Consider the network shown in Figure 4.21: (a) Write out the set covering problem formulation for this network, if the coverage distance is 25. Recall that facilities can cover demands at nodes that...

Consider the network shown in Figure 4.21:

(a) Write out the set covering problem formulation for this network, if the coverage distance is 25. Recall that facilities can cover demands at nodes that are not directly linked to the node at which the facility is located as long as the shortest path distance between the facility and the demand node is less than or equal to the coverage distance.

(b) With a coverage distance of 25, clearly indicate which, if any, locations can be eliminated because they are dominated by other locations (and specify the identity of the dominating node for each dominated node). Also, clearly indicate which, if any, rows of the constraint matrix may be eliminated and indicate why they may be eliminated.

(c) Based on the reduced problem that you obtain in part (b), solve the set covering problem (with a distance of 25). Justify your answer either in words or by stating how you would solve the optimization problem that results from part (b).

(d) Identify all alternate optima for the problem.