IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v49y2001i1p52-65.html
   My bibliography  Save this article

The Batch Loading and Scheduling Problem

Author

Listed:
  • Gregory Dobson

    (William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, New York 14627)

  • Ramakrishnan S. Nambimadom

    (Burning Glass Technologies, San Diego, California 92120)

Abstract

This paper discusses the problem of batching and scheduling of certain kinds of batch processors. Examples of these processors include heat treatment facilities, particularly in the steel and ceramics industries, as well as a variety of operations in the manufacture of integrated circuits. In general, for our problem there is a set of jobs waiting to be processed. Each job is associated with a given family and has a weight or delay cost and a volume. The scheduler must organize jobs into batches in which each batch consists of jobs from a single family and in which the total volume of jobs in a batch does not exceed the capacity of the processor. The scheduler must then sequence all the batches. The processing time for a batch depends only on the family and not on the number or the volume of jobs in the batch. The objective is to minimize the mean weighted flow time.The paper presents an integer programming formulation for this problem, generates a lower bound from a partial LP relaxation, provides a polynomial algorithm to solve a special case, and tests a set of heuristics on the general problem. The ability to pack jobs into batches is the key to efficient solutions and is the basis of the different solution procedures in this paper. The heuristics include a greedy heuristic, a successive knapsack heuristic, and a generalized assignment heuristic. Optimal solutions are obtained by complete enumeration for small problems.The conclusions of the computational study show that the successive knapsack and generalized assignment heuristics perform better than the greedy. The generalized assignment heuristic does slightly better than the successive knapsack heuristic in some cases, but the latter is substantially faster and more robust. For problems with few jobs, the generalized assignment heuristic and the knapsack heuristic almost always provide optimal solutions. For problems with more jobs, we compare the heruistic solutions' values to lower bounds; the computational work suggests that the heuristics continue to provide solutions that are optimal or close to the optimal. The study also shows that the volume of the job relative to the capacity of the facility and the number of jobs in a family affect the performance of the heuristics, whereas the number of families does not. Finally, we give a worst-case analysis of the greedy heuristic.

