An EOQ Model with Pareto Distribution for Deterioration, Trapezoidal Type Demand and Backlogging Under Trade Credit Policy

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