Inventory management subject to multiplicative inaccuracies

The standard literature on inventory modelling is rarely differentiating between the inventory records and the physical inventory. In the recent years, some empirical studies highlighted that errors and inventory perturbations may occur in the inventory system. Such errors result in a gap between what the informational system (IS) shows and what is actually available for sales and used to satisfy the demand. The impact of such errors is particularly important in a wholesaling/e-retailing context where customer' demands are remotely satisfied based on the inventory records shown in the IS. These errors could be modelled by an additive or multiplicative structure depending on the link between the error variability and the ordered quantity. The aim of the paper is to extend the existing literature by developing an inventory framework that permits the analysis and the performance improvement of an inventory system subject to a multiplicative errors setting. The multiplicative and stochastic settings also known as the stochastically proportional modelling of errors is not well developed in the literature despite the fact that such an assumption bears considerable association with reality. We provide comprehensive analytical and numerical studies and we also complete our contribution by a comparison between the additive and the multiplicative error settings where we derive interesting managerial insights about the impact of wrongly modelling errors. We also focus on the benefit of applying our results compared with the case where errors are ignored or not known.