Joint Effects of Carbon Emission, Deterioration, and Multi-stage Inspection Policy in an Integrated Inventory Model

This paper discusses an integrated inventory model between vendor and buyer for decayed type of products. The vendor produces perfect products but may arrive some defect products in the system. To control product quality, the manufacturer inspects all the products to separate the defective products. After the first-stage inspection, the defective products are reworked at a fixed cost and again inspection takes place for the reworked products in the second-stage inspection. After completion of the second-stage inspection, the defective products are disposed at some fixed cost and delivers good products to the buyer. The delivery of good products is done by single-setup multi-delivery (SSMD) policy by consideration of fixed and variable types of transportation cost. At any stage, the good quality of products may deteriorate and the constant deterioration rate is considered for vendor and buyer, separately. Carbon is emitted from every portion of the integrated system. This issue is studied in this model and finally the joint total cost of the inventory model is minimized with the help of algebraic method. To illustrate the model numerically, some numerical examples are provided along with the sensitivity analysis and the graphical representations of those examples.

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