Modeling and solving a capacitated stochastic location-allocation problem using sub-sources

We study a capacitated multi-facility location-allocation problem in which the customers have stochastic demands based on Bernoulli distribution function. We consider the capacitated sub-sources of facilities to satisfy demands of customers. In the discrete stochastic problem, the goal is 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 cost of the customers, expected values of servicing and outsourcing costs is minimized. The model is formulated as a mixed-integer nonlinear programming problem. Since finding an optimal solution may require an excessive amount of time depending on nonlinear constraints, we transform the nonlinear constraints of the problem to linear ones to arrive at a simple formulation of the model. Numerical results show that the LINGO 9.0 software is capable of solving small size problems. For medium and large-size problems, we propose two meta-heuristic algorithms, namely a genetic algorithm and a discrete version of colonial competitive algorithm. Computational results show that the proposed algorithms efficiently obtain effective solutions.