In the original Western Airlines set-covering model in Figure 14.52, we assumed that each city must be covered by at least one hub. Suppose that for added flexibility in flight routing, Western requires that each city must be covered by at least two hubs. How do the model and optimal solution change?

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Figure 14.52 Set-Covering Model D EF 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? =ModelSB$25:$8$36 ModelSB$39 =Model$8$21SM$21 4 5 lity AT во CH DE но LA NO NY PI SL SF SE 6 JAT 7 JB0 1 1 1 1 1 8 CH 9 DE 1 1 1 1 1 10 HO 0. 1 1 11 LA 12 NO 13 NY 14 PI 15 SL 16 SF 17 SE 18 19 Decisions: which cities to use as hubs 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 1 20 AT BO CH DE HO LA NO NY PI SL SF SE 21 Used as hub? 1 1 1 22 23 Constraints that each city must be covered by at least one hub 24 City 25 AT Hubs covered by Required 26 B0 1 27 |CH 28 DE Note that there are multiple optimal solutions to this mode, all of which require a total of 3 hubs. You might get a different solution from the one shown here. 1 1 1 29 HO 1 30 LA 31 NO 32 NY 33 PI 1 1 1 34 ISL 1 35 SF 36 SE 1 1 37 38 Objective to minimize 39 Total hubs IS