On real-time accounting of inventory costs in the newsvendor model and its effect on the service level

The newsvendor model is the cornerstone of most periodic inventory models; however, it distorts the correct timing of inventory costs and thus misses the optimal solution of the inventory system. This work presents a modification of the classical newsvendor model that considers the holding cost according to the stock-levels within the selling period rather than according to the stock-level at the end of it. The selling period (for example, a season) is divided into equal-time epochs (for example, one-day epochs), where demands are not necessarily identical across epochs or independently distributed. A mathematical model is formulated to find the optimal order quantity which maximizes the expected profit. We show: 1) that the profit function is concave; 2) that the structure of the optimality equation is similar to that of the classical newsvendor model; 3) how to attain the real tradeoff between the expected profit and the service level. Finally, we propose three heuristics to approximate the optimal order quantity and two bounds on its value, which are easy to implement in practice, and evaluate their performances using extensive numerical examples in a factorial experimental design.