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This paper investigates an EPQ model with the increasing demand and demand dependent production rate involving the trade credit financing policy, which is seldom reported in the literatures. The model considers the manufacturer was offered by the supplier a delayed payment time. It is assumed that the demand is a linear increasing function of the time and the production rate is proportional to the demand. That is, the production rate is also a linear function of time. This study attempts to offer a best policy for the replenishment cycle and the order quantity for the manufacturer to maximum its profit per cycle. First, the inventory model is developed under the above situation. Second, some useful theoretical results have been derived to characterize the optimal solutions for the inventory system. The Algorithm is proposed to obtain the optimal solutions of the manufacturer. Finally, the numerical examples are carried out to illustrate the theorems, and the sensitivity analysis of the optimal solutions with respect to the parameters of the inventory system is performed. Some important management insights are obtained based on the analysis.

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Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material etc., Hence, it is needed to develop inventory models with random replenishment. In this paper, an EPQ model for deteriorating items is developed and analyzed with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalized Pareto distribution and demand is a function of on hand inventory. Using the differential equations, the instantaneous state of inventory is derived. With suitable cost considerations, the total cost function is obtained. By minimizing the total cost function, the optimal ordering policies are derived. Through numerical illustrations, the sensitivity analysis is carried. The sensitivity analysis of the model reveals that the random replenishment has significant influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.