Abstract: This paper addresses a stochastic multistage location-inventory model with investment funds limnation for facilities location and market selection in each time stage,where the economies of scale and risk-pooling effects are handled by consolidating inventory sites,and forecast uncertainties of parameters in the problem are explicitly considered by specifying a set of scenarios. The goal of this model is to minimize the expected total cost that includes location,transportation,inventory,and lost revenues costs. We formulate this model as a nonlinear integer programming problem,for which we propose a Lagrangian relaxation-based solution algorithm. Finally,this algorithm is applied to several instances on problems in 3 different sizes,and our computational results show that our model can be solved efficiently via this algorithm.

Key words: distribution network design, facility location, inventory, lagrangian relaxation, scenario tree