A stochastic programming model for a capacitated location-allocation problem with heterogeneous demands

Abstract In this paper, we develop a stochastic programming model for the capacitated location-allocation problem in the heterogeneous environment where the demands are distributed according to the Bernoulli function with different probabilities. The capacitated sub-sources of facilities are also involved to satisfy customers’ demands in this work. This study aims to find optimal locations of facilities and optimal allocations of existing customers to the facilities so that the total cost of operating facilities, allocating the customers, expected servicing and outsourcing is minimized. Due to the large amount of customers with different demand probabilities, accurate estimation of the outsourcing function is unaffordable. To address this problem, we propose a new stochastic programming model using the normal approximation method to evaluate the probability distribution of the total demand requests of operating facilities. Three sets of test instances (i.e., small, medium and large), generated by Monte Carlo simulation technique, and an empirical study of an automobile manufacturer are employed to demonstrate and validate the efficiency of the proposed model and solution approach. Due to NP-hardness of the problem, an Extended Discrete Colonial Competitive Algorithm (EDCCA) is developed to solve the medium and large problems. The results reveal the proficiency of the proposed normal approximation technique and the EDCCA.