Intermittent demand is characterized by many periods with no demand at all, that are seemingly randomly interspersed with non-zero demand observations. The compound nature of intermittent demand complicates demand forecasting and efficient inventory management [1]. First, it is unknown when the next demand will occur. Second, there is uncertainty in the size of the demand when it does occur.

Specific approaches have been developed to tackle uncertainty in the demand. The analysis of intermittent demand times series is commonly decomposed to create separate estimates for the time between demand occurrences (the inter-demand interval) and the size of a demand occurrence. In the existing literature, these analyses implicitly assume that the time between demand occurrences is memoryless, i.e, the probability of observing a demand in a period is assumed to be independent of the time since the last demand observation. Data from practice, however, indicates that the times between demand events is often not memoryless, i.e., the probability of a demand occurrence does depend on the time since the last demand occurred. Consequently, the time since the last demand event is an important predictor for future demand.

This research is the outcome of a joint research project with a company in the chemical industry. This company observes intermittent demand for many of its items, and data suggests periodicity in the demand occurrences. We use the discrete compound renewal process to model such periodic intermittent demand. We consider a single stock-point under periodic review. Unsatisfied demand is backordered at a backorder penalty cost per time unit and inventory on-hand at the end of a period incurs a holding cost. We allow for positive lead times. We use a Markov decision process formulation to study the structure of optimal policies.