A Supply Chain Inventory Model for a Deteriorating Material under a Finite Planning Horizon with the Carbon Tax and Shortage in All Cycles

Abstract

We have framed an inventory replenishment model under a finite planning horizon in which replenishment cycle time and replenishment cycle length are different and don’t repeat. The finite planning horizon for different replenishment times and cycle lengths is a real-life scenario. Nowadays, every manufacturing industry wants to achieve maximum profit at a low cost. It is very difficult to maintain the optimal level of inventory, total cost, replenishment time, and replenishment cycle. Along with the health of people, increasing carbon emission also has a dangerous effect on today’s business environment. Therefore, this article analyses an optimal inventory replenishment policy and carbon emission due to deteriorating material and refrigeration while taking into account time, emission-dependent, and inventory-dependent quadratic demand. Materials deterioration affects a large and varied spectrum of business. Therefore, Material that suffers deterioration is considered. Shortage, some lost sales, and partial backlogging are also considered. Backlogging is dependent on the frequency of the waiting period for the next replenishment over a given finite time horizon and fluctuating replenishment cycle. The model has been developed theoretically. Also, a mathematical formulation has been obtained to find the optimal solution to the problem. Following the algorithm, a numerical illustration and a comparative evaluation are explained, along with a sensitivity analysis of each parameter. The tabular and graphical representations of sensitivity analysis were addressed using the Mathematica application version 12.