This paper formulates a new version of set covering models by introducing a customer-determined stochastic critical distance. In this model, all services are provided at the sites of facilities, and customers have to go to the facility sites to obtain the services. Due to the randomness of their critical distance, customers patronize a far or near facility with a probability. The objective is to find a minimum cost set of facilities so that every customer is covered by at least one facility with an average probability greater than a given level α. We consider an instance of the problem by embedding the exponential effect of distance into the model. An algorithm based on two searching paths is proposed for solutions to the instance. Experiments show that the algorithm performs well for problems with greater α, and the experimental results for smaller α are reported and analysed.
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