Effect of deteriorating items and promotional effort factor in fuzzy instantaneous replenishment model

摘要

This paper presents a stylized model for analyzing the effect of deteriorating items and the promotional effort in a fuzzy optimal instantaneous replenishment model for a finite planning horizon. Accounting for holding costs and ordering costs have traditionally been the case when modelling inventory systems in a fuzzy environment. These imprecise parameters, which are denned on a bounded interval on the axis of real numbers and the physical characteristics of stocked items, dictate the management and control of inventory policies . This paper postulates on some of these costs, the promotional effort cost. Thus a modified fuzzy EOQ (FEOQ) model with a promotional effort factor is introduced. It assumes that a percentage of the on-hand inventory is wasted due to deterioration and it is considered as an enhancement to the EOQ model to determine the optimal promotional effort and the replenishment quantity so that the net profit is maximized. Through the theoretical analysis, the necessary and sufficient conditions for the existence and uniqueness of the optimal solutions are proved and the concavity of the fuzzy net profit function is established. A computational algorithm using the LINGO 13.0 software is developed to find the optimal solution. The results of the numerical analysis enable decision-makers to quantify the effect of promotion policy on optimizing net profit for the retailer and reduce inventory wastage due to deterioration . Finally, a sensitivity analysis of the optimal solution with respect to the major parameter is also conducted. In terms of profit maximization, fuzzy decision making is shown to be superior to crisp decision making without the promotional effort.