The capacitated facility location-allocation problem under uncertain environment

Facility location-allocation (FLA) problem has been widely studied by operational researchers due to its many practical applications. In real life, it is usually very hard to present the customers' demands in a precise way and thus they are regarded to be uncertain. Since the uncertain demands can be estimated from historical data, researchers tried to describe FLA problem under stochastic environment. Although stochastic models can cater for a variety of cases, they are not sufficient to describe many other situations, where the probability distribution of customers' demands may be unknown or partially known. Instead we have to invite some domain experts to evaluate their belief degree that each event will occur. This paper will consider the capacitated FLA problem under small sample or no-sample cases and establish an uncertain expected value model based on uncertain measure. In order to solve this model, the simplex algorithm, Monte Carlo simulation and a genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, a numerical example is presented to illustrate the uncertain model and the algorithm.