Only need formulation *please explain in depth A new town in Maryland is plannin
ID: 383680 • Letter: O
Question
Only need formulation *please explain in depth
A new town in Maryland is planning its fire department and decides to open p fire stations in the State. In terms on planning, the state has been divided into n regions (p << n), each one of them candidate to obtain at most one station. Each station has to answer to any call from its own region and from the others that have been assigned to it. Therefore the decisions to be made are:
Locate p fire stations
Assign each region to only one station
The following information is given:
tij response time to region i from a station located in region j.
ai frequency of calls in region i
The objective is to minimize the total response time of the fire stations. Formulate an integer binary location model to address this problem.
Suppose now that the cost of opening a fire station in region j is equal to fj. Now the objective is to find in which regions stations have to be located so as to minimize total opening costs, so that no region has a station within more than T minutes (observe that now the number of stations is unknown). Formulate a new model obtain the number of facilities to locate and its locations.
Explanation / Answer
INCREMENTAL INITIAL INVESTMENT:
Demolishing cost = 8*16000 = 128000
Cost of building 4 perimeter stations =260000*4 = 1040000
Cost of helicopters and other equipments = 560000*4 = 2240000
Receipts from sale of 1/2 of equipment at interior stations = 180000*0.5*8 = -720000
Net Initial investment 2688000
INCREMENTAL ANNUAL OPERATIONAL CASH FLOWS:
Cost of operation of the old stations:
Staff compensation = $260000*8 = 2080000
Operating cost = 160000*8 = 1280000
Total annual cost of operating the old stations 3360000
Cost of operation of the new stations:
Staff compensation = $360000*4 = 1440000
Operating cost = 170000*4 = 680000
Total annual cost of operating the old stations 2120000
Saving in annual operating costs 1240000
PV of annual operating costs = 1240000*PVIFA(10,10)
= 1240000*6.145 = 7619800
Less: Initial investment 2688000
NPV 4931800
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.