A note on the facility location problem with stochastic demands

• Facility location problem with stochastic demands modeling by any distribution is presented.
• We study arbitrary distribution of the demand that is not only discrete or continuous.
• We note that the number of demand customers has a binomial distribution with known parameters.
• To derive the expected costs we use the conditioning on the number of demand customers instead of the total demand.
• We derive the expected costs for some discrete and continuous distributions.

In this research note that the single source capacitated facility location problem with general stochastic identically distributed demands is studied. The demands considered are independent and identically distributed random variables with arbitrary distribution. The unified a priori solution for the locations of facilities and for the allocation of customers to the operating facilities is found. This solution minimizes the objective function which is the sum of the fixed costs and the value of one of two different recourse functions. For each case the recourse function is given in closed form and a deterministic equivalent formulation of the model is presented. Some numerical examples are also given.