An integrated fuzzy production inventory model for manufacturer-retailer coordination under simple carbon tax system

This paper develops twin models towards integrated production inventory planning for manufacturer-retailer ecosystem in a sustainable supply chain setup. Decision-making models are developed in fuzzy environment and under purview of carbon taxation system. Novel conception of Fermatean fuzzy numbers is introduced for handling parameters imprecision. The first model addresses planning problem without considering green investments, whereas the second one additionally identifies optimal green investments for each player of ecosystem. Models are formulated as nonlinear optimization problems with objective of maximizing profit. Comparison of results from both models enables decision-makers to figure out the profitability of green investment option. Numerical instance with data from the existing literature is solved using Mathematica 12.1. Computational results for studied case report profitability of green investments for supply chain partners and significant reduction in carbon emissions as well. Variation analysis demonstrates stability of the proposed model. Developed models equip small-scale retailer-manufacture tie-ups prevalent in developing economies for discussed decisions.