Optimal price markup policy for an inventory model with random price fluctuations and option for additional purchase

In this paper, based on the analysis of empirical data of dealer and retailer prices and sales of cement – as a prototype of functional products – we develop a probabilistic inventory model for the situation when dealer′s selling price fluctuates and affects the retailer′s selling price. Demand is a function of price markup and retailer′s purchase price. Dynamic price markup policy is proposed and optimal length of replenishment cycle and order quantity is obtained. Concavity of the profit function with respect to price markup is discussed. A procurement policy which considers opportunity of purchase at a low price before the end of the optimal replenishment cycle is proposed and compared with other policies. Algorithm, numerical examples, sensitivity analysis and managerial insights are presented.