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Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues

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  • Warren B. Powell

    (Princeton University, Princeton, New Jersey)

Abstract

A general class of vehicle dispatching strategies for bulk arrival, bulk service queues is examined which consist of some combination of vehicle holding and cancellation strategies. The moments of the length of the queue at vehicle departure instants and in continuous time are solved for exactly using transform methods. Relationships between the moments of the waiting time and queue length distributions are developed without further use of transforms, resulting in an exact expression for the expected waiting time and an approximation for the variance. A simple approach for calculating the roots of a particular function, needed to find the moments of the queue length distribution, is presented and used to demonstrate that this task can be accomplished very easily. Finally, the model is used to compare alternative vehicle dispatching strategies in terms of costs and levels of service.

Suggested Citation

  • Warren B. Powell, 1985. "Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 19(4), pages 352-377, November.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:4:p:352-377
    DOI: 10.1287/trsc.19.4.352
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    Citations

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    Cited by:

    1. Katerina P. Papadaki & Warren B. Powell, 2003. "An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 742-769, October.
    2. Le-Duc, T. & de Koster, M.B.M., 2002. "Determining The Optimal Order Picking Batch Size In Single Aisle Warehouses," ERIM Report Series Research in Management ERS-2002-64-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Srinivas R. Chakravarthy & Serife Ozkar, 2024. "A Queueing Model with BMAP Arrivals and Heterogeneous Phase Type Group Services," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-30, December.
    4. Souvik Ghosh & A. D. Banik & Joris Walraevens & Herwig Bruneel, 2022. "A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service," 4OR, Springer, vol. 20(2), pages 241-272, June.
    5. Sila Çetinkaya & Chung-Yee Lee, 2000. "Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory Systems," Management Science, INFORMS, vol. 46(2), pages 217-232, February.
    6. Hall, Randolph W. & Sabnani, Vikas C., 2002. "Control of vehicle dispatching on a cyclic route serving trucking terminals," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(3), pages 257-276, March.
    7. Xu Jun Eberlein & Nigel H. M. Wilson & David Bernstein, 2001. "The Holding Problem with Real–Time Information Available," Transportation Science, INFORMS, vol. 35(1), pages 1-18, February.
    8. Chung-Yee Lee & Sila Çetinkaya & Wikrom Jaruphongsa, 2003. "A Dynamic Model for Inventory Lot Sizing and Outbound Shipment Scheduling at a Third-Party Warehouse," Operations Research, INFORMS, vol. 51(5), pages 735-747, October.
    9. Çetinkaya, SIla & Bookbinder, James H., 2003. "Stochastic models for the dispatch of consolidated shipments," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 747-768, September.
    10. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "Acceptance and Dispatching Policies for a Distribution Problem," Transportation Science, INFORMS, vol. 32(2), pages 127-141, May.
    11. Sıla Çetinkaya & Chung‐Yee Lee, 2002. "Optimal outbound dispatch policies: Modeling inventory and cargo capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 531-556, September.
    12. Papadaki, Katerina P. & Powell, Warren B., 2002. "Exploiting structure in adaptive dynamic programming algorithms for a stochastic batch service problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 108-127, October.
    13. M. A. A. Boon & A. J. E. M. Janssen & J. S. H. Leeuwaarden & R. W. Timmerman, 2019. "Pollaczek contour integrals for the fixed-cycle traffic-light queue," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 89-111, February.
    14. Warren B. Powell, 1987. "Waiting‐time distributions for bulk arrival, bulk service queues with vehicle‐holding and cancellation strategies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 207-227, April.

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