Cplex integer (or binary) programming model

 

Sunny Skies Unlimited is undertaking a major real-estate development project. The project is to develop a completely new retirement community (to be called Pilgrim Haven) that will cover several square miles. One of the decisions to be made is to locate 40 paramedic stations that have been allocated to the community to respond to medical emergencies. For planning purposes, Pilgrim Haven has been divided into 100 regions; with no more than one paramedic station to be located in any given region. Each region has to be assigned to exactly one paramedic station. Each station is to respond to all the medical emergencies that occur in the regions that are assigned to this station. No more than three regions can be assigned to a paramedic station. Thus, the management wants to decide on locations of the paramedic stations and the regions that are assigned to each paramedic station. The objective is to minimize the overall average response time to medical emergencies. The excel file gives the average response time, ????????????, to a medical emergency in region ????, if region ???? is served by a station region ????. For instance, the response time to a medical emergency in region 2 from the paramedic station in region 1 is 20 minutes, whereas the response time to a medical emergency in region 1 from the paramedic station in region 2 is 15 minutes (as highlighted in the excel file). The expected number of medical emergencies that would occur in each region per month is also provided in the excel file. 

Formulate an integer (or binary) programming model to decide where to open paramedic stations and the regions that are assigned to each paramedic station to minimize the overall average of the response time to medical emergencies.