A capacitated location-allocation problem with stochastic demands using sub-sources: An empirical study

In a recent work, Alizadeh et al. (2013) studied a capacitated multi-facility location-allocation problem in which customers had stochastic demands based on the Bernoulli distribution function. Authors considered capacitated sub-sources of facilities to satisfy customer demands. In this discrete stochastic problem, the goal was to find optimal locations of facilities among candidate locations and optimal allocations of existing customers to operating facilities so that the total sum of fixed costs of operating facilities, allocation costs of customers and expected values of servicing and outsourcing costs was minimized. The model was formulated as a mixed-integer nonlinear programming problem. Since finding an optimal solution may require an excessive amount of time depending on the nonlinear constraints, here we transform the nonlinear constraints of the problem to linear ones to obtain a simple formulation of the model. An empirical study of an automobile manufacturer, namely Geelran Motor and three sets of test problems of small, medium and large sizes were considered to show the applicability of the presented model and efficiency of the proposed meta-heuristic algorithms. Numerical results show that the LINGO 9.0 software package is capable of solving the empirical study and small problems. For medium and large problems, we propose two meta-heuristic algorithms, a genetic algorithm (GA) and a discrete version of the colonial competitive algorithm (CCA). Computational investigations illustrate the efficiency of the proposed algorithms in obtaining effective solutions.

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