Analysis and optimization of an EOQ inventory model with promotional efforts and back ordering under delay in payments

In this paper, economic order quantity (EOQ) inventory model is considered subject to promotional efforts. We adopt a demand function which is dependent on sales teams' initiatives in which shortages are allowed which are completely backlogged under the condition of permissible delay in payments with time-dependent holding cost. The main objective of this paper is to determine the optimal replenishment schedule and optimal order quantity to maximize the total profit. Expressions for various optimal indices are provided. First, we prove that a unique optimal replenishment schedule exists. Second, we present an effective iterative algorithm to obtain the optimal solution. Furthermore, we establish some useful theorems to characterize the optimal solution to determine the values of replenishment schedule and optimal order quantity. Third, we prove that the total profit is a concave function via differential calculus and present numerical examples using SCILAB 5.5.0 to illustrate the model. Finally, we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss managerial insights. This study suggests to the management of firms to determine the optimal order quantity, optimal inventory cycle length and sales teams' initiatives/promotional effort in order to achieve their maximum profits.