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In this work, a bi-objective multi-facility location-allocation problem is investigated, in which the locations of the customers and their arrivals are stochastic. We first formulate the problem as a continuous location-allocation model with no constraints on the capacity of the facilities. Then, we develop an approximated discrete model in which the facilities with limited capacities can be located on a set of candidate points. The proposed model has two objective functions that are evaluated using discrete event system simulation. The first objective is to minimize the expected total time the customers spend in the system until their services begin. The time that each customer spends in... 

We consider a multi-facility location problem in the presence of a line barrier with the starting point of the barrier uniformly distributed. The objective is to locate n new facilities among m existing facilities minimising the summation of the weighted expected rectilinear barrier distances of the locations of new facilities and new and existing facilities. The proposed problem is designed as a mixed-integer nonlinear programming model, conveniently transformed into a mixed-integer quadratic programming model. The computational results show that the LINGO 9.0 software package is effective in solving problems with small sizes. For large problems, we propose two meta-heuristic algorithms,... 

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... 

Abstract 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...