Lecture Introduction to Management Science with Spreadsheets: Chapter 6 - Stevenson, Ozgur

Chapter 6 - Supplement Transportation and assignment solution procedures, after completing this chapter, you should be able to: Use the transportation method to solve problems manually, deal with special cases in solving transportation problems, use the assignment (Hungarian) method to solve problems manually. deal with special cases in solving assignment problems.

Stevenson and Ozgur

First Edition

Introduction to Management Science

with Spreadsheets

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Chapter 6

Transportation,  Transshipment, and  Assignment Problems

Part 2 Deterministic Decision Models

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Learning Objectives

1 Describe the nature of transportation,

transshipment, and assignment problems

2 Formulate a transportation problem as a linear

programming model

3 Use the transportation method to solve problems with Excel

4 Solve maximization transportation problems,

unbalanced problems, and problems with prohibited routes

5 Solve aggregate planning problems using the

transportation model

After completing this chapter, you should be able to:

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Learning Objectives (cont’d)

6 Formulate a transshipment problem as a linear

programming model

7 Solve transshipment problems with Excel

8 Formulate an assignment problem as a linear

to other receiving locations.

–The solution of a transportation problem will indicate to

a manager the quantities and costs of various routes and the resulting minimum cost

–Used to compare location alternatives in deciding

where to locate factories and warehouses to achieve the minimum cost distribution configuration

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Formulating the Model

Formulating the Model

• A transportation problem

– Typically involves a set of sending locations, which are referred to as origins, and a set of receiving

locations, which are referred to as destinations

– To develop a model of a transportation problem, it is necessary to have the following information:

1 Supply quantity (capacity) of each origin.

2 Demand quantity of each destination.

3 Unit transportation cost for each origin­destination route.

–Involve the distribution of goods from intermediate

nodes in addition to multiple sources and multiple

destinations

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Assignment Problems

Assignment Problems

• The Assignment-type Problems

–Involve the matching or pairing of two sets of items such as jobs and machines, secretaries and reports, lawyers and cases, and so forth

–Have different cost or time requirements for different pairings

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Special Cases of Transportation Problems

Special Cases of Transportation Problems

–Certain origin-destination combinations may be

unacceptable due to weather factors, equipment

breakdowns, labor problems, or skill requirements that either prohibit, or make undesirable, certain

combinations (routes)

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Special Cases of Transportation Problems

(cont’d)

Special Cases of Transportation Problems

(cont’d)

• Unequal Supply and Demand

–Situations in which supply and demand are not equal such that it is necessary to modify the original problem

so that supply and demand are equalized

–Quantities in dummy routes in the optimal solution are not shipped and serve to indicate which supplier will hold the excess supply, and how much, or which

destination will not receive its total demand, and how much it will be short

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Problem

Problem

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Problem When the Shipping Route between Farm B and Project 1 Is Prohibited

Problem When the Shipping Route between Farm B and Project 1 Is Prohibited

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The manager of Harley’s Sand and Gravel Pit has decided to utilize two

intermediate nodes as transshipment points for temporary storage of topsoil The revised diagram of the transshipment problem is given in Figure 6-3.

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Transshipment Example

Transshipment Example

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Problem

Problem

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Using the Transportation Problem to Solve

Aggregate Planning Problems

Using the Transportation Problem to Solve

Aggregate Planning Problems

• Aggregate Planning

–Involves creating a long-term production plan for

achieving a demand-supply balance

–Aggregate planners usually avoid in terms of thinking

of individual products

–Planners are concerned about the quantity and timing

of production to meet the expected demand

–Aggregate planners attempt to minimize the

production cost over the planning horizon

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Example 6-3

Example 6-3

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Example 6-3

Example 6-3

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Using the Transportation Problem to Solve

Location Planning Problems

Using the Transportation Problem to Solve

Location Planning Problems

• Location Analysis

–Comparing transportation costs for alternative

locations for new facilities to minimize total cost

–Provides planners an opportunity to assess the impact

of each warehouse location on the total distribution

costs for the system

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jobs done It is further required that the jobs be performed

simultaneously, thus requiring one job being assigned to each

employee

In the past, to find the minimum-cost set of assignments, the

manager has resorted to listing all of the different possible

assignments (i.e., complete enumeration) for small problems such as this one But for larger problems, the manager simply guesses

because there are too many possibilities to try to list them For

example, with a 5X5 table, there are 5! = 120 different possibilities; but with, say, a 7X7 table, there are 7! = 5,040 possibilities.

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