# The government of Quebec is interested in locating a set of clinics in the metropolitan area of Mont Show more The government of Quebec is interested in locating a set of clinics in the metropolitan area of Montreal.

March 12, 2019
March 12, 2019

#### The government of Quebec is interested in locating a set of clinics in the metropolitan area of Mont Show more The government of Quebec is interested in locating a set of clinics in the metropolitan area of Montreal.

After analyzing several alternatives they have chosen a set of seven potential sites for the location of the clinics. A clinic placed at site j has a setup cost of cj. They are considering a set of 10 communities that have to be served by the new clinics. We say that a community i is served by clinic j if community I can be reached from j in 15 minutes (driving time). The times in minutes required to drive between the potential location of clinics and the communities are: 1 2 3 4 5 6 7 8 9 10 Site 1 19 11 18 7 5 11 13 28 23 10 Site 2 8 24 14 35 16 19 10 3 29 41 Site 3 2 35 12 24 18 29 11 21 16 27 Site 4 16 9 17 12 14 35 41 14 7 50 Site 5 13 17 11 31 7 32 10 10 18 14 Site 6 32 23 32 24 28 12 19 22 14 4 Site 7 47 2 7 20 10 48 1 9 43 2 Communities The setup cost (expressed in millions of dollars) for locating a clinic at site j is given by c=[125203189247198211179]. The objective is to choose the minimum-cost set of locations for the clinics such that each community can be served by at least one clinic in 15 minutes. Obtain a mathematical formulation for this problem. Clearly indicate the definition of the decision variables and provide and explanation for the objective function and the set of constraints. Show less

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