IJE TRANSACTIONS C: Aspects Vol. 27, No. 12, (December 2014) 1897-1906 Please cite this article as: H.R. Kamali, A. Sadegheih, M.A. Vahdat-Zad, H. Khademi-Zare, Deterministic and Metaheuristic Solutions for Closed- loop Supply Chains with Continuous Price Decrease, International Journal of Engineering (IJE), TRANSACTIONS C: Aspects Vol. 27, No. 12, (December 2014) 1897-1906 International Journal of Engineering Journal Homepage: www.ije.ir Deterministic and Metaheuristic Solutions for Closed-loop Supply Chains with Continuous Price Decrease H. R. Kamali*, A. Sadegheih, M. A. Vahdat-Zad, H. Khademi-Zare Department of Industrial Engineering, University of Yazd, Yazd, Iran PAPER INFO Paper history: Received 28 February 2014 Received in revised form 11 May 2014 Accepted 14 August 2014 Keywords: Closed-loop Supply Chain Continuous Price Decrease NP-hard Metaheuristic ABSTRACT In a global economy, an efficient supply chain as the main core competency empowers enterprises to provide products or services at a right time in a right quantity, and at a low cost. This paper is to plan a single-product, multi-echelon, multi-period closed-loop supply chain for high-tech products (which have continuous price decrease). Ultimately, considering components ralated to procurement, production, distribution, recycling and disposal, the final decisions are made. To solve the mixed integer linear programming model for closed-loop supply chain network plan of the paper, four heuristics-based methods including genetic algorithm, particle swarm optimization, differential evolution, and artificial bee colony are proposed. Finally, the computational results of these four methods are compared with the solutions obtained by GAMS optimization software. The solution reveales that the artificial bee colony methodology works well in terms of quality of solutions. doi: 10.5829/idosi.ije.2014.27.12c.13 1. INTRODUCTION 1 Supply chain (SC) is a result of linking different operational parts in which suppliers lie at the beginning and customers at the end. A SC points to the flow of materials, information, cash, and services from raw material suppliers to workshops and warehouses and finally to customers. It includes processes and organizations that create products, information, and services and delivers them to consumers. A closed-loop supply chain (CLSC) is a SC that has some extra parts for collecting returned products from customers, recycling and reusing them to produce new products. Nowadays, CLSC management is one of the topics discussed in the area of industrial management. It has been taken into consideration by industry owners for their vehement tendency to decrease costs, establish ever-increasing interaction among producers, suppliers 1 *Corresponding Author’s Email: hrk1357@gmail.com (H. R. Kamali) and distributers at various levels, and create more and more SCs as well as CLSCs for different products. The methods that have been used for SC or CLSC optimizing are also various. Analytical methods, such as branch and bound, present optimal solutions, but their performance highly declines by the increase in the dimensions of problems. Some other analytical methods are used only for certain problems in special conditions [1, 2]. Simulation of dynamic systems is a method that forecasts the behavior of a model by changing its parameters [3]. Heuristic methods provide approximate solutions to problems, and they usually have a simple structure and short running time [4]. Using metaheuristic algorithms is another way to optimize a SC or CLSC. These methods have a general structure and can be matched with different problems. They do not guarantee to make optimal solutions, but they usually find optimal or near optimal solutions. For example, some metaheuristic algorithms used for SC or CLSC optimization are genetic algorithm [5], differential evolution [6] and simulated annealing [7].