### Effect of Promotional Activities for a Product in Fuzzy Economic Order Quantity (FEOQ) Model

#### Abstract

This model studies the problem by proposing a continuous review inventory model under promotion by assuming that the units do not lost due to deterioration of the items. In this model optimization has been studied for applying promotional effort cost with promotion constraint. In this model, promotional effort and replenishment decision are adjusted arbitrarily upward or downward for profit maximization model in response to the change in market demand within the planning horizon with fixed ordering cost. The effect of deteriorating items on the instantaneous profit maximization replenishment model under promotion is considered in this model. The market demand may increase with the promotion of the product over time when the units do not lost due to deterioration. Accounting for holding cost per unit per unit time and ordering cost per order have traditionally been the case of modeling inventory systems in fuzzy environment. These imprecise parameters defined on a bounded interval on the axis of real numbers and the physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control in the production system. This model postulates the promotional effort cost to frame total inventory cost. Thus a modified fuzzy EOQ (FEOQ) model with promotional effort factor is introduced, it assumes that a percentage of the on-hand inventory is not wasted due to deterioration and considered as an enhancement to EOQ model to determine the optimal promotional effort and the replenishment quantity so that the net profit is maximized. In theoretical analysis, the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are proved and further the concavity of the fuzzy net profit function is established. Computational algorithm using the software LINGO 13.0 version 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 the net profit for the retailer and wasting the percentage of on-hand inventory due to deterioration are not allowed respectively. Finally, sensitivity analyses of the optimal solution with respect the major parameters are also carried out. Furthermore fuzzy decision making is shown to be superior then crisp decision making without promotional effort in terms of profit maximization. The objective of this model is to determine the optimal cycle length, the promotional effort and the replenishment quantity with fixed ordering cost so that the net profit is maximized.

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