Developing a two-stage model for a sustainable closed-loop supply chain with pricing and advertising decisions. (1st August 2021) - Khorshidvand, Behrooz
Abstract: Closed-Loop Supply Chain (CLSC) has become a critical problem due to its effects on various factors including economic motivations, environmental concerns, and social impacts. Moreover, there are coordination tools, such as pricing and advertising, which impact its performance. In this paper, we offer a two-stage approach to model and solve a sustainable CLSC, taking into account pricing, green quality, and advertising. In the first stage, optimal decisions on pricing, greening, and advertising are made, while in the second stage, a fuzzy multi-objective Mixed Integer Linear Programming (MILP) model is used to maximize the total profit, reduce CO2 emissions, and improve social impacts. Suitable solution methods are introduced according to the scale of the problem. For small-scale instances, an augmented ϵ-constraint method is used to solve the problem. For large-scale instances, approximations are required, and a Lagrangian relaxation algorithm solves the problem in polynomial time. The performance of the proposed model is evaluated through various numerical examples. The results illustrate the applicability and efficiency of the model, while confirming significant improvements in sustainable objectives under optimal pricing, green quality, and advertising. Besides, the proposed Lagrangian relaxation method significantly reduces the computational time for large-scale instances, with only a 2.308% deviation from the optimal results. Graphical abstract: Investigated CLSC network overview. Image 1 Highlights: The new two-stage modeling of a sustainable closed-loop supply chain is proposed. A new demand function using price, greenness, and advertisement is extended. Multi-objective programming for sustainable objectives is utilized. Fuzzy logic is incorporated to model missed workdays and green quality. Lagrangian relaxation algorithm decreases the computational time significantly.