalers and Single Manufacturer with Price-Dependent Demand Functions,Journal of the Operational Research Society, 42(2), pp157-164. (ISI Impact Factor0.839)
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Gas Lift Optimisation(1)
Underground oil reservoir
Multiple wells for oil extraction through gas injection
The total daily use of gas is limited.
Oil extracted from each well is a nonlinear function of thegas injected into a well and varies between wells.
The problem is to identify the optimal amount of gas thatneeds to be injected into each well to maximize the
amount of oil extracted subject to the constraints.
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Gas Lift Optimisation(2)
Formulated as an integer programming problem
Solved using an evolutionary algorithm
Our results show significant improvement overthe existing practices.
The multiobjective formulation is useful as iteliminates the need to solve such problems on a
daily basis.
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Gas Lift Optimisation(3)
Shell International tested our algorithm
World OilMagazine published a feature article on thiswork in April 2008
Key Publications: Ray, T. and Sarker, R. (2007) Genetic Algorithm for Solving a
Gas Lift Optimization Problem, Journal of Petroleum Scienceand Engineering, Elsevier, 59, pp84-96. (ISI Impact Factor0.824, A* Journal in Engineering)
Ray, T. and Sarker, R. (2007) Optimal Oil Production Planningusing an Evolutionary Approach, In Evolutionary Scheduling,Studies in Computational Intelligence, Springer-Verlag, pp273-292.
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J ob-Shop Scheduling
Number of jobs on a fixed number ofmachines
Makespan minimisation
Developed three heuristics to enhance theperformance of GAs
Process interruption
Machine breakdown and unavailability
Re-optimisation
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An example of a 6 jobs 6 machines problem
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Key Publications
S. M. K. Hasan, R. Sarker, D. Essam (2010) Genetic Algorithm for Job-Shop Scheduling with Machine Unavailability and Breakdown,International Journal of Production Research, 49(16), pp.4999-5015.
Hasan, S. M. K., Sarker, R., Essam, D. and Cornforth, D. (2009) MemeticAlgorithms for Solving Job-Shop Scheduling Problems, MemeticComputing, Springer Journal, 1(1), pp69-83.
S M K Hasan, R. Sarker, D. Essam, I. Kaceem (2011) A DSS for JobScheduling under Process Interruptions, Journal of Flexible Services andManufacturing, Springer, 23(2), pp.137-155.
Hasan, S. M. K., Sarker, R., Essam, D. and Cornforth, D. (2009) AGenetic Algorithm with Priority Rules for Solving Job-Shop SchedulingProblems, Natural Intelligence for Scheduling, Planning and PackingProblems, R. Chiong (ed.), Springer-Verlag series in Studies inComputational Intelligence, Accepted
S. M. K. Hasan, R. Sarker and D. Cornforth (2008) GA with Priority Rulesfor Solving Job-Shop Scheduling Problems, IEEE Congress onEvolutionary Computation (IEEE-CEC) within World Congress onComputational Intelligence (WCCI), 1-6 June, 2008, Hong Kong, pp1913-1920.
M hi L d
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Machine Layout andJ ob Scheduling
Combined machine layout and job assignment problem
Arranging Nmachines to Mlocations (/cells), M>= N
Assigning O operations of each product to Nmachines
Any layout type (linear, rectangular, circular, ) A machine can perform one to many operations
The number of machines of any particular type is notrestricted
A job may visit a subset of the machines and may visitone or more machines more than once
Any number of products or product type
M hi L d6000
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Machine Layout andJ ob Scheduling
Determine the machine layout and
The job scheduling
Minimise the system cost production cost
material handling cost
Bi-objective problem Minimize system cost
Minimize the machine load imbalance
1000
2000
3000
4000
5000
50833 53167 59833 62000
Cost
MachineLoadImbalance
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Key Publications
Ray, T. and Sarker, R. (2008) EA for solving combined machinelayout and job assignment problems, Journal of Industrial andManagement Optimization, 4(3), pp631-646 (ISI Impact Factor1.181)
Ray, T. and Sarker, R. (2007) Optimal Oil Production Planningusing an Evolutionary Approach, In P. Cowling, KC Tan and K.Dahal (eds.), Evolutionary Scheduling, Studies in ComputationalIntelligence, Springer-Verlag, pp273-292.
Sarker, R., T. Ray and J. B. da Fonseca (2007) An EvolutionaryAlgorithm for Machine Layout and Job Assignment Problems,IEEE Congress on Evolutionary Computation(IEEE-CEC),
September 25-28, 2007, Singapore, pp3991-3997.
I t M d l
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Inventory Modelswith GA
Inventory models
Multiple products
Capacity constraints Transport limitation
Nonlinear constrained model
Multimodal model
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Key Publications
Sarker, R. and Newton, C. (2002) Genetic Algorithm for SolvingEconomic Lot Size Scheduling Problem, International Journal ofComputers and Industrial Engineering, 42(2-4), pp189-198. (ISIImpact Factor 1.057)
Sarker, R., Maulloo, A., and Rahman, M. (2005) Evolutionary
Algorithm for Solving a Practical Multi-modal Problem: A CaseStudy, Complexity International, Volume 11, pp162-170.
Sarker, R., Runarsson, T. and Newton, C. (2001) GeneticAlgorithms for Solving A Class of Constrained Nonlinear IntegerPrograms,International Transaction in Operational Research, 8(1),pp61-74.
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