An EOQ model with backlogging

This paper deals with a new approach of linguistic dichotomous fuzzy variables for a classical backordered EOQ (Economic Order Quantity) model with PE (Promotional Effort) and selling price dependent demand rate. In practice, we have observed that the demand rate during a shortage period decreases with time. Based on these assumptions, we have developed a cost minimization problem (a crisp model) by trading off setup cost, inventory cost, backordering cost and cost for promotional effort. Then, we have studied a fuzzy model by considering the coefficient vectors as pentagon fuzzy numbers associated with some co-ordinates. Defuzzification is made with the help of the center-of-gravity method followed by a ranking index and the Euclidean distance of the objective function. Considering a numerical example, phi-(phi-)coefficients have been computed for each method and a decision is made according to the natural characteristics of the decision variables. Finally, conclusions are drawn, explaining the justification of the model.