Travel time in carousel systems

Nelly Litvak

University of Twente, The Netherlands


A carousel is an automated storage and retrieval system that is widely used in modern warehouses. The system consists of a circular disk with a large number of shelves or drawers along its circumference. The disk can rotate either direction past a picker who has a list of items to be collected from n different drawers. We model this process by assuming that the picker occupies a fixed position along a circle and that the drawers to be visited are distributed independently and uniformly along the circle. The picker might chose various routes for collecting the items. We first analyse the most natural Nearest Item heuristic where the next item to be picked is always the nearest one. Next, we study the shortest possible route. Along the way, we encounter rather curious properties of exponential random variables and a probability distribution with a most unusual behavior linked to Jacobi's theta functions. We also present some results for the case when the items' locations are not uniform and discuss the optimal allocation problem.

[Nelly Litvak]
[University of Twente, The Netherlands]