Chapter 14 Problems

Problem 15

In the RedBrand example, suppose the plants cannot ship to each other and the customers cannot ship to each other. Modify the model appropriately, and rerun Solver. How much does the total cost increase because of these disallowed routes?

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Problem 16

Modify the RedBrand example so that all flows must be from plants to warehouses and from warehouses to customers. Disallow all other arcs. How much does this restriction cost RedBrand, relative to the original optimal shipping cost?

 

Problem 17

In the RedBrand example, the costs for shipping from plants or warehouses to customer 2 were purposely made high so that it would be optimal to ship to customer 1 and then let customer 1 ship to customer 2. Use SolverTable appropriately to do the following. Decrease the unit shipping costs from plants and warehouses to customer 1, all by the same amount, until it is no longer optimal for customer 1 to ship to customer 2. Describe what happens to the optimal shipping plan at this point.

 

Problem 20

Suppose in the original Grand Prix example that the routes from plant 2 to region 1 and from plant 3 to region 3 are not allowed. (Perhaps there are no rail-road lines for these routes.) How would you modify the original model (Figure 14.14) to rule out these routes? How would you modify the alternative model (Figure 14.19) to do so? Discuss the pros and cons of these two approaches.

 

Problem 88

An oil company produces oil from two wells. Well 1can produce up to 150,000 barrels per day, and well 2 can produce up to 200,000 barrels per day. It is possible to ship oil directly from the wells to the company’s customers in Los Angeles and New York. Alternatively, the company could transport oil to the ports of Mobile and Galveston and then ship it by tanker to New York or Los Angeles, respectively. Los Angeles requires 160,000 barrels per day, and New York requires 140,000 barrels per day. The costs of shipping 1000 barrels between various locations are shown in the file P14_88.xlsx, where a blank indicates shipments that are not allowed. Determine how to minimize the transport costs in meeting the oil demands of Los Angeles and New York.

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