With economic depression spreading around the world, enterprises are paying great attention to supply chain management (SCM) and global logistics management.
One of the most important factors involved in implementing SCM is the efficient control of the physical flow of the supply chain. An efficient and effective logistics operation enables a company to quickly respond to a customer’s requirements and thus acquire a competitive edge over its competitors. In fact, logistics costs have a significant effect on a company’s total production and distribution costs. For example, transportation costs account for one thirds to two thirds of a company’s overall distribution cost in general. LaLonde and Zinszer (1976) showed that logistics costs account for approximately 10% of a company’s revenue, while Apte and Viswanathan (2000) argued that 30% of the final cost is incurred in the distribution process. In order to lower costs, increase profits, and improve a company’s overall performance, a well-organized and highly efficient logistics network appears to be essential.
Therefore, a Cross-docking (CD) system in the supply chain is considered to be a good method to reduce inventory and improve the responsiveness to various customer demands.
Cross-docking is the concept of keeping goods moving from the time they are received to shipping without ever storing them in a warehouse. It is also considered to be the optimal vehicle routing for the associated direct service fulfillment, subject to loading capacity and service time constraints (Sung and Song 2003). The primary objective is to avoid the inventory and handling costs; thus, ideally, no inventory is stored in the central warehouse. One of the earliest technical papers on Cross-docking systems was presented by Rohrer (1995). He stated that a successful Cross-docking system can bring companies significant benefits, including inventory reduction, low space requirements and transportation costs, increased customer responsiveness, and better control of the distribution process. Figure 1 shows the typical layout used in a Cross-docking operation. The physical flow of goods from suppliers to retailers is collaboratively optimized during both the pickup and delivery processes in order to achieve the no inventory and no delayed shipment scenario to reduce the overall transportation costs and increase customer satisfaction.
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Figure 1. A layout of the typical Cross-docking system.
This paper focuses on solving the vehicle routing problem with Cross-docking.
To effectively implement the Cross-docking system in a logistics network, the receiving (pickup) and shipping (delivery) processes must be considered at the same time. Lee et al. (2006) argued that the core issue in the pickup process is that all the routing vehicles must arrive at the Cross-docking depot simultaneously. In other words, a vehicle that returns early has to wait at the depot until all the other vehicles arrive from their pickup tasks. In addition, the amount of products arriving from suppliers has to equal to the amount of products ready to be delivered to customers from the depot. Then, through the sorting, repacking, and dispatching processes in the Cross-docking warehouse, the designated shipments are loaded on vehicles for delivery to their respective destinations. Moreover, in order to minimize the total operation time or maximize the throughput of the Cross-docking system, Yu and Egbelu (2006) studied a Cross-docking system with a temporary storage area in front of the dispatching dock. Their primary objective was to find the best truck docking sequence for both inbound and outbound trucks. Celik et.al (2009) studied ship docking facilities by using Fuzzy method to evaluate operation performance.
Because the VRPCD is a well-known non-deterministic polynomial-time hard (NP-hard) problem, applying an efficient heuristics technique is necessary in order to obtain the best or near-optimal solution within a reasonable amount of computation time. Bell and Mcmullen (2004) proposed a modified ant colony optimization (ACO) to solve vehicle routing problems and found that the proposed multi-ACO algorithm is competitive in terms of computation time, particularly when the number of customers is large. Mosheiov (1998) dealt with the pickup and delivery VRP using tour-partitioning heuristics. The goal was to obtain the optimal set of vehicle routes as well as to minimize the total traveling distance. Zachariadis et al. (2010) dealt with the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) using
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adaptive memory (AM) algorithm, which proved to be more effective and efficient than other heuristics. Furthermore, they found some new best known solutions of the numerous VRPSPD instances. Lai and Cao (2010) proposed an improved differential evolution algorithm (IDE) for solving the vehicle routing problem with simultaneous pickups and deliveries and time windows (VRP-SPDTW) and showed that the proposed method is effective for solving VRP-SPDTW. Figure 2 shows an example of the basic VRP problems with various constraints (Toth and Vigo 2001).
Figure 2. The basic VRP problems with various constraints.
In this paper, we proposed a novel algorithm, called sPSO, based on particle swarm optimization (PSO) to solve vehicle routing problems using the practical concept of Cross-docking in logistics networks. PSO is a newly developed evolutionary meta-heuristics in the field of swarm intelligence. It was introduced by Kennedy and Eberhart (1995) based on observations of a simplified social model for bird flocks. Shi and Eberhart (1998a; 1998b) introduced a newer version of PSO by adding an inertia weight, W, to the original PSO equation. The authors argued that this inertia weight plays a role in balancing between local search and global search.
Furthermore, they proved that a PSO with average inertia weight values ranging from 0.9 to 1.2 generates a better performance. On the other hand, a discrete binary version of the PSO was presented by Kennedy and Eberhart in 1997. The concept of the PSO function remains the same, except that the trajectories are changed in terms of probability. Lately, MirHassani and Abolghasemi (2011) applied the pure PSO algorithm to solve for open vehicle routing problem, while Marinakis, and Marinaki (2010) combined the genetic algorithm and the PSO Algorithm together into a hybrid model for the vehicle routing problem.
This paper is organized as follows. Section 2 presents the problem formulation.
The procedure for the sPSO algorithm is described in Section 3. Section 4 shows the
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computational experiments and provides an analysis of the results. Section 5 concludes the paper with a summary.