The multi-sourcing location inventory problem with stochastic demand

This paper deals with a multi-period location-inventory optimization problem in a multi-echelon supply chain network characterized by an uncertain demand and a multi-sourcing feature. The aim of the paper is to propose a generic modeling approach to integrate key features of the inventory planning decisions, made under a reorder point order-up-to-level (s, S) policy, with the location-allocation design decisions to cope with demand uncertainty. Given the hierarchical structure of the problem, a two-stage stochastic mathematical model that maximizes the total expected supply chain network profit is proposed. This optimization model is intractable due to its non-linearity. Therefore, a linear approximation is proposed and a sample average approximation approach is used to produce near-optimal solutions. Numerical experiments are conducted to validate the proposed modeling and solution approaches. The results show the efficiency of the linear approximation of the (s, S) policy at the strategic level to produce robust design solutions under uncertainty. They underline the sensitivity of the design solution to the demand type and the impact of the inventory holding costs and backorder costs, especially under non-stationary processes.