Modeling a four-layer location-routing problem

Abstract

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations.

Vehicle Routing in Multi-Echelon Distribution Systems with Cross-Docking: A Systematic Lexical-Metanarrative Analysis

“…Finally, Gonzalez-Feliu (2012b) and Hamidi et al (2012) attempt a unification of this problem by modeling respectively an N-echelon and a three-echelon LRP. The first is a theoretical work that proposes to solve the problem via branch-and-prize and obtain lower bounds by column generation without providing computational results.…”

A heuristic algorithm for a multi-product four-layer capacitated location-routing problem

“…Two-layer LRPs solve three problems (Hamidi et al, , 2012a(Hamidi et al, , 2012b: 1) location problem: given a series of candidate locations, how many depots should exist and where should they be placed?, 2) allocation problem: which customers should be assigned to which depot?, and 3) routing problem: how many tours are needed for each depot, which customers should be served on each tour, and what is the order of customers on each tour?. In this section some of the two-layer LRPs are reviewed.…”

“…This LRP is an extension of the LRP that we discussed in Hamidi et al (2012b). As we described in Hamidi et al (2011Hamidi et al ( , 2012aHamidi et al ( , 2012b, the four-layer LRP represents a distribution network consisting of plants (P), central depots (CD), regional depots (RD), and customers (C). This distribution network is depicted in Fig.…”

“…The LocationRouting Problem (LRP) integrates location, allocation, and vehicle routing problems to design efficient distribution networks (Hamidi et al, , 2012a(Hamidi et al, , 2012b. The location problem locates facilities in a series of locations.…”

A case analysis of a sustainable food supply chain distribution system—A multi-objective approach

“…Optimisation models for two-layer distribution systems are presented in Berger (1997) and Hassanzadeh et al (2009). The supply chain distribution system can also be extended to three-layers (Perl 1983;Perl and Daskin 1985) and also four-layers (Hamidi et al 2012). …”