Solution of an Economic Production Quantity model using the generalized Hukuhara derivative approach

Abstract

In this study, an economic production quantity (EPQ) model with deterioration is developed where the production rate is stock dependent and the demand rate is unit selling price and stock dependent. The low unit selling price and more stocks correspond high demandbut more stock corresponds to slow production because of the avoidance of unnecessary stocks. First of all, we develop the production model by solving some ordinary differential equations having deterministic profit function under some specific assumptions. Later, we develop the fuzzymodel by solving the fuzzy differential equations using Generalized Hukuhara derivative. In fact, the differential equation of the model has been split into two parts namely gH(L-R) and gH(R-L) on the basis of left(L) and right(R)𝛼 − cuts of fuzzy numbers for which the problem itself is transformed into multi-objective EPQ problem. A new formula of aggregation of several objective values obtained at different aspiration levelshas been discussed to defuzzify the fuzzy multi-objective problems.We solve the crisp and fuzzy models using LINGO software. Numerical and graphical illustrations confirm thatthe model under Generalized Hukuhara derivative of (R-L) type contributes more profit which is one of the basic novelties of the proposed approach.

An Insight into the Impacts of Memory, Selling Price and Displayed Stock on a Retailer’s Decision in an Inventory Management Problem

“…Khan et al [43] incorporated discount opportunities for the retailer through partial and fully advanced payments in an order quantity model of deteriorating goods with price-and stock-dependent demand and shortage. Rahaman et al [44] discussed a fuzzy economic production quantity model of decaying items, considering demand as a function of price and stock and production rate as a function of stock. They used the fuzzy differential equation approach to solve the problem.…”