The travel time in carousel systems under the nearest item heuristic

A carousel is an automated warehousing system consisting of a large number of drawers rotating in a closed loop. In this paper, we study the travel time needed to pick a list of items when the carousel operates under the nearest item heuristic. We find a closed form expression for the distribution and all moments of the travel time. We also analyse the asymptotic behaviour of the travel time when the number of items tends to infinity. All results follow fromprobabilistic argum ents based on properties of uniformorder statistics. A carousel is an automated warehousing system consisting of a large number of drawers rotating in a closed loop in either direction. Such systems are mostly used for the storage and retrieval of small and medium sized goods, which are requested moderately often. The picker has a fixed position in front of the carousel, which rotates the required items to the picker. For a recent review of literature on carousels, as part of a general overview of planning and control of warehousing systems, we refer the reader to (9). An important performance characteristic is the total time needed to pick a list of items. This consists of the pure pick time plus the travel time. Only the latter depends on the pick strategy. In this paper we consider the nearest itemheuristic, where the next itemto be picked is always the nearest one. We will study the statistical properties of the travel time under this heuristic. We model the carousel as a circle of length 1. For ease of presentation, we act as if the picker travels to the items, instead of the other way around. The picker travels at unit speed and has to pick n(> 0) items under the nearest item heuristic. Their positions are uniformly distributed on the circle. Using probabilistic arguments based on properties of uniform order statistics, we derive closed form expressions for the distribution and all moments of the travel time needed to pick n items. We also investigate the asymptotic behaviour of the travel time as n tends to infinity. The performance of the nearest item heuristic has also been investigated by Bartholdi and Platzman (3). They prove that the travel time under the nearest item heuristic is never greater