Question: Consider the facility location problem discussed in class. We are given a set 1 of potential facilities and a set 2 of demand (customer) points.

Consider the facility location problem discussed in class. We are given a set 1 of potential facilities and a set 2 of demand (customer) points. The capacity of potential facility 1 is units and the demand of customer 2 is units. The unit cost of shipping from potential facility 1 to demand point 2 is . The fixed operating cost of the potential facility 1 is . Suppose that there is an additional requirement that you have to open exactly facilities, where is an integer between 1 and |1 |.

(a) Suppose that = 1. What are the conditions under which the resulting problem will have a feasible solution? Be precise.

(b) Describe a simple algorithm for solving the problem in part (a) without using an integer linear programming formulation.

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