Mixed multi-echelon location routing problem with differentiated intermediate depots

Highlights

• A mixed logistics network which is better than two-echelon logistics network.

• Designing an efficient algorithm to solve the MME-LRP.

• Giving suggestions for express companies to redesign their logistics network.

Abstract

With the increasing of E-commerce parcels in China in recent years, the logistics networks of many express companies are more and more unreasonable. Considering the distribution of parcels is regionally related, we describe a mixed multi-echelon (MME) urban logistics network to handle the regionally distributed parcels. The MME network contains limited urban distribution centers (UDCs), many differentiated intermediate depots (IDs), and a large number of terminals. This research constructs a mixed integer linear programming (MILP) to solve the mixed multi-echelon location routing problem (MME-LRP) where the location and the type of IDs are determined. A hybrid heuristic algorithm based on iterated local search and intensified by path relinking (HH-ILS-PR) is proposed to tackle the problem. The quality of our algorithm and the practicability of the MME network are verified by three sets of instances: two of them are adapted from benchmark instances of 2E-LRP and one is developed from real-world data. In the real-world instance, MME urban logistics network reduces the cost by 11.08% compared with two-echelon urban logistics network. We also present several managerial implications to express companies.

Introduction

Urban logistics covers the circulation of goods related to national economy and people's livelihood within or between cities. It is defined as finding efficient and effective ways to transport goods in urban areas and considering the adverse effects on congestion, safety and environments (Savelsbergh & Van Woensel, 2016). Express industry, which supports parcel delivery, plays an important role in urban logistics. Since 2000, the fast-growing express industry has spawned many express companies, such as SF Express and YTO, and these companies have built their own logistics networks. However, as differences in the regional distribution of e-commerce packages have increased in recent years, express companies have severe misallocation in logistics facilities, causing high costs. For instance, in some high-demand areas, express companies opened some small-scale intermediate depots (IDs), which can be replaced by a large-scale ID, and in some low-demand areas, some oversize IDs can scale down. It is urgent to redesign their logistic networks.

One important feature of the express industry is the significant difference in the volume of E-commerce parcels in different function areas of the metropolises. For example, the number of parcels in residential areas, shopping malls, and office buildings are greater than that in recreation areas and some factory districts. The high-demand areas usually are intensively populated, leading to high housing price and less available space, while the opposite is true in the low-demand areas. Thus, in high-demand areas, express companies prefer to open large-scale IDs outside instead of small-scale IDs. Low-demand areas are on the contrary. This leads an application prospect of mixed multi-echelon (MME) network. The MME network consists of limited urban distribution centers (UDCs), several differentiated IDs, i.e., large intermediate depots (LIDs), medium intermediate depots (MIDs) and small intermediate depots (SIDs), and a large number of terminals. Different types of IDs function differently. In high-demand areas, SIDs are preferred as transshipping parcels to terminals and several LIDs are built in outer layer as sorting parcels from UDCs and transshipping them. In low-demand areas, express companies usually use MIDs to transship parcels. Therefore, parcels are first transshipped from UDCs to LIDs, then transferred to SIDs, and finally delivered to terminals in high-population-density areas, while they are transshipped from UDCs to MIDs and then delivered to terminals in low-demand areas.

A mixed multi-echelon location routing problem (MME-LRP) is proposed to redesign a high-quality logistics network where the location and the number of UDC and terminals are given. Most giant express companies possess one UDC, the location of which is known. Locations of terminals depend on characteristics of end-users, such as distance to the nearest terminal, population densities, parcel demands (Zhao et al., 2018). MME-LRP has two kinds of decisions: location and routing. Three types of IDs, i.e., LIDs, MIDs, and SIDs, should be chosen from ID candidates, where LIDs and MIDs have a joint candidate set, which means every location in the set can be used as either LID or MID, and SIDs have a separate candidate set. The problem involves three levels of vehicle routes: first-level routes from the UDC to LIDs and MIDs, second-level routes from LIDs to SIDs, and third-level routes from all types of IDs to terminals. As some terminals are close to LIDs, parcels can flow between LIDs and terminals directly. For example, in Fig. 1, square and circles are UDC and terminals, and they are predetermined. Rhombuses are joint candidate set and each one can be used as LID or MID. Triangles are seen as separate candidate set that they can only be used as SIDs. First-, second-, and third-level routes are named as primary, secondary and tertiary routes respectively. They are represented by three kinds of lines.

The main contributions of this paper are summarized as follows:

• We extend MME-LRP presented by Winkenbach et al. (2016). Winkenbach et al. (2016) put forward an MME network combining single-echelon and two-echelon, whereas our MME network is a two-echelon and three-echelon mixed network considering differentiated IDs. Three types of IDs in the MME urban logistics network perform distinct functions: LIDs undertake the sorting and transshipment functions between the UDCs and SIDs. MIDs have the same functions but work between the UDCs and terminals. SIDs are located between the LIDs and terminals as transshipment points. In the problem, LIDs and MIDs are chosen from a joint candidate set while SIDs have a separate candidate set. Several terminals are allowed to be allocated to LIDs directly.

• We put forward a hybrid heuristic algorithm based on iterated local search and intensified by path relinking (HH-ILS-PR) to solve the MME-LRP. The HH-ILS-PR extends and improves the MS-ILS + PR (Nguyen et al., 2012a) that is originally proposed to solve 2E-LRP. We design two characteristic mechanisms to exchange status between two open-type for each used joint candidate and allow direct assignment of terminals to LIDs. Moreover, we embed a new perturbation in our algorithm.

• We put forward some suggestions for express companies to redesign and optimize their urban logistics networks. In areas with large-volume parcels, it is more cost efficient to transship parcels through LIDs and SIDs successively, while in areas with small volume parcels, transshipment through MIDs is more suitable. Additionally, LIDs can cover terminals directly when these terminals are close to LIDs.

The paper is organized as follows. Section 2 briefly surveys literature on relative problem. In Section 3, the problem is described and the MILP formulation is presented. A hybrid heuristic is proposed in Section 4. The computational results are reported and analyzed in Section 5. Finally, concluding remarks are given in Section 6.