Set-covering models such as the original Western model in Figure 6.22 often have multiple optimal solutions. See how many alternative optimal solutions you can find. Of course, each must use three hubs because this is optimal. Use various initial values in the decision variable cells and then run Solver repeatedly.

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.