Application of Triangular Fuzzy Neutrosophic Number to an Effective Economic Order Quantity Model

Introduction

The production manager executes a much effective manufacturing process to avoid defective units to be manufactured. But still, substandard products are manufactured and supplied to the retailers. So that, according to Salameh and Jaber (2000), in every cycle the retailer received a lot of substandard items, and to rectify this issue, the retailer enforces a screening process once replenishing a lot. This paper focuses on the advance payment option that is the acquisition cost should be paid in advance as multiple equal payments instead of paying at the time of replenishment.

This research studies a two-warehouse EOQ model with imperfect quality items and the advance payment on acquiring cost under fuzzy environment and neutrosophic environment. Once a lot received, the screening process takes place and separates the flawed items from the inventory in both the warehouses and sold them at a lower price after the screening period in one shot. Since the demand can be satisfied during the screening period with perfect items, it is considered that the screening rate is always more than the demand rate. The retailer utilizes the advance payment on acquisition cost offered by the supplier with some price discount on prepaid items. In this advance payment option, the fraction of acquiring cost to be paid in advance with equal payments at multiple intervals. Since the defective proportion in every lot is unpredictable, the proposed study utilizes a fuzzy notion for an effective outcome. As an enlargement of the fuzzy set and intuitionistic fuzzy set, Smarandache established the neutrosophic set to attain more approximate outcomes for uncertain situations rather than the fuzzy set and intuitionistic fuzzy set. Thus, the present model is framed under the neutrosophic arena to reach the most approximate solution for unpredictable defective rate than the crisp model and fuzzy model.

The inventory model under fuzzy arena is also developed to compare the study with the neutrosophic model. Initially, the crisp EOQ model is obtained by presuming the proportion of defective items as uniform distribution then the fuzzy EOQ model is designed by presuming the proportion of substandard items as Triangular Fuzzy Number [TFN] and defuzzified by computing the expected value of TFN. Finally, the inventory model under neutrosophic sense is framed by considering the defective rate as Triangular Fuzzy Neutrosophic Number [TFNN] and de-neutrosophication of the proposed model has been performed by using expected value of TFNN. Finally, the model is illustrated with a numerical example and the sensitivity, as well as the comparative analysis, is discussed.

The main objective of the research is to maximize the retailer’s expected profit for the EOQ model with substandard products under a double warehouse system. The proposed study scrutinizes under both fuzzy and neutrosophic arena to attain the approximate profit for the unpredictable parameter. This study motivates the retailer to pay the advance payment offered by the supplier who provides the price discount on the prepaid amount which leads to upticks in the retailer profit.

The elementary definitions of fuzzy set, intuitionistic fuzzy set, neutrosophic set, and the expected value of TFNN are provided in section 2. Followed by the notations and the assumptions, the crisp EOQ model is formulated in section 3. Further, the proposed crisp model is flourished by fuzzy model by presuming the substandard proportion as TFN, and also the neutrosophic EOQ model is framed by presuming the substandard proportion as TFNN in the same section. In section 4, the numerical computation and sensitivity analysis is performed with the comparative studies. Finally, the results of this research are given in section 5.