The use of outsourced logistics services is currently quite significant and still increasing worldwide, which gives logistics service providers a great opportunity to make more profit while at the same time confronting them with fiercer competition than ever before. According to the Thirteenth Annual (2008) Third-Party Logistics Study, domestic transportation has turned out to be the most frequently outsourced activity that mainly includes forward distribution and reverse collection. Therefore, the main goal of this study is to develop innovative routing strategies that optimally integrate forward distribution and reverse collection to help logistics service providers reduce their operating costs and thereby enhance their market competitive power to reap additional profits.
The problem of simultaneously handling forward distribution and reverse collection can be basically viewed as a routing problem with pickups and deliveries. As indicated in Nagy and Salhi (2005), there are three main routing strategies involving pickups and deliveries in real life: (1) mixed pickups and deliveries; (2) simultaneous pickups and deliveries; and (3) delivery first, pickup second. The routing strategy of simultaneous pickups and deliveries serves the pickup and delivery in relation to a customer at the same time. In the mixed pickup and delivery strategy, the pickups and deliveries can, however, occur in any sequence on a vehicle path. On the other hand, the strategy of delivery first, pickup second allows vehicles to pick up goods only after they have finished delivering all of the cargo. In the case where all three strategies are applicable, while some of them may not be allowed in reality, it is not difficult to verify that the routing strategy of mixed pickups and deliveries is the best among the three possible strategies. Therefore, this paper focuses on the mixed routing strategy of optimally integrating forward distribution and reverse collection. Forward distribution deals with delivering goods to demand points, and reverse collection is responsible for the picking up of previously shipped products from collection points for possible remanufacturing, recycling, or disposal. The need to handle such operations is quite common in many industries and countries; nonetheless, there exist very few related studies in the literature.
In this study, the integrated routing problem is formulated as the mixed pickup-delivery asymmetric traveling salesman path problem (mixed-PDATSPP). It is noted that since return items are usually collected and brought back to a returns processing center that is different from the depot, we thus deal with a 'path-type' instead of a 'circuit-type' routing problem. It has been pointed out that the asymmetric traveling salesman path problem (ATSPP) is NP-hard (Chekuri and Pál, 2007). It follows that the mixed-PDATSPP is also NP-hard, as it generalizes the ATSPP arising when the set of pickup customers or delivery customers is empty. Therefore, the aims of this research are to first model the mixed-PDATSPP, and then propose an efficient and effective heuristic solution technique to the problem.
To show that our proposed algorithm can apply to real-life settings, we consider a daily truck delivery routing problem faced by 7-Eleven, the largest convenience store in Taiwan. The numerical results show that our proposed algorithm can effectively and efficiently solve the mixed-PDATSPP. In addition, the proposed algorithm is robust in terms of both computational time and solution quality.
The remainder of this paper is organized as follows: Section 2 defines the mixed-PDATSPP; Section 3 describes the network-transformation procedures for constructing the network used to define the mixed-PDATSPP; Section 4 discusses the related problems in the literature; Section 5 details the mathematical model of the mixed-PDATSPP; Section 6 explains how we develop the solution algorithm to the mixed-PDATSPP; Section 7 contains numerical results to evaluate the algorithm's performance and illustrate its characteristics; and, finally, Section 8 concludes the paper.