Optimal picking of large orders in carousel systems

A carousel is an automated storage and retrieval system which consists of a circular disk with a large number of shelves and drawers along its circumference. The disk can rotate either direction past a picker who has a list of items that have to be collected from $n$ different drawers. In this paper, we assume that locations of the $n$ items are independent and have a continous non-uniform distribution over the carousel circumference. For this model, we determine a limiting behavior of the shortest rotation time needed to collect one large order. In particular, our limiting result indicates that if an order is large, then it is optimal to allocate {\it less} frequently asked items {\it close} to the picker's starting position. This is in contrast with picking of small orders where the optimal allocation rule is clearly the opposite. We also discuss travel times and allocation issues for optimal picking of sequential orders