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 to be made is where to locate the two paramedic stations that have been allocated to the community to respond to medical emergencies. For planning purposes, Pilgrim Haven has been divided into five tracts, with no more than one paramedic station to be located in any given tract. 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 decisions to be made consist of (1) the tracts to receive a paramedic station and (2) the assignment of each of the other tracts to one of the paramedic stations. The objective is to minimize the overall average of the response times to medical emergencies. The following table gives the average response time to a medical emergency in each tract (the 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.
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 to be made is where to locate the two paramedic stations that have been allocated to the community to respond to medical emergencies. For planning purposes, Pilgrim Haven has been divided into five tracts, with no more than one paramedic station to be located in any given tract. 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 decisions to be made consist of (1) the tracts to receive a paramedic station and (2) the assignment of each of the other tracts to one of the paramedic stations. The objective is to minimize the overall average of the response times to medical emergencies. The following table gives the average response time to a medical emergency in each tract (the 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.
| Response times (minutes) to a medical emergency in tract | Paramedic Station in Tract | Average Frequency of Medical Emergencies per Day | ||||
|---|---|---|---|---|---|---|
| Tract 1 | Tract 2 | Tract 3 | Tract 4 | Tract 5 | ||
| Tract 1 | 5 | 20 | 15 | 25 | 10 | 2 |
| Tract 2 | 12 | 4 | 20 | 15 | 25 | 1 |
| Tract 3 | 30 | 15 | 6 | 25 | 15 | 3 |
| Tract 4 | 20 | 10 | 15 | 4 | 12 | 1 |
| Tract 5 | 15 | 25 | 12 | 10 | 5 | 3 |
Formulate and solve a BIP model on a spreadsheet for this problem.
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Determine the minimum overall average of the response times to medical emergencies.
Note: Leave no cells blank. Enter "0" wherever required.
Track
Track 1 Track 2 Track 3 Track 4 Track 5 Track 1 Track 2 Track 3 Track 4 Track 5 Track 6 -
Determine the station in tract.
Note: Leave no cells blank. Enter "0" wherever required.
Station Tract -
Determine the average response time.
Note: Round your answer to 1 decimal place.
Average response time:
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