Reference no: EM131806003

Only need formulation *please explain in depth

A new town in Maryland is planning its fire department and decides to open p fire stations in the State. In terms on planning, the state has been divided into n regions (p << n), each one of them candidate to obtain at most one station. Each station has to answer to any call from its own region and from the others that have been assigned to it. Therefore the decisions to be made are:

Locate p fire stations

Assign each region to only one station

The following information is given:

tij response time to region i from a station located in region j.

ai frequency of calls in region i                      

The objective is to minimize the total response time of the fire stations. Formulate an integer binary location model to address this problem.

Suppose now that the cost of opening a fire station in region j is equal to fj. Now the objective is to find in which regions stations have to be located so as to minimize total opening costs, so that no region has a station within more than T minutes (observe that now the number of stations is unknown). Formulate a new model obtain the number of facilities to locate and its locations.