Question

An increasing number of Americans are moving to a warmer climate when they retire. To take advantage of this trend, 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 is where to locate the paramedic stations. For planning purpose, Pilgrim Haven has been divided into five tracts. Each station is to respond to all the medical emergencies that occur in the tract in which it is located as well as in the other tracts that are assigned to this station.

Thus, the decision to be made consist of the tracts to receive a paramedic station.

1. At most 3 stations have been allocated to the community for medical emergencies.
2. Each Tract must be assigned to 1 station only
3. Because of the limited resources, if the station is located in Tracts 1 and 2, a maximum of 1 tract can be served.
4. If the station(s) is located in Tracts 3, 4, and 5, it can serve at most 5 tracts.
5. In addition, Tracts 3 and 4 can only have 1 station in a total.

The following table gives the average response time to a medical emergency in each Tract (rows) if that tract is served by a station in a given Tract (the columns). The last column gives the forecasted average number of medical emergencies that will occur in each of the tracts per day.

		Paramedic Station in Tract					Average Frequency of Medical Emergencies per Day
	Tract	1	2	3	4	5
Response times (min.) to a medical emergency in tract	1	8	20	15	25	10	2
	2	12	8	20	15	25	1
	3	30	15	8	25	15	3
	4	20	10	15	8	12	1
	5	15	25	12	10	8	3

The objective is to minimize the overall average of the response times to medical emergencies. Formulate a BIP model and solve it using Excel Solver for this problem.

Answer 1

The solution is: