Locating Paramedic Stations in Pilgrim Haven

Do problem 10.12 (part b only) in the text. The text pages for this problem are also available electronically

on Canvas. Note that the average frequency of medical emergencies per day data is only relevant for

problem 10.11 and not needed for problem 10.12. You only need to assure that there is at least one

station within 15 minutes of each tract. Build a linear integer programming spreadsheet model and solve

it using Solver. (Be sure to set Integer Optimality in Solver Options to 0%.)

SSS 10.11. 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 allo- caled to the communily 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 ali 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 para- medic 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. Paramedic Average Station in Tract Frequency of ~~ Medical Emergen- 4123 4 5 cies per Day Response 41 5270 1525 10 2 Gmes HN 349 4-90 16 35 1 toa medical emergency 3 30 15 6 25 15 3 Ce 4 2010 15 4 12 1 5 15 25 12 10 5 3 Formulate and solve a BIP model on a spreadsheet for this problem, Identify any constraints that correspond to mutually exclusive allernalives or contingent decisions. 10.12. Reconsider Problem 10.11. The management of Sunny Skies Unlimited now has decided that the decision regarding the locations of the paramedic stations should be based mainly on costs. The cost of locating a paramedic station in a tract is $200,000 for tract 1, $250,000 for tract 2, $400,000 for tract 3, $300,000 for tract 4, and $500,000 for tract 5. Management's objective now is to determine which tracts should receive a station to mini- mize the total cost of stations while ensuring that each tract has al least one station close enough to respond to 4a medical emer- gency in no more than 15 minutes. In contrast to the original problem, note that the total number of paramedic stations is no longer fixed. Furthermore, if a tract without a station has more than one station within 15 minutes, it is no longer necessary to assign this tract to just one of these stations. a. Formulate the algebraic form of a pure BIP model with five binary variables for this problem. b. Display and solve this model on a spreadsheet