Article: Solving an exploitation-based Marxian fuzzy EOQ model Journal: International Journal of Mathematics in Operational Research (IJMOR) 2024 Vol.29 No.4 pp.511 - 541 Abstract: This article deals with the clinical study of Marxian economic order quantity (M-EOQ) model under fuzzy environment. Initially the model has been viewed as multi-objective cost minimisation and profit maximisation problem under optimum rate of exploitation. Then we transform the multi-objective optimisation problem into single objective optimisation problem under suitable constraints. For optimising this objective function, we need to solve analytically a biquadratic equation where order quantity assumes as one of the decision variables. According to the nature of the roots of this biquadratic equation, we split the model into various sub models where the exploitation varies differently with the change of demand function. Incorporating the negative root of the biquadratic equation, we have formulated three different backlogging EOQ models. Considering a case study, we perform the numerical experimentation with the help of a solution algorithm. Moreover, to capture the non-random uncertainty of the model parameters, we construct an equivalent fuzzy shortage model. Our findings reveal that, shortage model is more beneficial than other sub-models for the decision maker all the time. Finally, numerical illustrations, sensitivity analysis, graphical illustrations and comparative study are done for justify the model followed by managerial insight, conclusion and scope of future work. Inderscience Publishers - linking academia, business and industry through research

Title: Solving an exploitation-based Marxian fuzzy EOQ model

Authors: Biswajit Roy; Kousik Bhattacharya; Sujit Kumar De

Addresses: Department of Mathematics, Garhbeta College, Garhbeta, WB, India; Department of Mathematics (UG&PG), Midnapore College (Autonomous), Midnapore, India ' Department of Mathematics (UG&PG), Midnapore College (Autonomous), Midnapore, India ' Department of Mathematics (UG&PG), Midnapore College (Autonomous), Midnapore, India

Abstract: This article deals with the clinical study of Marxian economic order quantity (M-EOQ) model under fuzzy environment. Initially the model has been viewed as multi-objective cost minimisation and profit maximisation problem under optimum rate of exploitation. Then we transform the multi-objective optimisation problem into single objective optimisation problem under suitable constraints. For optimising this objective function, we need to solve analytically a biquadratic equation where order quantity assumes as one of the decision variables. According to the nature of the roots of this biquadratic equation, we split the model into various sub models where the exploitation varies differently with the change of demand function. Incorporating the negative root of the biquadratic equation, we have formulated three different backlogging EOQ models. Considering a case study, we perform the numerical experimentation with the help of a solution algorithm. Moreover, to capture the non-random uncertainty of the model parameters, we construct an equivalent fuzzy shortage model. Our findings reveal that, shortage model is more beneficial than other sub-models for the decision maker all the time. Finally, numerical illustrations, sensitivity analysis, graphical illustrations and comparative study are done for justify the model followed by managerial insight, conclusion and scope of future work.

Keywords: EOQ model; Marx's theory; exploitation; fuzzy set; algorithm; optimisation.

DOI: 10.1504/IJMOR.2024.143391

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.4, pp.511 - 541

Received: 21 Jun 2023
Accepted: 21 Jul 2023
Published online: 17 Dec 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article

Title: Solving an exploitation-based Marxian fuzzy EOQ model

Keep up-to-date