This paper discusses the existence of defective items in a manufacturing process. A rework strategy is implemented to rectify the defective items. A rework cost function under fuzzy environment which includes both synchronous and asynchronous items. The paper develops fuzzy optimal total cost function and fuzzy production quantity using trapezoidal numbers and applying Lagrangian method. A numerical example follows to justify the solution procedure. Keywords Economic order quantity (EOQ), Fuzzy inventory, Graded mean integration and Lagrangian method.
The concept of KM-algebras has been originated in 2019. KM-algebra is a generalization of some of the B-algebras such as BCK, BCI, BCH, BE, and BV and also d-algebras. KM-algebra serves two purposes in mathematics and computer science as follows: a tool for application in both fields and a strategy for creating the foundations. On the fuzziness of KM-algebras, an innovative perspective on fuzzy product KM-algebras as well as some related features is offered. Moreover, the notion of KMM-ideals is described and also initiated the concept of the KM-Cartesian product of fuzzy KM-algebras, and related outcomes are examined. Some of the innovative results in fuzzy KMM-ideals and KM-Cartesian product of fuzzy KM-subalgebras are analyzed, and some are as follows: arbitrary intersection of fuzzy KMM-ideals is again a fuzzy KMM-ideal, order reversing holds true in every KMM-ideal, every fuzzy KM-subalgebra is a fuzzy KMM-ideal, and KM-Cartesian product of two fuzzy KM-subalgebras is again a fuzzy KM-subalgebra.
This paper considers an EOQ inventory model with varying demand and holding costs. It suggests minimizing the total cost in a fuzzy related environment. The optimal policy for the nonlinear problem is determined by both Lagrangian and Kuhn-tucker methods and compared with varying price-dependent coefficient. All the input parameters related to inventory are fuzzified by using trapezoidal numbers. In the end, a numerical example discussed with sensitivity analysis is done to justify the solution procedure. This paper primarily focuses on the aspect of Economic Order Quantity (EOQ) for variable demand using Lagrangian, Kuhn-Tucker and fuzzy logic analysis. Comparative analysis of there methods are evaluated in this paper and the results showed the efficiency of fuzzy logic over the conventional methods. Here in this research trapezoidal fuzzy numbers are incorporated to study the price dependent coefficients with variable demand and unit purchase cost over variable demand. The results are very close to the crisp output. Sensitivity analysis also done to validate the model.
In this article, a fuzzy inventory model with allowable shortage is formulated and solved. Fuzziness is introduced by allowing the cost components (holding cost, ordering cost, shortages cost and demand). In fuzzy environment, all related inventory parameters are represented to be octagonal fuzzy numbers .These fuzzy numbers have been used in order to determine the optimal order quantity and optimal total cost for the inventory model. The calculation of EOQ is carried out through defuzzification by using ranking function method. The model is solved using Kuhn-tucker conditions method. The results of the models are illustrated with numerical example.
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