Multi-objective optimization of location and distribution in a closed-loop supply chain by considering market share in competitive conditions

Document Type : Research Paper


1 Industrial Engineering Department, Faculty of Engineering, University of Isfahan, Isfahan, Iran

2 Department of Industrial Engineering, Arak University, Arak, Iran


Development of supply chains is one of the practical concepts in the field of production and sales in competitive conditions. Accordingly, it is necessary to properly study the competitive conditions in which supply chain networks can be designed. In this regard, the present research contributes to the field by incorporating the market share and customer satisfaction to the competitive conditions of supply chains. For this purpose, a nonlinear mathematical model is presented in order to find locations and perform distributions in a closed-loop supply chain under competitive conditions. This model has two objectives including profit maximization and market share maximization. To solve the model, LP-metric and goal programming are implemented, and then the results of these two methods are discussed. Comparisons are also made in terms of the value of the objective functions as well as the solution time. Finally, the simple weighted sum method is used to select the superior method. The results show that the LP-metric method is worth performing to solve the mathematical model of the research.


Aghighi, A., Goli, A., Malmir, B., and Tirkolaee, E. B. (2021). The stochastic location-routing-inventory problem of perishable products with reneging and balking. Journal of Ambient Intelligence and Humanized Computing, pp. 1-20.
Alinaghian, M., Tirkolaee, E. B., Dezaki, Z. K., Hejazi, S. R., and Ding, W. (2021). An augmented Tabu search algorithm for the green inventory-routing problem with time windows. Swarm and Evolutionary Computation, Vol. 60, pp. 100802.
Amin, S. H., and Zhang, G. (2013). A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Applied Mathematical Modelling, Vol. 37(6), pp. 4165-4176.
Amiri, A. S., Torabi, S. A., and Ghodsi, R. (2018). An iterative approach for a bi-level competitive supply chain network design problem under foresight competition and variable coverage. Transportation research part E: Logistics and transportation review, Vol. 109, pp. 99-114.
Aryanezhad, M. B., Jabbarzadeh, A., and Zareei, A. (2009, December). Combination of genetic algorithm and LP-metric to solve single machine bi-criteria scheduling problem. IEEE International Conference on Industrial Engineering and Engineering Management (pp. 1915-1919). IEEE.
Chen, L., Peng, J., and Zhang, B. (2017). Uncertain goal programming models for bicriteria solid transportation problem. Applied Soft Computing, Vol. 51, pp. 49-59.
Deb, K. (2014). Multi-objective optimization. In Search methodologies (pp. 403-449). Springer, Boston, MA.
Dhiman, G., and Garg, M. (2020). MoSSE: a novel hybrid multi-objective meta-heuristic algorithm for engineering design problems. Soft Computing, Vol. 24(24), pp. 18379-18398.
Ghavamifar, A., Makui, A., and Taleizadeh, A. A. (2018). Designing a resilient competitive supply chain network under disruption risks: A real-world application. Transportation Research Part E: Logistics and Transportation Review, Vol. 115, pp. 87-109.
Goli, A., Tirkolaee, E. B., Malmir, B., Bian, G. B., and Sangaiah, A. K. (2019). A multi-objective invasive weed optimization algorithm for robust aggregate production planning under uncertain seasonal demand. Computing, Vol. 101(6), pp. 499-529.
Govindan, K., Soleimani, H., and Kannan, D. (2015). Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future. European journal of operational research, Vol. 240(3), pp. 603-626.
Kannan, G., Sasikumar, P., and Devika, K. (2010). A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling. Applied mathematical modelling, Vol. 34(3), pp. 655-670.
Kaya, O., and Urek, B. (2016). A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain. Computers & Operations Research, Vol. 65, pp. 93-103.
Khakbaz, A., and Babaee Tirkolaee, E. (2021). A sustainable hybrid manufacturing/remanufacturing system with two-way substitution and WEEE directive under different market conditions. Optimization, pp.1-24.
Mahmoodi, M. (2019). A new multi-objective model of agile supply chain network design considering transportation limits. Production & Manufacturing Research, Vol. 7(1), pp. 1-22.
Pahlevan, S. M., Hosseini, S. M. S., and Goli, A. (2021). Sustainable supply chain network design using products’ life cycle in the aluminum industry. Environmental Science and Pollution Research, pp. 1-25.    
Talaei, M., Moghaddam, B. F., Pishvaee, M. S., Bozorgi-Amiri, A., & Gholamnejad, S. (2016). A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry. Journal of Cleaner Production, Vol. 113, pp. 662-673.
Tirkolaee, E. B., Abbasian, P., and Weber, G. W. (2021). Sustainable fuzzy multi-trip location-routing problem for medical waste management during the COVID-19 outbreak. Science of the Total Environment, Vol. 756, pp. 143607.
Wang, J., Wang, X., and Yu, M. (2020). Multi-period multi-product supply chain network design in the competitive environment. Mathematical Problems in Engineering, in press.
Wei, J., Govindan, K., Li, Y., and Zhao, J. (2015). Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information. Computers & operations research, Vol.54, pp. 257-265.
Wei, J., Govindan, K., Li, Y., and Zhao, J. (2015). Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information. Computers & operations research, Vol.54, pp. 257-265.
Zohal, M., and Soleimani, H. (2016). Developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry. Journal of Cleaner Production, Vol. 133, pp. 314-337.