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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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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Ch 6: Transportation and Assignment
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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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Ch 6: Transportation and Assignment
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Transportation Model Example
(4)
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Transportation Model Example
(5)
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Transportation Model Example
(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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Transportation Model Example
(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.
The Assignment Model
Characteristics
Ch 6 T t ti d A i tTh A i t M d l
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The Assignment Model
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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Ch 6: Transportation and Assignment
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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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Ch 6: Transportation and Assignment
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Assignment Model Example 2
(1)
Ch 6: Transportation and AssignmentAssignment Model Example 3
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Assignment Model Example 3
(1)
Ch 6: Transportation and AssignmentAssignment Model E ample 4
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Assignment Model Example 4
(1)
Ch 6: Transportation and AssignmentAssignment Model Example 4
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Assignment Model Example 4
(2)
Ch 6: Transportation and AssignmentAssignment Model Example
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Assignment Model Example
(3)
Ch 6: Transportation and AssignmentAssignment Model Example
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Assignment Model Example
(4)
Ch 6: Transportation and Assignment
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Assignment Model Example 5(1)
Ch 6: Transportation and AssignmentAssignment Model Example 5
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Assignment Model Example 5
(2)
Ch 6: Transportation and Assignment
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C 6: T a spo tat o a d ss g e t
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Assignment Model Example 6
(1) (minimize)
Ch 6: Transportation and AssignmentAssignment Model Example 6
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Assignment Model Example 6
(2) (minimize)
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Assignment Model Example 6
(4) (minimize)
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