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

Organization

Introduction

Previous studies

Proposed Model

Solution

Application

Conclusion

INTRODUCTION

Supply Chain Management- procurement of resource till final delivery to the customer

Supply Chain Planning- coordination & integration of key businesses

Supply Chain Management & Planning

Partitioning of decision-making

Long term planning

Strategic SCP

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

Current state of the art

Previous Studies Classification scheme-

Type of study

Type of modelling

Supply chain environment

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

Proposed Model

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

Uses network concept

Allocates optimum resources

Derive maximum profits

Proposed PLP Model

Production

Outsourcing

Sales quantity

Outsourcing amount for resources

Decision Variables in the proposed model

Outsourcing and production decisions for some products/resources limited

DCp : capacity limit for product p

Capacity limit constraint

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

Total sales revenue of firm

Fp: sales price of product p

Product Outsourcing cost

Resource consumption cost

Resource outsourcing additional cost

Total Cost

Objective function

Additional objective function defined to minimise fuzziness of the profit

Concept of entropy used

Solution of multi-objective PLP

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

Left support (L), most possible value (M), right support (R)

A and B: 2 fuzzy numbers

TFN

LP 1

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

Conversion of PLP model to LP 2

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

Change in yield rate

Effect of demand change

Variation of price and cost

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.

Scenarios:

1.)Demand increase2.)Capacity decrease

Results of the scenarios

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.

Questions??

Comments

THANK YOU