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348 CHAPTER 8 THE TRANSPORTATION AND ASSIGNMENT PROBLEMS

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Supplement to this Chapter: A Case Study with Many Transportation Problems See Appendix 1 for documentation of the software.

■ PROBLEMS

The symbols to the left of some of the problems (or their parts) have the following meaning: D: The demonstration example just listed may be helpful. 1: We suggest that you use the relevant interactive procedure in IOR Tutorial (the printout records your work). C: Use the computer with any of the software options avail-able to you (or as instructed by your instructor) to solve the problem. An asterisk on the problem number indicates that at least a partial answer is given in the back of the book. 8.1-1. Read the referenced article that fully describes the OR study summarized in the application vignette in Sec. 8.1. Briefly describe how the model for the transportation problem was applied in this study. Then list the various financial and nonfinancial benefits that resulted from this study. 8.1-2. The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec-tively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below:

Distance Distribution Center 1 2 3 4 Plant 1 2 3 800 miles 1,100 miles 600 miles 1,300 miles 1,400 miles 1,200 miles 400 miles 600 miles 800 miles 700 miles 1,000 miles 900 miles

The freight cost for each shipment is $100 plus 50 cents per mile, How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost? (a) Formulate this problem Lb a transportation problem by con structing the appropriate parameter table. (b) Draw the network representation of this problem. c (c) Obtain an optimal solution. 8.1-3.* Tom would like 3 pints of home brew today and an add tional 4 pints of home brew tomorrow. Dick is willing to sell maximum of 5 pints total at a price of $3.00 per pint today an $2.70 per pint tomorrow. Harry is willing to sell a maximum 4 pints total at a price of $2.90 per pint today and $2.80 per pint tomorrow. Tom wishes to know what his purchases should be to mini-mize his cost while satisfying his thirst requirements. (a) Formulate a linear pmgranuning model for this problem, and construct the initial simplex tableau (see Chaps. 3 and 4). (b) Formulate this problem as a transportation problem by con-structing the appropriate parameter table. (c) Obtain an optimal solution. N. 8.1-4. The Versatech Corporation has decided to produce three new products. Five branch plants now have excess product capacity. The unit manufacturing cost of the first product would be $41, $39, $42, $38, and $39 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $55, $51, $56, $52, and $53 in Plants 1, 2, 3, 4, and 5, respectively. The unit man-ufacturing cost of the third product would be $48, $45, and $50 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have the capability for producing this product. Sales forecasts indicate that 700, 1,000, and 900 units of products 1, 2, and 3, respec. tively, should be produced per day. Plants I, 2, 3, 4, and 5 have the capacity to produce 400, 600, 400, 600, and 1,000 units daily,

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