Amortized efficiency of list update and paging rules
Communications of the ACM
On-line single-server dial-a-ride problems
Theoretical Computer Science
Online Dial-a-Ride Problems: Minimizing the Completion Time
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Competitive Analysis of Algorithms
Developments from a June 1996 seminar on Online algorithms: the state of the art
Order-batching methods for an order-picking warehouse with two cross aisles
Computers and Industrial Engineering
Batching orders in warehouses by minimizing travel distance with genetic algorithms
Computers in Industry - Special issue: Application of genetics algorithms in industry
On minimizing the maximum flow time in the online dial-a-ride problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Online single machine batch scheduling
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Computers and Industrial Engineering
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In manual order picking systems, order pickers walk or ride through a distribution warehouse in order to collect items required by (internal or external) customers. Order batching consists of combining these - indivisible - customer orders into picking orders. With respect to order batching, two problem types can be distinguished: in off-line (static) batching, all customer orders are known in advance; in on-line (dynamic) batching, customer orders become available dynamically over time. This paper considers an on-line order batching problem in which the maximum completion time of the customer orders arriving within a certain time period has to be minimized. The author shows how heuristic approaches for off-line order batching can be modified in order to deal with the on-line situation. In a competitive analysis, lower and upper bounds for the competitive ratios of the proposed algorithms are presented. The proposed algorithms are evaluated in a series of extensive numerical experiments. It is demonstrated that the choice of an appropriate batching method can lead to a substantial reduction of the maximum completion time.