A perceptions framework for categorizing inventory policies in single-stage inventory systems

In this paper we propose a perceptions framework for categorizing a range of inventory decision making that can be employed in a single-stage supply chain. We take the existence of a wide range of inventory decision making processes, as given and strive not to model the reasons that the range persists but seek a way to categorize them via their effects on inventory levels, orders placed given the demand faced by the inventory system. Using a perspective that we consider natural and thus appealing, the categorization involves the use of conceptual perceptions of demand to underpin the link across three features of the inventory system: inventory levels, orders placed and actual demand faced. The perceptions framework is based on forecasting with Auto-Regressive Integrated Moving Average (ARIMA) time series models. The context in which we develop this perceptions framework is of a single stage stochastic inventory system with periodic review, constant leadtimes, infinite supply, full backlogging, linear holding and penalty costs and no ordering costs. Forecasting ARIMA time series requires tracking forecast errors (interpolating) and using these forecast errors and past demand realizations to predict future demand (extrapolating). So called optimal inventory policies are categorized here by perceptions of demand that align with reality. Naturally then, deviations from optimal inventory policies are characterized by allowing the perception about demand implied by the interpolations or extrapolations to be primarily different from the actual demand process. Extrapolations and interpolations being separate activities, can in addition, imply differing perceptions from each other and this can further categorize inventory decision making.