Solving an exploitation-based Marxian fuzzy EOQ model

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.