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<p>This study develops a centralized three echelon open loop supply chain optimization model that integrates circular input adoption with coordinated pricing and cooperative advertising decisions. In the proposed setting, recycled materials and usable components are supplied through an external recycling market and become available for procurement by supply chain members as circular inputs. Circularity is represented through echelon specific circular input utilization decision variables at the supplier, manufacturer, and retailer levels, allowing the model to capture the economic and demand side effects of circular input adoption under market availability constraints. Customer demand is formulated as a function of selling price, cooperative advertising effort, and average circular input utilization, thereby linking market response with sustainability oriented operational decisions. Key cost parameters are modeled as triangular fuzzy numbers and transformed into crisp equivalents using the signed distance method. The resulting nonlinear constrained optimization problem maximizes total supply chain profit subject to advertising budget, inventory capacity, recycled input availability, and circularity related feasibility constraints. Sequential Quadratic Programming is used as the main solution approach and is compared with genetic algorithm, pattern search, and minimax methods. The numerical results show that the SQP based solution achieves the highest profit while maintaining feasible and balanced decision values across pricing, advertising, and circular input utilization variables. Sensitivity analysis further indicates that profitability is most affected by recycled input availability and circular cost adjustment, while incentive strength provides a secondary but consistent improvement. The proposed framework provides a quantitative decision support tool for firms seeking to coordinate pricing, advertising, and circular input adoption decisions while maintaining profitability under realistic market and policy conditions.</p>

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Mathematical modeling and optimization of a three-echelon supply chain management by incorporating circular consumption, cooperative advertisement cost, and selling price decisions

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  • 出版模式：

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  • 发表日期：

    2026年6月19日

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  • Mohammed AlKahtani

摘要

This study develops a centralized three echelon open loop supply chain optimization model that integrates circular input adoption with coordinated pricing and cooperative advertising decisions. In the proposed setting, recycled materials and usable components are supplied through an external recycling market and become available for procurement by supply chain members as circular inputs. Circularity is represented through echelon specific circular input utilization decision variables at the supplier, manufacturer, and retailer levels, allowing the model to capture the economic and demand side effects of circular input adoption under market availability constraints. Customer demand is formulated as a function of selling price, cooperative advertising effort, and average circular input utilization, thereby linking market response with sustainability oriented operational decisions. Key cost parameters are modeled as triangular fuzzy numbers and transformed into crisp equivalents using the signed distance method. The resulting nonlinear constrained optimization problem maximizes total supply chain profit subject to advertising budget, inventory capacity, recycled input availability, and circularity related feasibility constraints. Sequential Quadratic Programming is used as the main solution approach and is compared with genetic algorithm, pattern search, and minimax methods. The numerical results show that the SQP based solution achieves the highest profit while maintaining feasible and balanced decision values across pricing, advertising, and circular input utilization variables. Sensitivity analysis further indicates that profitability is most affected by recycled input availability and circular cost adjustment, while incentive strength provides a secondary but consistent improvement. The proposed framework provides a quantitative decision support tool for firms seeking to coordinate pricing, advertising, and circular input adoption decisions while maintaining profitability under realistic market and policy conditions.