Bi-objective optimization modeling of a three-level supply chain in production planning and scheduling considering price-dependent demand: a case study of a soap factory

Effective competition in the manufacturing industry requires careful planning and scheduling of production activities, commonly referred to as production planning and scheduling (PPAS). Furthermore, today, all organizations are striving to preserve the environment and improve the climate by reducing greenhouse gas emissions. This study presents a bi-objective mathematical model for a three-level supply chain. The primary objective of the model is to maximize profit, while the secondary objective is to minimize greenhouse gas emissions. By adopting this model, companies can strive towards achieving their business goals while simultaneously contributing to a sustainable future. Numerical experiments demonstrate the applicability of the developed model, and a case study in a soap factory is presented to calculate the optimal production quantities and determine the best price to increase demand while achieving profit. Finally, by conducting sensitivity analysis, optimal strategic decisions and useful management insights have been identified. According to the results and examination of the experiments, expanding the capacity and production rate, especially when the market potential for buying products is higher, fulfills the main goals. Also, in times of market recession, the variety of quality and price of products will lead to more profit.