Allocation balancing and minimization of the expected costs in a bi-objective stochastic capacitated location problem

摘要

We consider a stochastic location-allocation problem where optimal locations of facilities among potential locations and optimal allocations of stochastic customers to the facilities are determined. Our two main assumptions are: (1) the customer demands have Bernoulli distributions, and (2) the capacity of a facility for accepting customers is limited so that if the number of allocated customers to the facility is more than its capacity, a shortage will occur. The problem is formulated as a bi-objective mathematical programming model where the total sum of fixed costs of establishment of the facilities and the expected values of servicing and shortage costs and also, the differences of the facility workloads have to be minimized. To solve the proposed model, the augmented £-constraint method is used. A sample problem is tested and analyzed to show the performance of the proposed model.