Optimal order quantity integrating operations and carbon emission costs in production delivery supply chain

Abstract

This thesis develops a mathematical model that incorporate both the operational and the carbon emission costs to find the optimal order quantity (Q) in a production-delivery supply chain. In this model the order quantity (Q) is set equal to α (a real positive multiplier) times the demand (D). We derive a formula by applying the calculus method of differentiation for determining the optimal order quantity (Q). For an illustrated numerical example problem, the optimal α value is found to be as 0.1290, along with the optimal order quantity (Q) of 12,900 units and the minimum annual total cost of 970,057.23 BDT (total operational cost of 886,453.31 BDT plus carbon emission costs of 83,603.92 BDT). A sensitivity analysis shows that the optimal order quantity and the total supply chain cost including operational and carbon emission costs respond to adjustment of the demand, production rate and other operational parameters. This model has the capability of helping organizations in making eco-friendly business choices leading to better sustainable practices. The result highlights the importance of integrating environmental attentions with operational efficiency in supply chain management. This research presents an actionable recommendation to optimize the order quantity (Q) by minimizing the total cost of managing operations together with the reduction in carbon emission, which in turn measures for creating effective and environmentally responsible supply chain operations. The research findings enhance both theoretical understanding of sustainable supply chain optimization and its practical applications.