Solving a fuzzy backlogging economic order quantity inventory model using volume of a fuzzy Hasse diagram.

This article deals with a backorder economic order quantity (EOQ) model where the demand rate splits into two parts, one of which assumes constant value and the other part varies with the number of customers. First of all, a crisp model is developed to optimize the average inventory cost under some constraints. Due to the flexible nature of the several cost parameters involved in the model, considering a case study a fuzzy mathematical model is also developed. Moreover, since the fuzzy set has the versatile nature used by several decision makers participating in the inventory process itself so, a power set of the native fuzzy set is considered to develop the original fuzzy model. In fact, a Hasse diagram of fuzzy power set is considered based on partial order relations. Simultaneously, metric distances among various fuzzy sets have been calculated. Then a fuzzy optimization problem is defined and the model has been defuzzified with the help of some novel ranking methods utilizing the volume of the proposed Hasse diagram. A solution algorithm is developed to solve the problem. Numerical study reveals that the optimum solution exists due to the application of Hasse diagram whose sides are computed by taking supremum among several fuzzy sets compared to some other existing state-of-arts. Finally, sensitivity analysis and graphical illustrations are done to justify the novelty of the proposed approach. [ABSTRACT FROM AUTHOR]