Parametric Optimization of an Interval Sustainable Supply Chain with Green–Thermal-Linked Demand Rate

This work aims to study the optimal policy of a sustainable supply chain problem under interval uncertainty. In this chain, the customers’ demand is fluctuated within an interval and its rate is shaped by three factors: the selling price, green level, and heat-resistance efficiency. To handle this fluctuation, all interval-valued demand parameters and cost components are presented in a parametric form. And this leads to the building of imprecise profit functions in parametric form for both the centralized and decentralized scenarios of the supply chain. This work differs from existing interval-valued models by jointly incorporating green-level and heat-resistance-dependent demand within a parametric optimization framework. Now, the core research question of this study is as follows: how can one find the optimal policy of the system under imprecise parametric settings? To answer this question, this work introduces a new optimization technique, named parametric optimization, to study the optimal policy of the imprecise parametrized profits of different scenarios of the system. Using this parametric optimization technique and game-theoretic approach, the formulae for finding optimal values of decision variables along with optimal profits in all scenarios are obtained. Then, numerical examples are provided to demonstrate the optimal policy of the proposed model. Finally, a post-optimality analysis is performed to examine the effects of variations in key system parameters on optimal policies of the system. This research offers practical insights to study how the supply chain’s partners can navigate uncertainty by meeting sustainability goals.