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Optimization of the vendor's inventory model with multisupplier and multiretailer using fuzzy parameters

This paper explores the multi‐item vendor's inventory (VI) model in which the vendor replenishes the products from various suppliers and satisfies the retailers' demand. Different types of products scrutinize this model under two cases. The first case considers the products are replenished in bulk and packed in small quantities by the vendor and sent to the retailers. The second case presumes that the vendor replenishes the packed items from the supplier and sent to retailers without the packaging process. The wastage of products during the packaging process occurs in the first case and the deterioration of items occurs in both cases. The unpredictable parameters such as the proportion of wastage products and the proportion of deteriorated products lead the model under fuzzy logic. The VI model and the Vendor's fuzzy inventory (VFI) are framed. VFI model is formulated by assuming the wastage rate and the deterioration rate as triangular fuzzy numbers (TFN) as well as trapezoidal fuzzy numbers. The defuzzification method of TFN and trapezoidal fuzzy numbers by the combination of Beta distribution and a uniform distribution is utilized in this paper. For both cases, the optimal ordering and purchasing period, the optimal retailer's replenishment period, and the optimal packaging period for case (i) is computed which minimizes the vendor's total cost. The computational example and sensitivity analysis are performed to flourish the study more effectively.