A Nonlinear Model For A Capacitated Location-Allocation Problem With Bernoulli Demand Using Sub-Sources

Providing permanent services for customers is one of our today’s difficulties. in this paper, a capacitated multi-facility location-allocation model with stochastic demands based on a well-known bernoulli distribution function proposed to solve the problem. in this discrete environment, besides the capacitated facilities, the capacitated sub-sources of each facility could be utilized to satisfy the demands of customers. the proposed model is capable of allowing each facility to be interacted with its sub-source as well as other facility and their sub-sources. 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. thus, 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