Optimizing emissions control investments in inventory systems for imperfect items with quantity discounts: a case study in refrigerator retailing

Emissions reduction strategies are essential for sustaining both economic competitiveness and environmental responsibility. This study develops an optimization model for inventory management in Bangladesh’s refrigerator retail sector, integrating profitability with sustainability objectives. The proposed model uniquely incorporates defective items, bulk purchase discounts, and multiple carbon regulation schemes, namely carbon tax (CT), cap-and-trade (CAT), cap-and-price (CAP), and carbon offset (CAO). It determines the optimal replenishment cycle and investment level in emissions control technologies that maximize annual profit under regulatory constraints. The inventory system is formulated as a constrained nonlinear optimization problem and is analytically solved using Karush-Kuhn-Tucker (KKT) conditions to obtain closed-form solutions. A customized algorithm is developed to identify the global optimum under an all-units discount (AUD) pricing scheme. A case study based on realistic parameters from the Bangladeshi refrigerator market validates the proposed model. Sensitivity analyses reveal that holding costs and transportation fuel consumption significantly influence both profit and emissions. Green investments improve performance under strict regulatory environments; however, diminishing returns indicate inherent technological limitations. Notably, a 50% reduction in holding costs increases profit by 2.72% and extends the optimal cycle by 29.42%. The findings underscore the importance of advancing green technologies and aligning inventory policies with environmental objectives.