Mathematical Modeling on Sustainable Supply Chain Management with Controllable Carbon Emission

Abstract

To achieve a sustainable supply chain‚ a mathematically-based inventory model is proposed by incorporating green products‚ investment in conservation‚ and the impact of carbon tax policies‚ and demand of the product is conceived in terms of market potential‚ pricing policies‚ and environmentally sustainable consumption of the product․ The model is general enough to recognise the perishability of items‚ use the investment in preservation technology variable to balance the loss rate and environmental cost‚ recognise conditions under which shortages are expected in the horizon period and allow the backlogging of items in part‚ which helps in realworld application․ The objective of the proposed inventory systems is to minimise the total cost of the system․ The total cost includes the cost of ordering‚ brining‚ holding‚ purchasing‚ shortage‚ lost sales‚ preservation investments‚ and carbon emissions․ The environmental sustainability‚ technologies for conservation‚ and timing of the shortage are the variables to be modelled․ The mathematical model is based on the application of inventory differential equations‚ costs and optimization with first-order and second-order conditions․ The inventory is the central focus of the paper․ The variables are supply‚ demand and price of environmental sustainability and conservation technologies․ The optimality of the model is proved by the calculation of the Hessian matrix‚ and the validity of the proposed model is illustrated by a numerical example․ A sensitivity analysis is presented in the end to see the influence of the main parameters on the total cost․ Furthermore‚ the study establishes that investments in preservation and cost of green products can lessen damage and carbon emissions․ Besides this‚ the costs of ordering‚ holding‚ deterioration rate‚ cycle length and selling price are the main factors determining the optimal total cost․ The research contributes to sustainable supply chain management by introducing a mathematical model that factors in cost optimisation constraints‚ a carbon tax regulatory framework‚ green initiatives and preservation technology investments․