Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands

Location-Routing Problem (LRP) is related to logistics system of supply chain. In LRP, aims are facility location problem and vehicle routing problem that are considered simultaneously. As shown in recent researches, the costs in distribution systems may be excessive if routes are ignored when locating depots. In this paper, a heuristic method in four phases is developed to solve Capacitated Location-Routing Problem (CLRP). In phase 1, the customers are clustered according to greedy search method. Second phase, chooses the proper depots among candidates to be established. Third phase, allocates the clusters to depots. In final phase, Ant Colony System (ACS) is used for routing among depots and customers. The experimental results show the efficiency of our approach. 1. Introducción Location-routing problem is usually related to distribution systems and supporting supply chain. This problem is so important and valuable for supply chains that delivery goods to customers on time is of primary objective of every manager in a company. LRP has many applications in various fields such as: health, military and communications. The main interest about LRP is when customers demand is permanent (like collecting garbage) or when the depots are temporary (like demand in different seasons) (see Prodhon, 2007). For the first time, Maranzana (1964, p.216) points out that: “the location of factories, warehouses and supply points in general ... is often influenced by transport costs.” (Researchers consider this paper as the first publication on the LRP). Rand (1976), and Salhi and Rand (1989) showed that separating depot location problem and vehicle routing problem may face some suboptimal answers. Nagy and Salhi (2007) presented a review of early works on LRP and summarizes the different types of formulations, solution methods and problems with non-standard hierarchical structure of work published prior to 2007. Min et al. 1998 mentioned in their survey, most early published papers considered either capacitated routes or capacitated depots, but not both (see Laporte et al. 1988; Chien 1993; Srivastava 1993). In CLRP, the situation is that demand and supply points are given on the plane. Customers’ demands are given according to previous patterns and data. The capacity and ability of keeping the goods are determined from candidate depot centers. The vehicles transfer the goods with specific capacity and type from depots to the customers and then return to related centers. The aim is to determine optimum depot centers and also to provide and distribute the