Abstract
This study investigates a classic stochastic location problem in a service system with immobile servers that are represented by M/G/1 queues. It shows that the basic integer nonlinear optimization model of the problem can be reformulated as different mixed-integer linear models. It also proposes effective valid inequalities to enhance the linear reformulations. The models are applied to tackle a robust counterpart of the problem when demand rates are uncertain. Our results can generally be used for similar decision problems with congestion.
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