The two-echelon multi-products location-routing problem with pickup and delivery: formulation and heuristic approaches

Abstract

The two-echelon location-routing problem (LRP-2E) considers the first-level routes that serve from one depot a set of processing centres, which must be located and the second-level routes that serve customers from the opened processing centres. In this paper, we consider an extension of the LRP-2E, where the second-level routes include three constraints that have not been considered simultaneously in the location routing literature, namely multi-product, pickup and delivery, and the use of the processing centre as intermediate facility in the second-level routes. This new variant is named two-Echelon Multi-products Location-Routing problem with Pickup and Delivery (LRP-MPPD-2E). The objective of LRP-MPPD-2E is to minimise both the location and the routing costs, considering the new constraints. The first echelon deals with the selection of processing centres from a set of potential sites simultaneously with the construction of the first-level routes, such that each route starts from the main depot, visits the selected processing centres and returns to the main depot. The second echelon aims at assigning customers to the selected processing centres and defining the second-level routes. Each second-level route, starts at a processing centre, visits a set of customers, through one or several processing centres, and then returns to the first processing centre. We present a mixed-integer linear model for the problem and use a Cplex solver to solve small-scale instances. Furthermore, we propose non-trivial extensions of the nearest neighbour and insertion approaches. We also develop clustering-based approaches that have not been extensively investigated with regards to location routing. Computational experiments are conducted to evaluate and to compare the performances of the proposed approaches. The results confirm the effectiveness of clustering approaches.

Location-Routing Problem with Simultaneous Home Delivery and Customer’s Pickup for City Distribution of Online Shopping Purchases

“…A normalized Hamming distance based on pickup points' status, customers' service options and the assignments of two individuals is adopted to show the difference between solutions. The distance is computed according to Formula (22).…”

Model and algorithm for bilevel multisized terminal location‐routing problem for the last mile delivery

“…Among these researches, a variety of LRP variants were demonstrated: multitrip LRP (Rath and Gutjahr, ), LRP with time windows (Ponboon et al., ), LRP with subcontracting options (Stenger et al., ), LRP with simultaneous delivery and pickup (Karaoglan et al., ; Rieck et al., ; Yu and Lin, , 2016; Rahmani et al., , ), LRP with demands split (Rath and Gutjahr, ; Wang et al., ), LRP with depots connected with ring (Gianessi et al., ), and more complex variants such as LRP with multiperiod planning (Prodhon and Prins, ; Klibi et al., ) and LRP with inventory management etc. (Liu and Lee, ; Guerrero et al., ; Rath and Gutjahr, ).…”

A two-echelon location-routing model for designing a pooled distribution supply chain

“…They proposed a branchand-cut) algorithm and an Adaptive Large Neighborhood Search (NSAIDS) algorithm based on the idea that the 2E -LRP can be decomposed into two standard LRPS (one on each level). Rahmani et al 2015 [42] address a new extension of 2E-LRP named LRP-MPPD-2E (The Two-Echelon Multi-products Location-Routing problem with Pickup and Delivery). They developed a clustering based approach to solve the problem.…”