Optimal order strategy with time-varying demand under permissible delay in payments linked to order quantity

This study presents a deterministic economic order quantity model for a retailer to determine its optimal replenishment number and replenishment schedule in a finite time horizon. The retailer's demand rate is time dependent and the supplier offers a trade credit to the retailer when the retailer's order quantity exceeds a given pre-specified quantity. To maximize the retailer's profit, a mathematical model is developed when the demand rate is a generalized function of the time and the trade credit linked to order quantity is adopted. By analyzing the retailer's profit function, we develop some useful results to characterize the optimal solution and provide an iterative algorithm to find the replenishment schedule and the retailer's order quantities. Numerical examples with different types of demand function are presented to validate the proposed model and the algorithm. Sensitivity analysis of the major parameters including of the quantity at which the delay in payments permitted and the trade credit period are presented.