Abstract
The present paper considers a manufacturing supply chain of deteriorating type inventories. The problem addresses the extra rented warehouse (RW) to store extra inventories if the manufacturer is producing more inventories than their owned warehouse (OW) capacity. Now, the problem is which inventories should be used first with minimum cost and minimum deterioration. To solve this problem, we have assumed a MFIFO (mixed first in first out) dispatching policy and constant demand rate over a finite time horizon. Along with these we have also assumed an inspection policy during the supply chain to separate deteriorated items and a carbon tax policy is also considered to control carbon emissions. The rate of deterioration depends on the number of inspections. If the number of inspections increases, it minimizes the rate of the decaying process. Due to the adoption of the inspection policy, the supply chain moves toward a green supply chain as it removes deteriorated inventories that minimize further decay by contact, and simultaneously separated deteriorated products can be utilized for other purposes that solve the problem of the disposal of deteriorating inventories and reduce emission generation. We have also established the uniqueness of the established model. The motto of solving the mathematical model is to find the values of the optimum value of N, the number of cycles, and n, the number of inspections that helps to minimize total cost. At last, we illustrate the result with the help of a numerical example.