A pollution-sensitive multistage production-inventory model for deteriorating items considering expiration date under Stackelberg game approach

In this study, we formulate a multilayer sustainable production-inventory supply chain (SC) model with deterioration and pollution. The SC members are the supplier of raw materials, the producer (vendor/manufacturer) and the retailer. The demand rate of the items follows a comprehensive function of the unit selling price and freshness (related to expiration dates) function at the retailer's shop. Considering a case study, a multi-layer SC model has been studied with the help of the inclusion of a new pollution function. Basically, the manufacturer's and retailer's individual nonlinear average profit functions have been analyzed under various parametric conditions. The retailer's profit function has been optimized with the help of convexity/concavity criteria over Hessian matrix and eigenvalue characterization theorem. With the help of a new solution algorithm via Stackelberg game approach, we obtain the optimal decisions of the supply chain also. Finally, numerical illustrations, sensitivity analysis and graphical illustrations are made to validate the proposed model.

Automated summary

In this study, a multilayer sustainable production-inventory supply chain model is proposed, taking into account deterioration and pollution factors. Through a case study and numerical illustrations, the model is validated and shown to be significant in optimizing the economic benefits of various stages in the supply chain.