One or more sites among the 7 candidate sites in the undirected network below may be selected to build emergency center(s) by the City Authority. Emergency response vehicles from the selected site(s) must be able to reach all the nodes within 10 minutes along the shortest time routes in this network. Travel times along the edges of the network are shown in the table below.

where fi is the annual cost to operate an emergency center at location i,i = 1,2,3,4,5,6,7 ; = 20.0 is a parameter to convert the total travel time to an annual monetary cost value.

1) In the above model, a set of constraint inequalities is missing. Present the missing constraints so that the model will be complete for solving the considered problem.

2) Use any method based on a valid approach or use common-sense observations to find the values of aij.

3) Indicate, with brief explanations, the minimum number of emergency centers to build in order to have all sites covered.

4) Based on the given data and calculated results from 2), suggest the site(s) to build the emergency center(s) for the City Authority with brief explanations.

5) Is the solution suggested in 4) optimal? Briefly explain.

Problem 2 Data: Travel Time (Minutes) along Each Edge Problem 2 Data: Annual Fixed Facility Cost The authority has decided to use the following mathematical model to select the site(s). Minimizei=17fiyi+i=17j=1,j=i7tijxij Subject to j=1,j=i7aijxij1,i=1,2,3,4,5,6,7