In the original Western set-covering model in Figure 6.22, we used the number of hubs as the objective to minimize. Suppose instead that there is a fixed cost of locating a hub in any city, where these fixed costs can possibly vary across cities. Make up some reasonable fixed costs, modify the model appropriately, and use Solver to find the solution that minimizes the sum of fixed costs.

Figure 6.22

A B D E F H K N P 1 Western Airlines hub location model 2 3 Input data: which cities are covered by which potential hubs Potential hub Range names used: Hubs_covered_by Total hubs Used_as_hub =Model$B$25:$B$ 36 =Model!$B$39 =Model!$B$21:$M$21 4 5 |City 6 JAT 7 IBO AT BO CH DE LA NO NY PI SL SF SE 6 1 1 1 1 0. 1. 8 CH 0. 1. 1. 9 DE 1 1 0. 10 HO 0. 0. 1. 0. 0. 11 |LA 1. 12 INO 1. 1. 0. 13 NY 1. 14 PI 1 1. 0. 15 SL 1. 16 SF 17 SE 1 1. 1 18 19 Decisions: which cities to use as hubs 20 AT BO CH DE LA NO NY PI SL SF SE 21 JUsed as hub 1. 1 1 22 23 Constraints that each city must be covered by at least one hub 24 City Hubs covered by Required 25 AT 2 1 >= 26 BO 1 27 CH 28 DE 1 >= 1 1 1 29 IHO 1 30 LA 31 INO 1 1 1 32 NY 1 33 PI 34 ISL >= 1 1. 1 35 ISE 1. 1. . 36 ISE 1 >= 1 37 38 Objective to minimize 39 Total hubs 3.