A multi-path routing-inventory problem for a closed-loop supply chain considering the heterogeneous fleet of vehicles

ABSTRACT

In this paper, the inventory-routing problem is studied for a closed-loop supply chain. This closed-loop supply chain considers suppliers, manufacturers, whole-sellers, and disposal centers. To formulate this problem, a mixed integer linear programming model is proposed. This mathematical model minimizes the total costs of the supply chain, including the fixed and variable costs of vehicles, and holding inventory costs of final products and scraps. The proposed model considers the road roughness degree, multi-path setting and the heterogeneous fleet of vehicles, which increases its flexibility and the quality of solutions. Then, two symmetry-breaking constraints are proposed to reduce the complexity of the mathematical model. In order to evaluate the integrity of the proposed model, 20 instances of different sizes are randomly generated and solved. Finally, a comprehensive sensitivity analysis is conducted with respect to five key features of the problem, such as the impact of the symmetry-breaking constraints on the CPU time, multi-path setting, fixed cost of vehicles, heterogeneous fleet of vehicles, and lost sales. The results indicate that the consideration of multi-path setting and the heterogeneous fleet of vehicles improves the quality of solutions significantly.

KEYWORDS:

• Closed-loop supply chain
• inventory control
• vehicle routing problem
• heterogeneous fleet of vehicle
• multi-path

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Amirhossein Moosavi

Amirhossein Moosavi has received his MSc and BSc from the IAU Karaj Branch at Industrial Engineering. He has published some papers in some of the most reputable journals of Management Science, like Computers & Industrial Engineering. His interest research area consists of the applications of operations research, scheduling, supply chain management, healthcare decision-making and heuristic/metaheuristic algorithms.

Adel Nikfarjam

Adel Nikfarjam got his BSc in industrial Engineering at the Azad University of Qazvin (QIAU); in addition, he got his MSc in Industrial Engineering at the IAU Karaj Branch. His research interests are Supply Chain, Inventory management, and Transportation. At the present time he is an employee in a Private Company.