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.
The purpose of this study is to solve a complex multi-product four-layer capacitated locationrouting problem (LRP) in which two specific constraints are taken into account: 1) plants have limited production capacity, and 2) central depots have limited capacity for storing and transshipping products. The LRP represents a multi-product four-layer distribution network that consists of plants, central depots, regional depots, and customers. A heuristic algorithm is developed to solve the four-layer LRP. The heuristic uses GRASP (Greedy Randomized Adaptive Search Procedure) and two probabilistic tabu search strategies of intensification and diversification to tackle the problem. Results show that the heuristic solves the problem effectively.
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