This seminar focuses a two-stage stochastic discrete facility location problem involving a finite set of potential locations for the facilities and a set of customers with a demand described by a Bernoulli random variable. In other words, demand regards a service request and not a quantity of some commodity. The facilities are capacitated in terms of the number of customers they can serve. A here-and-now decision is to be made concerning the facilities to open and the (single) allocation of the customers to the selected facilities. Since this decision is made prior to knowing which customers are in fact calling for being served, a facility may end up facing a demand higher than its capacity. In this case, a recourse action is required that is assumed to be associated with outsourcing. Two outsourcing strategies are studied. In the first one—facility outsourcing— extra capacity is acquired for those facilities running out of capacity. In the second one— customer outsourcing—an external service provider is considered for fulfilling the missing capacity. The goal of the problem is to minimize the total setup cost for the facilities plus the expected service and outsourcing costs.
Modeling aspects and solution procedures that have been studied for the problem are discussed. A distinction is made between the homogeneous and the non-homogeneous cases. In the former setting, all customers have the same probability of requesting the service. This allows deriving compact mathematical programming formulations for the problem that can be tackled by an off-the-shelf optimization solver to solve to optimality instances of realistic size. In the latter, we must resort to approximations since the recourse function becomes intractable even for toy instances of the problem.
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