Question

A new large scale senior community is being developed, and one of the decisions to be made is where to locate the two fire stations that have been allocated to the community. For planning purposes, the community has been divided into five tracts, with no more than one fire station to be located in any given tract. Each station is to respond to all of the fires that occur in the tract in which it is located as well as in the other tracts that are assigned to this station. The following table gives the average response time (in minutes) to a fire in each tract (the columns) if that tract is served by a station in a given tract (the rows). The bottom row gives the forecasted average number of fires that will occur in each of the tracts each year. Formulate this problem situation as an integer programming model. 4 20 10 15 4 12 30 15 20 15 25 10 12 4 20 15 25 15 25 12 25 15 4 Frequency of Emergenc

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Decision Variables: Li (refer cell H12:H16) represent the location of fire station, Li = 1 if it is in location i, otherwise 0

Xij (refer cell C12:G16) represent the tract that the fire station is assigned to. Xij = 1, if fire station situated in i is assigned to tract j, otherwise 0

Objective function: ∑XijTijFij

s.t. ∑Li <= 2

∑Xi1 = ∑Xi2 = ∑Xi3 = ∑Xi4 = ∑Xi5 = 1

Xij, Li = binary

E19 | =SUMPRODUCT(C4:G8,C12:G16, 14:M8) Response Time, Tij Frequency, F 3 Station Fire 1 2 3 4 5 1 2 3 4 5 5 12 30 20 15 20 4 15 10 25 15 20 6 15 12 25 1525 4 10 10 2515 12 5 4 2 1 3 13 2 1 3 13 2 1 3 13 Solver Parameters 10 Firestation location, Xij Location Set Target Cell: 11 Station Fire 1 2 3 4 5 of fire stn 12 13 14 15 16 17 18 19 20 21 Equal To: O Max By Changing Cells: 0 Min Value of: 10 $C$12:$G$16, SH$12:$H$16 0 1 1 0 0 Subject to the Constraints: Options sC$12:$G$12 <- $H$12 $C$12:$G$16 binary $C$13:$G$13< $H$13 1 0 0 1 1 Total Reset All SC$15:$G$15 $H$15 $C$16:$G$16$H$16 Delete Objective function: 85Solver Parameters EX Set Target Cell SE$19 Solve Equal To: Max By Changing Cells: Min yalue of 0 Close $C$12:$G$16,$H$12:$H$16 | | Guess Subject to the Constraints: Options Add Change SC$17:$G$17 1 sHS12:sHS16 = binary Help

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