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

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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.