t3 - of B dollars has been allocated for firehouse...

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Next note that di , the distance from district i to its assigned firehouse, is given by: di = JX j=1 di j xi j , since one xi j will be 1 and all others 0. Also, the total population serviced by site j is: s j = IX i=1 pi xi j . Assume that a central district is particularly susceptible to fire and that either sites 1 and 2 or sites 3 and 4 can be used to protect this district. Then one of a number of similar restrictions might be: y1 + y2 # 2 or y3 + y4 # 2. We let y be a binary variable; then these alternative constraints become: y1 + y2 # 2y, y3 + y4 # 2(1 - y). Next assume that it costs f j (s j ) to build a firehouse at site j to service s j people and that a total budget

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Unformatted text preview: of B dollars has been allocated for firehouse construction. Then JX j=1 f j (s j ) # B. Finally, one possible social-welfare function might be to minimize the distance traveled to the district farthest from its assigned firehouse, that is, to: Minimize D, where D = max di ; or, equivalently, to Minimize D, subject to: D # di (i = 1, 2, . . . , I ). Collecting constraints and substituting above for di in terms of its defining relationship di = JX j=1 di j xi j ,...
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This note was uploaded on 10/15/2011 for the course MBAHRM 565 taught by Professor Profbhattacharya during the Spring '11 term at IIT Kanpur.

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t3 - of B dollars has been allocated for firehouse...

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