I am trying to figure out the objective function and associated constraints for optimization of the following problem:
There is a set of Demand points I, which have to be covered by a set of Supply Points J
Not all Demand Points need be covered
Not all Supply Points need Supply
Constraint- If a Supply Point j is selected for supplying, at least four demand points 'i' must be covered by it, or in other words, any supply point supplies to any demand center at all, it must do so for at least four demand centers
Constraint- There is a travel time constraint, that all demand centers which are covered, must be covered by a supply point which is not more than 60 minutes in travel time. The information of travel times for the set of IxJ is available.
Objective- The objective is to maximize coverage of demand points I. Any no. of supply points may supply, as long as the constraints are met.
We are looking to formulate the optimization equations for this problem. We are thinking of assigning decision variables 'Ai' and 'Bj' which take value of 0 or 1 for both demand centers and supply points, 1 if demand center is covered (and 1 if supply center supplies), and 0 if demand center is not covered (and 1 if supply center does not supply>
Looking for your help on this :)