Journal of Quality Engineering and Production Optimization

Journal of Quality Engineering and Production Optimization

A robust fuzzy stochastic programming model for a dual-channel closed-loop supply chain network design with delivery lead-time sensitive customers and price-dependent uncertain demands

Articles in Press

Document Type : Research Paper

Authors
Behnam Afsharpour
Azizolah Jafari
Department of Industrial Engineering, Faculty of Engineering, University of Science and Culture, Tehran, Iran
10.22070/jqepo.2026.21219.1315
Abstract
The number of customers who want to make purchases online is growing daily due to the Internet's expanding functionality and e-commerce developments. This study offers a mixed integer programming approach for developing a reliable dual-channel closed-loop supply chain network with hybrid uncertainties. The model attempts to maximize overall profit. In this study, it is considered that customer demand in the offline sales channel depends on the price offered by offline retailers. Additionally, it is considered that customer demand via the online channel is influenced by the lead-time for product delivery. The hybrid uncertainties in the problem data were addressed here by utilizing a robust fuzzy stochastic programming optimization approach found in the present research literature. The numerical calculations demonstrate the accuracy of the model and the proposed solution method. Significant findings are obtained from sensitivity analyses of essential parameters. Outcomes indicate that the value of the objective function declines when the minimum level of satisfaction of the uncertainty parameters increases. Furthermore, as the delivery lead-time rises from 0.1 to 0.6, the objective function increases by 24% and 25% at the minimum satisfaction levels of 0.6 and 0.8, respectively. Additionally, the results show that by increasing the number of price levels from 3 to 10, the objective function increases by 2.5% and 2.6% at the minimum satisfaction levels of 0.6 and 0.8, respectively.
Keywords
Closed-loop supply chain
Delivery lead-time
Dual-channel
Pricing
Uncertainty
Journal of Quality Engineering and Production Optimization

Articles in Press, Accepted Manuscript
Available Online from 01 July 2026