A model on an EOQ optimal ordering policy with varying time-propotional deterioration, generalised time-varying demand and the conditions of delay in payment

The objective of the proposed research is to study the effect of the time-proportional deterioration rate, the generalised time-varying demand rate and permissible delay in payments within the economic order quantity (EOQ) framework. The EOQ inventory model for a deteriorating item is developed with the following characteristics: 1) the grace period is known and fixed; 2) supplier offers the customer a grace in paying back for the purchase cost; 3) deteriorating items follow the two-parameter Weibull distribution deterioration rate; 4) demand pattern is deterministic and cubic function of time; 5) shortages are not allowed to occur during the cycle under consideration. In order to settle, an inventory model has been developed, considering the two main cases of grace period: Case 1 - the grace period is less than the cycle time and Case 2 - the grace period is greater than the cycle length of the system. An easy-to-use solution procedure is provided to determine the optimum values of cycle length, average total system cost and order quantity by using calculus technique of maxima and minima. At the end, the results have been validated by a couple of numerical examples and sensitivity analysis of several system parameters on the optimum solution has been performed.