A closed-loop logistic model with a spanning-tree based genetic algorithm

Abstract

Due to the problem of global warming, the green supply chain management, in particular, closed-loop logistics, has drawn the attention of researchers. Although there were logistics models that were examined in the literatures, most of them were case based and not in a closed-loop. Therefore, they lacked generality and could not serve the purposes of recycling, reuse and recovery required in a green supply chain. In this study, the integration of forward and reverse logistics was investigated, and a generalized closed-loop model for the logistics planning was proposed by formulating a cyclic logistics network problem into an integer linear programming model. Moreover, the decisions for selecting the places of manufactories, distribution centers, and dismantlers with the respective operation units were supported with the minimum cost. A revised spanning-tree based genetic algorithm was also developed by using determinant encoding representation for solving this NP model. Numerical experiments were presented, and the results showed that the proposed model and algorithms were able to support the logistic decisions in a closed-loop supply chain efficiently and accurately.

Statement of scope and purposes

This study concerns with operations of 3R in the green supply chain logistics and the location selection optimization. Based on ‘cradle to cradle’ principle of a green product, a “closed-loop” structure of a network was proposed in order to integrate the environmental issues into a traditional logistic system. Due to NP-hard nature of the model, a Genetic Algorithm, which is based on spanning tree structure was developed. Test problems from the small size for accuracy to the large scale for efficiency have been demonstrated with comparison. The promising results have shown the applicability of the proposed model with the solution procedure.

Introduction

Due to the awareness of the environmental protection, how to reduce the utilization of the materials by reusing and remanufacturing the used products has been a critical issue for an enterprise. This induces the concept of the green supply chain management and has led to a problem of the closed-loop supply chain management. Different from a conventional supply chain, planning a green supply chain requires an additional function of recycling and thus, a closed-loop chain is a necessary infrastructure for a material flow. Then, with well-managed reverse logistics, 3R of reduce, recovery and reuse for the environmental protection can be achieved with cost savings in the procurement, the disposal and the transportation [19].

Technically, the closed-loop logistics comprises two parts: forward logistics and reverse logistics. For the forward logistics, as a conventional logistics, after manufactory, the distributors will deliver the final products to the customers to satisfy their demands and the position of the customers is typically the end of the process. For the reverse logistics, the flow of used products is processed from the customers back to the dismantlers to do the sorting or disassembling for recovery, reuse or disposal [3], [15], [23], [26], [29]. The closed-loop logistics management is to ensure the least waste of the materials by following the Conservation Law along the life cycles of the materials.

Generally speaking, for a network planning problem, there are three issues needed to be considered: the validity of the model, the efficiency of the solution and the applicability. For a closed-loop logistics problem, the status quo of these issues can be summarized as follows:

• For modeling: Most of the studies only discussed the reverse logistics model. Some studies have proposed the closed-loop models, but the loops were considered as a “prolonged supply chain” by lacking of the relation between forward and reverse flows [9], [28], [31]. Therefore, instead of sharing the same capacity, the models often assumed the unlimited capacities for the reverse logistics or did not state the relation between forward and reverse flows, which are not valid for representing the real situations.

• For applications: Because of the assumed unlimited capacities for the facilities of distribution centers or dismantlers in the reverse logistics, it has resulted in unrealistic route design for the used materials from the customers for recovery, reused or disposal [25].

• For solutions: A logistics planning problem with the location selection is an NP-hard problem [8], [14], [18], [30]. Efficient solution procedure remains a challenge for researchers and practitioners.

To cope with these issues, in this study, we shall investigate the features and purposes of a green logistics management and in particular, the difference of a “prolonged supply chain” and a closed-loop supply chain for green products. Based on the findings, we shall develop a comprehensive green logistics model to support decisions of facility locations and material flows through a closed-loop capacitated supply chain when the realistic applications of 3R green materials logistics are expected with minimum total cost. Furthermore, an efficient algorithm will be developed and evaluated.

After the literature review of closed-loop logistics and Genetic Algorithms in Section 2, a mathematical model for closed-loop logistics will be proposed with the specification of its properties in Section 3. Estimation of its complexity will be done with numerical illustrations. In 4 Revised spanning-based genetic algorithm, 5 Evaluation of the algorithm, a revised spanning-tree based genetic algorithm is proposed to resolve this model, which is evaluated using large-scale problems. Finally, in Section 6, the conclusion will be drawn.