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<p>This study presents a joint economic lot size model for a single manufacturer-a single buyer mathematical programming problem for a two-level supply chain (vendor–buyer). This study develops an economic lot size model that incorporates greenhouse gas (GHG) penalties, addressing the complexities of managing imperfect items and partial backlogging. The proposed model integrates environmental considerations into supply chain decision-making by accounting for emissions-related costs, including penalties for exceeding permissible GHG limits. This paper makes a significant contribution to the inventory and sustainable supply chain literature by integrating, for the first time, all four key dimensions frequently studied separately: imperfect items, partial backlogging, screening/inspection, and greenhouse gas (GHG) emissions. The analysis explores the interplay between production quantities, defect rates, and backlogging levels, offering insights into how environmental regulations impact operational efficiency and cost structures. Based on the vendor's production rate, greenhouse gas emissions are assumed to be a function of vendor production rate. We have developed a vendor/buyer integrated inventory system which represents a production framework creating things of perfect and also defective quality product. A model developed for the purpose of minimizing the total supply chain cost is based on the determination of the optimal production rate (subsequently the joint lot sizing policy), taking into account the requirements for emission certification, penalties for exceeding the emission quota, and the capital investment required to increase the emission limit by purchasing new certificates. Numerical experiments demonstrate the model’s effectiveness in reducing both total costs and GHG emissions, offering practical insights for firms aiming to adopt greener practices in inventory management. Numerical examples are provided to demonstrate the model's applicability and the effects of varying GHG penalties on inventory and production decisions. The findings underscore the importance of integrating sustainability measures into traditional inventory models, enabling businesses to balance economic objectives with environmental responsibilities.</p>

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Greenhouse gas penalty for a supply chain inventory model with imperfect items and partial backlogging

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Rinki Chaudhary,
  • Shrestha Pundir

摘要

This study presents a joint economic lot size model for a single manufacturer-a single buyer mathematical programming problem for a two-level supply chain (vendor–buyer). This study develops an economic lot size model that incorporates greenhouse gas (GHG) penalties, addressing the complexities of managing imperfect items and partial backlogging. The proposed model integrates environmental considerations into supply chain decision-making by accounting for emissions-related costs, including penalties for exceeding permissible GHG limits. This paper makes a significant contribution to the inventory and sustainable supply chain literature by integrating, for the first time, all four key dimensions frequently studied separately: imperfect items, partial backlogging, screening/inspection, and greenhouse gas (GHG) emissions. The analysis explores the interplay between production quantities, defect rates, and backlogging levels, offering insights into how environmental regulations impact operational efficiency and cost structures. Based on the vendor's production rate, greenhouse gas emissions are assumed to be a function of vendor production rate. We have developed a vendor/buyer integrated inventory system which represents a production framework creating things of perfect and also defective quality product. A model developed for the purpose of minimizing the total supply chain cost is based on the determination of the optimal production rate (subsequently the joint lot sizing policy), taking into account the requirements for emission certification, penalties for exceeding the emission quota, and the capital investment required to increase the emission limit by purchasing new certificates. Numerical experiments demonstrate the model’s effectiveness in reducing both total costs and GHG emissions, offering practical insights for firms aiming to adopt greener practices in inventory management. Numerical examples are provided to demonstrate the model's applicability and the effects of varying GHG penalties on inventory and production decisions. The findings underscore the importance of integrating sustainability measures into traditional inventory models, enabling businesses to balance economic objectives with environmental responsibilities.