Abstract
This paper presents an inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a fuzzy environment by employing fuzzy triangular numbers. It is assumed that the imperfect items identified by Screening are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterward, the items are returned to the supplier to be reworked. Also, a discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error-free. An overlapping order scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. In the fuzzy model, the graded mean integration method is taken to defuzzify the model and determine its approximation of a profit function and optimal policy. In doing so, numerical examples are rendered to represent the model behavior, and, eventually, the sensitivity analysis is presented.
Highlights
The importance of inventory management systems is growing every day, and many researchers are trying to solve management problems using mathematical models
By exploring the literature review on inventory systems, it is realized that many efforts have been conducted to provide inventory models in order to eliminate the limitations of the economic order quantity (EOQ) model
The effect of imperfect items on inventory systems has become one of the interesting topics for many researchers to provide more practical models. [1] followed by Rosenblatt and Lee, presented the significant connection between imperfect quality and lot sizing. [2] assumed that the imperfect items received in the lot would result in the inspection cost
Summary
The importance of inventory management systems is growing every day, and many researchers are trying to solve management problems using mathematical models. [26] investigated an EPQ model without any shortages by fuzzifying the decision variable and cycle time and proposed the EOQ model considering fuzzy triangular numbers for the demand and lead time As it is obvious from the above-mentioned literature, none of the authors has presented an imperfect EOQ inventory model, either scrap or re-workable, along with receiving reparative batch considering various holding costs for perfect and scrap items under fuzzy conditions in the model parameters. The major distinction between this paper and others lies in fuzziness in the model parameter, the various assumptions on imperfect items, employing an overlapping scheme to prevent shortages during the inspection period, discount rate provision of the purchasing cost to maintain a cooperative relationship, and considering receiving reparative.
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