Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery

Highlights

• We introduce an extension of the many-to-many location-routing problem.

• We provide a test set and perform an extensive computational study.

• A mixed-integer linear model is developed.

• A fix-and-optimize heuristic and a genetic algorithm are developed.

Abstract

In this paper, we consider a variant of the many-to-many location-routing problem, where hub facilities have to be located and customers with either pickup or delivery demands have to be combined in vehicle routes. In addition, several commodities and inter-hub transport processes are taken into account. A practical application of the problem can be found in the timber-trade industry, where companies provide their services using hub-and-spoke networks. We present a mixed-integer linear model for the problem and use CPLEX 12.4 to solve small-scale instances. Furthermore, a multi-start procedure based on a fix-and-optimize scheme and a genetic algorithm are introduced that efficiently construct promising solutions for medium- and large-scale instances. A computational performance analysis shows that the presented methods are suitable for practical application.

Introduction

Trading, industrial, and commercial service companies, as well as logistic service providers operate in transport networks that connect supply and delivery points. Particularly, when a company is launched, or decides to expand its operations, the efficient design of a transport network is an important key factor for business success. In order to configure a network such that all transport needs may be satisfied at the lowest transportation costs, companies usually decide to route shipments through a hub-and-spoke system. Instead of driving with partially loaded vehicles from supply to delivery points, full vehicles are sent to central transhipment facilities (hubs), where shipments are sorted and consolidated for further transport. In particular, strategic network design decisions comprise the determination of the numbers and locations of hub facilities, as well as the allocation of supply and delivery points to one or more hubs in order to specify possible transportation paths between pairs of origins and destinations (location-allocation problem). Once facilities are located, routes have to be planned for vehicles moving within the network (vehicle routing problem).

Location-allocation problems typically consider the positioning of facilities while taking into account serving customer locations on a straight-line trip between facility and customer. However, the assumption of direct transports rather than vehicle routes leads to less realistic transportation cost estimations. In order to compensate for that shortcoming, location-routing problems consist of determining the location of facilities and defining the routes for vehicles such that customer demands are satisfied, vehicle capacities are not exceeded, and the minimization of facility fixed and operating costs, as well as of routing costs is realized.

Location-routing problems (LRPs) usually occur in practice when customer locations are known in advance and therefore stable vehicle routes can be constructed. For example, Or and Pierskalla (1979) presented a study focusing on regionalization of blood banking systems. Jacobsen and Madsen (1980) considered a newspaper printing and distribution system in Denmark. Nambiar, Gelders, and Van Wassenhove (1989) investigated the problem of locating central rubber processing factories to process smallholder’s rubber, collected daily from a number of stations in Malaysia. Kulcar (1996) considered a project dealing with waste collection management, and Wasner and Zäpfel (2004) developed an optimal network structure for an Austrian parcel delivery service.

Various classification schemes have been presented for LRPs, where the differentiation is generally based on hierarchical levels, nature of demand or supply, number of facilities or vehicles, facility layers, and objectives (cf. e.g., Laporte, 1988, Min et al., 1998, Nagy and Salhi, 2007). In this paper, we consider a three layer network configuration consisting of supply and delivery points on the one hand and hub facilities to be located on the other hand. Supply and delivery points are situated at known locations and each point has a given demand that must be picked up or delivered (deterministic data). For hub facilities a set of potential locations is given. In order to meet the long-term characteristic of the location problem, we study one aggregate, representative planning period (static problem). To cope with the lack of reliable information on how conditions might change in future, as well as to allow decision-makers to explore the consequences of their decisions, appropriate scenarios are designed, where cost and demand variations are considered.

In Section 2, we describe the underlying location-routing problem and a possible application area. Since the problem contains problem components known from the literature that have not been considered in combination before, related literature is presented. In Section 3, we introduce a mixed-integer linear model for the problem. In order to strengthen the according formulation, Section 4 describes valid inequalities that may be added within the optimization process. Sections 5 Multi-start procedure, 6 Genetic algorithm are devoted to a multi-start procedure and a genetic algorithm that efficiently construct near-optimal solutions. The results of extensive computational experiments, where instances with problem-specific structural characteristics are considered, are given in Section 7. Finally, conclusions are presented in Section 8.