# GE330practice4 - Problem 1(Facility Lo cation Problem Given...

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Given a set of potential facility locations N = { 1 , 2 , · · · , n } and a set of customers I = { 1 , 2 , · · · , m } . A facility placed at location j costs c j for j N . The total cost of satisfying the demand of client i from a facility at j is h ij . The optimization problem is to choose a subset of locations at which to place facilities and then to assign the clients to these facilities so as to minimize total cost. Note: The demand of a Figure 1: Uncapacitated facility location problem customer can be satisﬁed by more than one facilities. (a) Give a formulation of this optimization problem. (b) Now suppose facility place at j has capacity u j for j N and customer i has demand b i for i I . Moreover, the unit cost of serving customer i by facility at j is s ij . Formulation this problem again. Solution: (a) Deﬁne variables as follows: x j := ± 1 if a facility is placed at j 0 otherwise , y ij := the fraction of the demand of customer i that is satisﬁed from a facility at j. 1

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GE330practice4 - Problem 1(Facility Lo cation Problem Given...

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