The present study is an attempt to develop an inventory model for deteriorating items with negative exponential demand. Shortages are allowed with partial back logging. This model is different from the existing models where deterioration is a function of time. Accordingly, three different types of probabilistic deterioration functions have been considered to find the associated decision variables and also to make comparisons among them. The optimality is illustrated with numerical values of system parameters and the graphical representations are given to depict the trend. The necessary observations in obtaining optimal values of decision variables are analyzed in the light of the practical aspect of the developed model. Finally, considering the numerical values of system parameters, sensitivity analyses are carried out to study the effect of changes in most important system parameters.
Traditional economic production quantity (EPQ) model assumes that the production products are perfect. However, this assumption does not hold for many real production systems due to several weaknesses. This paper considers production inventory model with defective items for deteriorating items. In this paper, production rate is considered to be greater than demand rate. Mathematical model is developed for finding optimal order quantity, cycle time and total profit. Moreover, a numerical example is provided to illustrate the proposed model. Next, sensitivity analysis is established to demonstrate the model developed. Finally, some conclusions and future research directions are proposed.