The SITATION program plots a trade off curve showing the percentage of the total demand that is covered as a function of the number of facilities that are located. In many practical decision contexts, we would also like to know the trade off between the minimum number of facilities that are needed to attain a given level of service (e.g., 90% coverage) as a function of the coverage distance. In other words, we would like a trade off curve that plots the number of facilities needed on the Y-axis and the coverage distance on the X-axis for a specified level of service.
(a) For a level of service of 100% (i.e., total coverage), find the trade off curve between the minimum number of facilities needed and the coverage distance. Use distances of 100, 200, 300, 400, 500, 600, and 700 miles with the 88-node data set, CITY1990.GRT (and the first set of demands representing the 1990 city populations). Note that for a level of service of 100% you are implicitly using the maximum covering algorithm to solve a set covering problem..
(b) Repeat part (a) using a level of service of 90%.
(c) Repeat part (a) using a level of service of 80%.
(d) Plot the results you obtained in parts (a)–(c) using a good spreadsheet program.
(e) Briefly explain how the results obtained in parts (a)–(d) of this exercise (or similar results) might be useful to a firm in the clothing business in locating warehouses that supply retail stores by truck deliveries from the warehouses. In particular, how might these results be used in determining the number of warehouses, the level of service to provide to the stores, and the fraction of the stores that should be promised this level of service? To solve this problem for such a firm, what additional information would you want to have?