1. Transportation, Transshipment, and Assignment Problems
Part 2 Deterministic Decision Models
Chapter 6
Transportation, Transshipment, and Assignment Problems

2. Learning Objectives
After completing this chapter, you should be able to:
Describe the nature of transportation, transshipment, and assignment problems.
Formulate a transportation problem as a linear programming model.
Use the transportation method to solve problems with Excel.
Solve maximization transportation problems, unbalanced problems, and problems with prohibited routes.
Solve aggregate planning problems using the transportation model.
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3. Learning Objectives (cont’d)
After completing this chapter, you should be able to:
Formulate a transshipment problem as a linear programming model.
Solve transshipment problems with Excel.
Formulate an assignment problem as a linear programming model.
Use the assignment method to solve problems with Excel.
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4. Transportation Problems
A distribution-type problem in which supplies of goods that are held at various locations are to be distributed 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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5. 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:
Supply quantity (capacity) of each origin.
Demand quantity of each destination.
Unit transportation cost for each origin-destination route.
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6. Transshipment Problems
A transportation problem in which some locations are used as intermediate shipping points, thereby serving both as origins and as destinations.
Involve the distribution of goods from intermediate nodes in addition to multiple sources and multiple destinations.
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7. 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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8. Figure 6–1 Schematic of a Transportation Problem
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9. Table 6–1 Transportation Table for Harley’s Sand and Gravel
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10. Special Cases of Transportation Problems
Maximization
Transportation-type problems that concern profits or revenues rather than costs with the objective to maximize profits rather than to minimize costs.
Unacceptable Routes
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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11. 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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12. Exhibit 6-1 Input and Output Worksheet for the Transportation (topsoil) Problem
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13. Exhibit 6-2 Parameter Specification Screen for the Topsoil Transportation Problem
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14. Exhibit 6–3 Solver Options Screen
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15. Exhibit 6–4 Solver Results
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16. Exhibit 6–5 Answer Report for the Topsoil Transportation Problem
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17. Exhibit 6–6 Sensitivity Report for the Topsoil Transportation Problem
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18. Exhibit 6–7 Input and Output Sheet for the Revised Transportation (topsoil) Problem When the Shipping Route between Farm B and Project 1 Is Prohibited
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19. Figure 6–2 A Network Diagram of a Transshipment Problem
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20. Table 6–2 Cost of Shipping One Unit from the Farms to Warehouses
Example 6-2
Transshipment Problem
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.
Table 6–2 Cost of Shipping One Unit from the Farms to Warehouses
Table 6–2 Cost of Shipping One Unit from the Warehouses to Projects
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21. Figure 6–3 A Network Diagram of Harley’s Sand and Gravel Pit Transshipment Example
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22. Exhibit 6–8 Excel Input and Output Screen for the Transshipment Problem
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23. Exhibit 6–9 Parameter Specifications Screen for the Transshipment Problem
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24. Using the Transportation Problem to Solve Aggregate Planning Problems
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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25. Table 6–4 Transportation Table for Aggregate Planning Purposes
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26. Example 6-3
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27. Table 6–5 Transportation Table for the Aggregate Planning Problem of Example 6-3
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28. 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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29. Table 6–6 System with Chicago Warehouse
Table 6–7 System with Detroit Warehouse
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30. Example 6-4
A manager has prepared a table that shows the cost of performing each of five jobs by each of five employees (see Table 6-8). According to this table, job I will cost $15 if done by Al. $20 if it is done by Bill, and so on. The manager has stated that his goal is to develop a set of job assignments that will minimize the total cost of getting all four 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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31. Table 6–8 Numerical Example for the Assignment Problem
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32. Exhibit 6–10 Excel Input and Output Worksheet for the Assignment Problem
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33. Exhibit 6–11 Parameter Specifications Screen for the Assignment Problem
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34. Exhibit 6–12 Excel Worksheet for the Transportation Problem in Solved Problem 1
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35. Exhibit 6–13 Parameter Specification Screen for Solved Problem 1
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36. Exhibit 6–14 Excel Worksheet for the Assignment Problem in Solved Problem 2
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37. Exhibit 6–15 Parameter Specification Screen for Solved Problem 2
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38. Exhibit 6–16 Excel Worksheet for the Transportation Problem in Solved Problem 3
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39. Exhibit 6–17 Parameter Specification Screen for Solved Problem 3
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