The newsvendor problem with a non-stationary demand process and exact accounting of holding costs

This work presents an extension of the classical newsvendor model that considers the inventory costs more accurately based on the actual stock-level within the selling period, and not on the stock-level at the end of it. The new feature of this model is that the selling period, which is relatively long, is comprised of n epochs, where the demand distribution in each epoch is known but is not stationary, and holding costs are considered only for the epochs in which the item was stored. A mathematical model is developed to calculate the expected profit, and an optimality equation is provided from which the optimal order quantity can be derived. Using a numerical analysis in a factorial experimental design of a non-homogeneous Poisson demand process, we evaluate the performance of the suggested model in comparison to two approximated standard newsvendor models that disregard the exact inventory costs.