In the original Western Airlines set-covering model in Figure 14.52, 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 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 14.52 Set-Covering Model F K M. 1 Western Airlines hub location model 3 Input data: which cities are covered by which potential hubs Potential hub Range names used: Hubs covered by Total hubs Used as hub? 4 EModelSB$25:$B$36 5 ity 6 JAT 7 BO AT CH DE LA NO NY PI SL SF SE Model SB$39 Modell$B$21:$M$21 1 1. 1 8 IH 1 1 1. 9 DE 10 IHO 1 1 11 LA 1 12 NO 13 NY 14 PI 1 1 1 15 SL 16 SF 1 1. 1 1 17 SE 1 1. 18 19 Decisions: which cities to use as hubs AT 20 BO CH DE LA NO NY SL SF PI SE 21 Used as hub? 22 23 Constraints that each city must be covered by at least one hub 24 City 25 AT 1 Hubs covered by Required 21 > 1 26 BO 1 27 CH 28 DE 29 HO 30 LA Note that there are multiple optimal solutions to this model, all of which require a total of 3 hubs. You might get a different solution from the one 1 1 1 1 shown here. 1 31 INO 1 1 32 INY 33 PI 1 34 ISL 1 35 SF 36 SE 1 37 38 Objective to minimize 39 Total hubs H00O 1.