Set-covering models such as the original Western Airlines model in Figure 14.52 often have multiple optimal solutions. See how many alternative optimal solutions you can find. Of course, each must use three hubs because we know this is optimal.

Figure 14.52 Set-Covering Model D E F G H K M 1 Western Airlines hub location model 2 3 Input data: which cities are covered by which potential hubs Range names used: Hubs covered by Total hubs Used as hub? Potential hub -ModelSB$25:5B$36 Model SB$39 =Model ISBS21:SMS21 4 5 City AT BO CH DE HO LA NO NY PI SL SF SE 6 JAT 7 IBO 1 1 1 1 1 1 8 CH 1 1 1 9 IDE 1 10 IHO 1 1 1 11 LA 1 1 12 NO 13 NY 14 PI 1. 1 1 1 1 15 SL 16 SF 1 1 1 17 SE 1 18 19 Decisions: which cities to use as hubs 20 AT BO CH DE LA NO NY PI SF SE 21 Used as hub? 22 23 Constraints that each city must be covered by at least one hub 24 City 25 AT 26 BO 27 CH 28 DE Hubs covered by Required 2 1 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 shown here. 1 1 1 1 29 HO 1 30 LA 31 NO 32 NY 33 PI 34 SL 35 SF 36 ISE 1 1 1 1 1 1 1 1 1 37 38 Objective to minimize 39 Total hubs