Closest open location rule under stochastic demand

In modelling automated storage/retrieval systems, the assumption of random storage has been widely used to approximate the activity of the closest open location rule. Considering that the closest open location rule is so popular in practice, it is significant to validate the assumption, or identify under what conditions the assumption could be justified. In this study we show how the "true" activity distribution of the closest open location rule can be approximated by a "modified" uniform distribution. The modified distribution is then used to approximate the expected travel distance, which is simple to use yet accurate enough for practical purposes. We also show that the uniform approximation is valid even for different streams of demand and batch arrivals.