Inventory Model with Stochastic Demand Using Single-Period Inventory Model and Gaussian Process

Abstract

Proper inventory management is vital to achieving sustainability within a supply chain and is also related to a company’s cash flow through the funds represented by the inventory. Therefore, it is necessary to balance excess inventory and insufficient inventory. However, this can be difficult to achieve in the presence of stochastic demand because decisions must be made in an uncertain environment and the inventory policy bears risks associated with each decision. This study reports an extension of the single-period model for the inventory problem under uncertain demand. We proposed incorporating a Gaussian stochastic process into the model using the associated posterior distribution of the Gaussian process as a distribution for the demand. This enables the modeling of data from historical inventory demand using the Gaussian process theory, which adapts well to small datasets and provides measurements of the risks associated with the predictions made. Thus, unlike other works that assume that demand follows an autoregressive or Brownian motion model, among others, our approach enables adaptability to different complex forms of demand trends over time. We offer several numerical examples that explore aspects of the proposed approach and compare our results with those achieved using other state-of-the-art methods.