A Local Search approach for the Two–Echelon Multi-products Location–Routing problem with Pickup and Delivery

This paper deals with the two-Echelon Multi-products Location-Routing problem with Pickup and Delivery (LRP-MPPD-2E). The LRP-MPPD-2E is a generalisation of the classical LRP-2E. The first-level routes consist of a set of processing centers that must be served from one depot, and the second-level routes serve customers from the opened processing centers. The second level routes include three constraints, multi-product, pickup and delivery and using the processing center as intermediate facility. The objective of LRP-MPPD-2E is to minimize both the location and the routing costs. In this study, we present two types of Local Search methods for the LRP-MPPD-2E, namely, the routing improvement Local Search and the processing centers location improvement Local Search. The concept of 2-Opt is extended to deal with the pickup and delivery, and multi-products constraints. A new Local Search specific to the LRP-MPPD-2E, named Merging Product (MP) is introduced. Computational experiments are conducted to evaluate and to compare the performances of the proposed Local Search methods.