An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit

This paper deals with an economic order quantity (EOQ) inventory model under both nonlinear stock dependent demand and nonlinear holding cost. This inventory model is developed from retailer's point of view, where the supplier offers a trade credit period to the retailer. In this paper, we relax the traditional assumption of zero ending inventory level to a non-zero ending inventory level. Consequently, the ending inventory level can be positive, zero or negative. When the ending inventory level is negative means that the shortages are permitted and partially backlogged with a constant backlogging rate. Basically, two inventory models are developed: (i) an inventory model with shortage and (ii) an inventory model without shortage. The primary objective of both inventory models is to determine the optimal ordering quantity and the ending inventory level which maximizes the retailer's total profit per unit time. In order to obtain the optimal solution, lemmas, and theorems are derived along with a solution procedure. The proposed inventory models are a general framework as several previously published inventory models are particular cases of the inventory models derived in this paper. Some numerical examples and a sensitivity analysis are conducted to illustrate the findings of the inventory models and some observations are also discussed.