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MS 301: MANAGEMENT CONCEPTS & TECHNIQUES
GROUP NO. 5
Pranjal Nautiyal, 2011104Sameer Rathi, 2011131
Suraj Soni, 2011155Surbhi Namdeo, 2011156Yash Pachaury, 2011179
Shubham Srivastava, 2011225Sunil, 2011261
September 25, 2013
Probabilistic Linear Programming Approach
for supply chain networking decisions
Ozgur Kabak and Fusun Ulengin
Supply Chain Management- procurement of resource till final delivery to the customer
Supply Chain Planning- coordination & integration of key businesses
Supply Chain Management & Planning
Supply chain: dynamic network of several business entities
Involve a high degree of imprecision
Crisp decisions: may lead to irrelevant & irreversible long term decisions
Uncertainty
Demand: main source
System uncertainty: unreliability of production processes
Supply uncertainty: variability of supplier’s performance
Interplay between system and supply uncertainty
Uncertainty types
Fuzzy decisions recommended for strategic SCP
Network based
Fuzzy set theory to model uncertainties
Possibilistic linear programming model developed
Proposed Model
Theoretic No example Hypothetical example
Applied Real world problems
Mixed Theoretical and applied
Literature Reviews
Type of the study
Deterministic single objective
Deterministic multiple objective
Stochastic
Hybrid(Deterministic & Stochastic)
Fuzzy set theory
Type of modelling
Two stage SC One vendor, one buyer One vendor, multiple buyers Multiple vendors, multiple buyers. Multiple vendors, one buyer.
Serial SC
Network SC
SC Environment
Theoretical Models
Deterministic Single objective Models
Consideration to only two stage SC. Network and serial SC’s are not frequenty encountered in the existent literatures.
Existent literature case studies
Possibilistic Linear Programming model used
Decision Variables: FuzzyCoefficients: Crisp
Demand & yield rates: fuzzy variable
Other inputs (unit cost rates, capacities): crisp
Which products should be produced internally?
Which resources should be allocated to the production of which products?
Which products should be outsourced, and to what extent?
Which market demands should be satisfied?
Questions being addressed by the proposed model
Production
Outsourcing
Sales quantity
Outsourcing amount for resources
Decision Variables in the proposed model
In proposed model, system uncertainty is represented by yield rates
- Production uncertainty- product yield rate
- Outsourcing uncertainty- outsourcing yield rate
System uncertainty
Total amount Sum of amount of of production/ > product used for other outsourcing product & amount sold
BOMpu is the bill of materials that represent the amount of product p required to produce product u
Production amount has resource constraint KKpr: amount of resource r used to produce product p
Outsourcing constrained to the capacity of suppliers KCr: capacity of resource r
DKCr: outsourcing capacity for resource
Main source of uncertainty in SCP
Represented by fuzzy numbers
: demand for product p
Objective: profit maximisationTherefore,
DEMAND
PLP model converted into LP
Triangular Fuzzy Numbers: represent fuzzy parameters in the model
Normalisation of fuzzy objective functions
LP model proposed to find lower and upper bounds of objective function
PLP converted to LP (2)- conversion of fuzzy constraints to crisp ones- aggregating normalized objective functions
Solution strategy
Represents all fuzzy parameters and variables
Are sufficient to represent uncertainty in demand and yield rates
Mathematical operations can be easily applied
Triangular Fuzzy Numbers
Proposed model is profit maximisation model
If demand will increase, profit will increase
If capacity will increase, profit will increase
To find the upper bound of the profit function: the yield rates and the demands are set at their highest level (i.e., the right supports of the corresponding TFNs).
To find the lower bound of the profit function: the yield rates and the demands are set at their lowest level (i.e., the left supports of the corresponding TFNs).
Conversion of PLP to LP-1
Normalisation of first objective function of PLP
Normalization of second objective function(for entropy minimisation)
This function is called certainty function
Normalization of objective functions
Automotive industries (MBT) Perform strategic resource planning. Main resource is labour . Production process
a) Tube processing b) Sheet processing c) Welding
Yield occurs in the production system , related to outsourced products.
Application
3 types of experiments are designeda) Change in yield rateb) Effect of demand changec) Variation of price and cost
Sensitivity analysis for consistency
Development of a strategic planning guide for MBT
Managers at MBT indicated insufficient capacity as major problem.
In the current MBT production-planning process there is no product that is produced and outsourced at the same time.
Price-1 the prices are considered to beequal to the production cost under optimistic yield rates
Price2-prices are considered to be equal to the production cost under pessimistic yield rates
Prices are considered to be 5% higher than Price 2
Prices
CONCLUSION PLP model is proposed to make strategic
resource planning decisions in the SC context.
It provides important guide in preparing strategic plans, taking into account the fuzziness of long term plans.
Propose model is solved using two LP models
Cont..
Model is used to analyse the resource utilization.
It improves previous model because of its fuzzy and multi-objective nature.
Future Research Model can be further improved by offering
more detailed methodologies for determining the fuzzy inputs.
Further research may create a generalized solution procedure for a generalized PLP model.
Additional improvement could be done by integration of this model into the enterprise resource planning software of the companies under study.