chap6tta

byAsst. Prof. Sami FethiDepartment of Business AdministrationSPRING 2007-08Management Science 2007 Pearson Education

Chapter 6 - Transportation, Transshipment, and Assignment Problems

2007/08, Sami Fethi, EMU, All Right Reserved. Operations Research Ch 6: Transportation and Assignment

Chapter TopicsThe Transportation Model

Solution of a Transportation Problem

The Assignment Model

Solution of an Assignment Problem



OverviewPart 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 Excel and QM for windows.



The Transportation ModelCharacteristicsA product is transported from a number of sources to a number 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.



The Transportation ModelCharacteristics

Transportation modelling is an iterative procedure for solving problems that involve minimizing the cost of shipping products from a series of sources to a series of destinations.

Origin Points (or sources) can be factories, warehouses, car rental agencies like AVIS or any other points from which goods are shipped.

Destinations are any points that receive goods.

Transportation models are useful when considering alternative facility locations. The choice of a new location depends on which will yield the minimum cost for the entire system



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 eachThe destination points and the demand per period at eachThe 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 a transportation problem we have m origins, with origin i processing ai items and n destinations (possibly different number from m) with destination j requiring bj items, and with ai = bj.



We are given the m.n costs associated with shipping one item from any origin to any destination, and are asked to empty 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 of transportation 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



Transportation Model Example1 (1)



Transportation Model Example (2 )



Transportation Model Example (3)






Transportation Model Example(5)






Transportation Model Example 2(1)












Special form of linear programming model similar to the transportation model.

Supply at each source and demand at each destination limited to one unit.

In a balanced model supply equals demand.

In an unbalanced model supply does not equal demand.The Assignment ModelCharacteristics



The Assignment ModelCharacteristics



Assignment Model Example 1(1)



Assignment Model Example(2)















Assignment Model Example (3)



Assignment Model Example (4)



Assignment Model Example 5 (1)



Assignment Model Example 5 (2)



Assignment Model Example 6 (1) (minimize)












End of chapter


chap6tta

Documents

balanced transportation

assignment problems

assignment solution

assignment problemchapter

operations research

number of destinations

number of sources

origin points