An Order Quantity Model for Delayed Deteriorating Items with Time-Varying Demand Rate and Holding Cost, Time Dependent Partial Backlogging Rate, and Two-Level Pricing Strategies under Trade Credit Policy

In this study, an economic order quantity model is developed for non-instantaneous deteriorating items with two-level pricing strategies under trade credit policy, two-phase demand rates, linear holding costs, and time-dependent partial backlog rates; the demand rate is assumed to be continuous and time-dependent quadratic before deterioration sets in, and to be constant until the inventory is fully depleted; the holding cost is assumed to be linear and time-dependent, and the unit selling price is higher before deterioration sets in is higher than that after, shortages and time-dependent partial backlogs are acceptable. The model's objective is to determine the optimal period for positive inventory, cycle length, and order amount to maximize the inventory system's overall profit. The necessary and sufficient conditions for optimal solutions to exist and be unique have been identified. Numerical experiments have been used to illustrate the model's theoretical result. Together with sensitivity analysis of specific model parameters on the choice factors, recommendations for optimizing the overall profit were also given.