The facility location problem with Bernoulli demands

Abstract

In this paper we address a discrete capacitated facility location problem in which customers have Bernoulli demands. The problem is formulated as a two-stage stochastic program. The goal is to define an a priori solution for the location of the facilities and for the allocation of customers to the operating facilities that minimize the expected value of the recourse function. A closed form is presented for the recourse function and an approximation is proposed for situations in which it can not be evaluated exactly. The stochastic assignment problem resulting from setting the operating facilities is studied and a procedure is proposed to approximate its optimal solution. We formulate the capacitated facility location problem with Bernoulli demands under perfect information and, finally, we propose a heuristic to find an a priori solution. Computational results are presented for the homogeneous case.

Fixed-Charge Facility Location Problems

“…Indeed the problems studied in this chapter can be seen as simplifications of more realistic models that take into account additional issues. We have studied deterministic static problems, without taking uncertainty into account (see, for instance, Lin 2009;Albareda-Sambola et al 2011, 2013Gao 2012) or temporal aspects (see, for instance, Albareda-Sambola et al 2009a, 2010. Also, the way we have considered capacity constraints on the facilities may seem simplistic, since modular capacities (incurring their corresponding costs) can be more realistic (see, for instance, Gouveia and Saldanha da Gama 2006;Gourdin and Klopfenstein …”

Designing e‐commerce supply chains: a stochastic facility–location approach

“…Albareda‐Sambola et al. () model a situation in which it is unknown whether a customer will place an order. This is modeled using a Bernoulli distribution, which lends itself to find an analytical solution of the recourse problem.…”

“…Many algorithms have been developed for solving the associated stochastic‐programming models. If the applications resulted in few facilities and customers, exact solvers are usually able to solve the deterministic equivalent model or DEM (Wang et al., ; Beraldi et al., ; Albareda‐Sambola et al., ). Exact approaches, such as a branch‐and‐cut L‐shaped procedure or a Lagrangian‐relaxation procedure combined with branch and bound, are presented in Laporte et al.…”

Networks, uncertainty, applications and a crusade for optimality

“…In [Snyder, 2006] one can find an excellent review on Facility Location under uncertainty, describing contributions not only from the stochastic but also from the RO perspective. More recent references to Facility Location under uncertainty include [Snyder and Daskin, 2005, Averbakh, 2005, Snyder and Daskin, 2006, Cui et al, 2010, Shen et al, 2011, Albareda-Sambola et al, 2011, Adjiashvili, 2012, Gao, 2012, Alumur et al, 2012, Albareda-Sambola et al, 2013, Gïlpinar et al, 2013 and [Li et al, 2013].…”