Textbook Problem

The Lafferty Company wants to locate a warehouse from which it will ship products to four customers. The location (in the x-y plane) of the four customers and the number of shipments per year needed by each customer are given in Table 7.1. (All coordinates are in miles, relative to the point x = 0 and y = 0.) A single warehouse must be used to service all of the customers. Lafferty wants to determine the location of the warehouse that minimizes the total annual distance traveled from the warehouse to the customers.

Modify the warehouse location model as suggested in Modeling Issue 2. Specifically, assume that the same four customers have the same annual shipments, but now, there are only two possible warehouse locations, each with distances to the various customers. (These distances, along with other inputs, are in the file P07_27.xlsx.) The company can build either or both of these warehouses. The cost to build a warehouse is $50,000. (You can assume that this cost has been annualized. That is, the company incurs a building cost that is equivalent to $50,000 per year.) If only one warehouse is built, it will ship to all customers. However, if both warehouses are built, then the company must decide which warehouse will ship to each customer. There is a traveling cost of $1 per mile.

1. a. Develop an appropriate model to minimize total annual cost, and then use Solver to optimize it. Is this model an NLP or an IP model (or both)?
2. b. Use SolverTable with a single input, the traveling cost per mile, to see how large this cost must be before the company builds both warehouses rather than just one.