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

Document Type : Article


1 Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India

2 Department of Applied mathematics with oceanology and computer programming, V.U, Midnapore-721102, W.B, India

3 Department of Mathematics, Midnapore College (Autonomous), Midnapore-721101, W.B, India

4 Department of Applied Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia-741249, W.B, India


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 demand but 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 fuzzy model 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 levels has been discussed to defuzzify the fuzzy multi-objective problems. We solve the crisp and fuzzy models using LINGO software. Numerical and graphical illustrations confirm that the model under Generalized Hukuhara derivative of (R-L) type contributes more profit which is one of the basic novelties of the proposed approach.


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