This paper studies and analyzes an inventory model with the assumption that the lifetime of the commodity is random and follows a generalized Pareto distribution. It is also assumed that demand rate is of Trapezoidal type, i.e., the demand rate is a piecewise linear function and this demand rate is used when stock is available as well as during shortage period. Shortage is completely backlogged and backlogging rate is of Trapezoidal type. This study considers the traditional hypothesis that at the end of credit period, the retailer makes a partial payment of the total purchasing cost and pays off the remaining balance by loan from bank. With suitable cost consideration, the total cost function is obtained. Minimizing total cost function, the optimal ordering quantity and optimal time are obtained. The numerical examples are presented to illustrate the model.

The conceptual inventory models assume the perfect case that the value of inventory items is unchanged by time and replenishment takes place instantaneously. In real life cases, however, the perfect case is not quite applicable. Preservation of the decaying goods is a considerable problem in supply chain of almost all business systems. Many of the items deteriorate over time. Items like fruits, clothes, etc., are subject to direct spoilage when set aside in store. Highly volatile items like gasoline, alcohol, etc., undergo physical depletion over time through the process of fading. Items used in information technology, radioactive substance, photographic film, grain, etc., deteriorate through a gradual latency or loss of utility with the passage of time.

A model with exponentially decaying inventory was initially proposed by Ghare and Schrader (1963). Covert and Philip (1973) and Tadikamalla (1978) developed an Economic Order Quantity (EOQ) model with Weibull and Gamma distributed deterioration rates, respectively. Many scholars have discussed the inventory models for deteriorating/decaying items. In the analysis of inventory models for deteriorating items, the lifetime of the product plays a leading role. Some researchers have used Pareto lifetime in their work. There are so many probabilistic functions that are used for the lifetime of a product. In this paper, we have considered the Pareto distribution, named after the Italian economist, Vilfredo Pareto. It is a power law probability distribution, and Pareto originally used this distribution to describe the allocation of wealth among individuals since it seemed to show rather well the way a larger portion of the wealth of any society is owned by a smaller percentage of people in that society. It gave a better rate as compared to other distributions like Poisson, Beta, Gamma, etc. This idea is at times expressed more simply as the Pareto Principle or the `80-20 rule', which says that 20% of the population controls 80% of the wealth.

Computational Mathematics Journal, Pareto Distribution, Trade Credit Policy, Inventory Model, Information Technology, Photographic Film, Business Systems, Economic Order Quantity Model, Classical EOQ Model, Financial Management, Inventory Replenishment Policy, Product Life Cycle.