PICKING CLUMPY ORDERS ON A CAROUSEL

Authors:
Yat-Wah Wan;Ronald W. Wolff
Affiliations:
Department of Industrial Engineering and Engineering Management, University of Science and Technology, Clear Water Bay, Hong Kong, E-mail: ieywan@ust.hk;Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, E-mail: wolff@ieor.berkeley.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2004

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Abstract

Carousels are rotatable closed-loop storage systems for small items, where items are stored in bins along the loop. An order at a carousel consists of (say) n different items stored there. We analyze two problems: (1) minimizing the total time to fill an order (travel time) and (2) order delays as they arrive, are filled, and depart. We define clumpy orders and the nearest-end-point heuristic (NEPH) for picking them. We determine conditions for NEPH to be optimal for problem (1), and under a weak stochastic assumption, we derive the distribution of travel time. We compare NEPH with the nearest-item heuristic. Under Poisson arrivals and assumptions much weaker than in the literature, we show that problem (2) may be modeled as an M/G/1 queue.