A Nonlinear Model for a Capacitated Location-allocation Problem with Bernoulli Demand using Sub-sources

This study presents a capacitated multi-facility location-allocation problem with stochastic demands based on a well-known distribution function. In this discrete environment, besides the capacitated facilities, we can employee the capacitated sub-source of each facility for satisfying demands of customers. The objective function is to find the optimal locations of facilities among a finite number of potential locations and optimal allocation of the demand points (customers) to the operated facilities so that the total sum of establishment costs of the facilities, costs of allocation the costumers to the operated facilities and the expected values of servicing and outsourcing costs are minimized. To display the applicability of the model, a numerical example is provided and computational results are reported.