decision science dgsdgppt

8/11/2019 Decision Science dgsdgPpt

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Department of Business Administration

SPRING 2007-08

Management Science

byAsst. Prof. Sami Fethi

2007 Pearson Education


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2007/08, Sami Fethi, EMU, All Right Reserved.Operations Research

Ch 6: Transportation and Assignment

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Chapter Topics

The Transportation Model

Solution of a Transportation Problem

The Assignment Model

Solution of an Assignment Problem


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Overview

Part of a larger class of linear programming problems

known as network flow models.

Possess special mathematical features that enabled

development of very efficient, unique solution methods.

Methods are variations of traditional simplex procedure.Detailed description of methods is contained in CD-ROM

Module B, Transportation and Assignment Solution

Methods.

Text focuses on model formulation and solution with Exceland QM for windows.


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The Transportation Model

Characteristics

A product is transported from a number of sources to anumber of destinations at the minimum possible cost.

Each source is able to supply a fixed number of units of the

product, and each destination has a fixed demand for the

product.The linear programming model has constraints for supply at

each source and demand at each destination.

All constraints are equalities in a balanced transportation

model where supply equals demand.

Constraints contain inequalities in unbalanced models

where supply does not equal demand.


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The Transportation

Model Characteristics

To use the transportation model we need to know the following:

The origin points and the capacity or supply per period at each

The destination points and the demand per period at each

The cost of shipping one unit from each origin to each

destination The transportation problem can be regarded as a generalization of the

assignment problem. In an assignment problem we have a number of origins

each processing one item, and the same number of destinations each

requiring one item and are asked to empty the origins and fill the

destinations in such a way the Total Effectiveness is optimized. In atransportation problem we have m origins, with origin i processing ai

items and n destinations (possibly different number from m) with

destination jrequiring bjitems, and with

ai = bj.


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We are given the m.n costs associated with shipping one

item from any origin to any destination, and are asked toempty the origins and fill the destinations in such a way that

the total cost is minimized.

The assignment problem is seen to be a special case oftransportation problem in which m = n,all the ai and bj are

unity.

The iterative routine to be presented as the mode of the

solution of the transportation problem involves a succession

of feasible solutions of gradually diminishing cost;

eventually the minimum achievable cost is reached, and the

corresponding feasible solution is optimal.

The Transportation Model Characteristics

T t ti M d l E l 1




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Transportation Model Example1

(1)




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Transportation Model Example

(2 )


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(4)




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(5)




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(6)




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Transportation Model Example 2

(1)


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Ch 6 T i d A i




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(4)

Ch 6 T i d A i




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Special form of linear programming model similar to the

transportation model.

Supply at each source and demand at each destinationlimited to one unit.

In a balanced model supply equals demand.

In an unbalanced model supply does not equal demand.


Characteristics

Ch 6 T t ti d A i tTh A i t M d l




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Characteristics

Ch 6 Tr p rt ti d A i tA i t M d l E l 1




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Assignment Model Example 1

(1)

Ch 6: Transportation and AssignmentA i t M d l E l


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Assignment Model Example

(2)

Ch 6: Transportation and AssignmentA i t M d l E l 2


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(1)

Ch 6: Transportation and AssignmentAssignment Model Example 3


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(1)

Ch 6: Transportation and AssignmentAssignment Model E ample 4


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(1)



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(2)

Ch 6: Transportation and AssignmentAssignment Model Example


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(3)

Ch 6: Transportation and AssignmentAssignment Model Example


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(4)



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Assignment Model Example 5(1)



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(2)



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C 6: T a spo tat o a d ss g e t

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(1) (minimize)



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(2) (minimize)


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(4) (minimize)



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