Designing two-echelon distribution networks under uncertainty

With the high growth of e-commerce and the continuous increase in cities population contrasted with the rising levels of congestion, distribution schemes need to deploy additional echelons to offer more dynamic adjustment to the requirement of the business over time and to cope with all the random factors. In this context, a two-echelon distribution network is nowadays investigated by the practitioners. In this thesis, we first present a global survey on distribution network design problems and point out many critical modeling features, namely the two-echelon structure, the multi-period setting, the uncertainty and solution approaches. The aim, here, is to propose a comprehensive framework for the design of an efficient two-echelon distribution network under multi-period and stochastic settings in which products are directed from warehouse platforms (WPs) to distribution platforms (DPs) before being transported to customers. A temporal hierarchy characterizes the design level dealing with facility-location and capacity decisions over a set of design periods, while the operational level involves transportation decisions on a daily basis. Then, we introduce the comprehensive framework for the two-echelon distribution network design problem under uncertain demand, and time-varying demand and cost, formulated as a multi-stage stochastic program. This work looks at a generic case for the deployment of a retailer's distribution network. Thus, the problem involves, at the strategic level, decisions on the number and location of DPs along the set of design periods as well as decisions on the capacity assignment to calibrate DP throughput capacity. The operational decisions related to transportation are modeled as origin-destination arcs. Subsequently, we propose alternative modeling approaches based on two-stage stochastic programming with recourse, and solve the resulting models using a Benders decomposition approach integrated with a sample average approximation (SAA) technique. Next, we are interested in the last-mile delivery in an urban context where transportation decisions involved in the second echelon are addressed through multi-drop routes. A two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP) is defined in which facility-location decisions concern both WPs and DPs. We model the problem using a two-stage stochastic program with integer recourse. To solve the 2E-SM-CLRP, we develop a Benders decomposition algorithm. The location and capacity decisions are fixed from the solution of the Benders master problem. The resulting subproblem is a capacitated vehicle-routing problem with capacitated multi-depot (CVRP-CMD) and is solved using a branch-cut-and-price algorithm. Finally, we focus on the multi-stage framework proposed for the stochastic multi-period two-echelon distribution network design problem and evaluate its tractability. A scenario tree is built to handle the set of scenarios representing demand uncertainty. We present a compact formulation and develop a rolling horizon heuristic to produce design solutions for the multi-stage model. It provides good quality bounds in a reasonable computational times.