Suggested Citation

  • Gregory Dobson & Ramakrishnan S. Nambimadom, 2001. "The Batch Loading and Scheduling Problem," Operations Research, INFORMS, vol. 49(1), pages 52-65, February.
  • Handle: RePEc:inm:oropre:v:49:y:2001:i:1:p:52-65
    DOI: 10.1287/opre.49.1.52.11189
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.49.1.52.11189
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.49.1.52.11189?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Dorit S. Hochbaum & Dan Landy, 1997. "Scheduling Semiconductor Burn-In Operations to Minimize Total Flowtime," Operations Research, INFORMS, vol. 45(6), pages 874-885, December.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    4. Javad H. Ahmadi & Reza H. Ahmadi & Sriram Dasu & Christopher S. Tang, 1992. "Batching and Scheduling Jobs on Batch and Discrete Processors," Operations Research, INFORMS, vol. 40(4), pages 750-763, August.
    5. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ruyan Fu & Ji Tian & Shisheng Li & Jinjiang Yuan, 2017. "An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1187-1197, November.
    2. Yang, Fan & Davari, Morteza & Wei, Wenchao & Hermans, Ben & Leus, Roel, 2022. "Scheduling a single parallel-batching machine with non-identical job sizes and incompatible job families," European Journal of Operational Research, Elsevier, vol. 303(2), pages 602-615.
    3. Vishnu Erramilli & Scott Mason, 2008. "Multiple orders per job batch scheduling with incompatible jobs," Annals of Operations Research, Springer, vol. 159(1), pages 245-260, March.
    4. Yuan Gao & Jinjiang Yuan, 2019. "Unbounded parallel-batch scheduling under agreeable release and processing to minimize total weighted number of tardy jobs," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 698-711, October.
    5. Lawrence C. Leung & Yer Van Hui & Yong Wang & Gang Chen, 2009. "A 0--1 LP Model for the Integration and Consolidation of Air Cargo Shipments," Operations Research, INFORMS, vol. 57(2), pages 402-412, April.
    6. Perboli, Guido & Brotcorne, Luce & Bruni, Maria Elena & Rosano, Mariangela, 2021. "A new model for Last-Mile Delivery and Satellite Depots management: The impact of the on-demand economy," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    7. Yuan Gao & Jinjiang Yuan & Zhigang Wei, 2019. "Unbounded parallel-batch scheduling with drop-line tasks," Journal of Scheduling, Springer, vol. 22(4), pages 449-463, August.
    8. Alessandro Druetto & Erica Pastore & Elena Rener, 2023. "Parallel batching with multi-size jobs and incompatible job families," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 440-458, July.
    9. Laub, Jeffrey D. & Fowler, John W. & Keha, Ahmet B., 2007. "Minimizing makespan with multiple-orders-per-job in a two-machine flowshop," European Journal of Operational Research, Elsevier, vol. 182(1), pages 63-79, October.
    10. Payman Jula & Robert C. Leachman, 2010. "Coordinated Multistage Scheduling of Parallel Batch-Processing Machines Under Multiresource Constraints," Operations Research, INFORMS, vol. 58(4-part-1), pages 933-947, August.
    11. Salim Haddadi, 2019. "Variable-fixing then subgradient optimization guided very large scale neighborhood search for the generalized assignment problem," 4OR, Springer, vol. 17(3), pages 261-295, September.
    12. Li, Xueping & Zhang, Kaike, 2018. "Single batch processing machine scheduling with two-dimensional bin packing constraints," International Journal of Production Economics, Elsevier, vol. 196(C), pages 113-121.
    13. Koh, Shie-Gheun & Koo, Pyung-Hoi & Kim, Dong-Chun & Hur, Won-Suk, 2005. "Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families," International Journal of Production Economics, Elsevier, vol. 98(1), pages 81-96, October.
    14. Chakhlevitch, Konstantin & Glass, Celia A. & Kellerer, Hans, 2011. "Batch machine production with perishability time windows and limited batch size," European Journal of Operational Research, Elsevier, vol. 210(1), pages 39-47, April.
    15. Fehmi Tanrisever & Erhan Kutanoglu, 2008. "Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: Single machine problem," Annals of Operations Research, Springer, vol. 159(1), pages 5-24, March.
    16. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    17. Yong-Jae Kim & Byung-Soo Kim, 2022. "Population-Based Meta-Heuristic Algorithms for Integrated Batch Manufacturing and Delivery Scheduling Problem," Mathematics, MDPI, vol. 10(21), pages 1-22, November.
    18. A H Kashan & B Karimi, 2008. "Scheduling a single batch-processing machine with arbitrary job sizes and incompatible job families: An ant colony framework," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1269-1280, September.
    19. Thomas Schmitt & Bruce Faaland, 2004. "Scheduling recurrent construction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1102-1128, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    2. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    3. Sung, Chang Sup & Kim, Young Hwan & Yoon, Sang Hum, 2000. "A problem reduction and decomposition approach for scheduling for a flowshop of batch processing machines," European Journal of Operational Research, Elsevier, vol. 121(1), pages 179-192, February.
    4. Sup Sung, Chang & Hwan Kim, Young, 2003. "Minimizing due date related performance measures on two batch processing machines," European Journal of Operational Research, Elsevier, vol. 147(3), pages 644-656, June.
    5. Koh, Shie-Gheun & Koo, Pyung-Hoi & Kim, Dong-Chun & Hur, Won-Suk, 2005. "Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families," International Journal of Production Economics, Elsevier, vol. 98(1), pages 81-96, October.
    6. Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    7. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Discussion Paper 2008-100, Tilburg University, Center for Economic Research.
    8. Tang, Lixin & Zhao, Yufang, 2008. "Scheduling a single semi-continuous batching machine," Omega, Elsevier, vol. 36(6), pages 992-1004, December.
    9. C S Sung & H C Rim, 2004. "Receiver set partitioning and sequencing for multicasting traffic in a WDM lightwave single-hop network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 630-639, June.
    10. Chung Keung Poon & Wenci Yu, 2005. "On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 167-186, March.
    11. Jolai, Fariborz, 2005. "Minimizing number of tardy jobs on a batch processing machine with incompatible job families," European Journal of Operational Research, Elsevier, vol. 162(1), pages 184-190, April.
    12. Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.
    13. Lin, B.M.T. & Cheng, T.C.E. & Chou, A.S.C., 2007. "Scheduling in an assembly-type production chain with batch transfer," Omega, Elsevier, vol. 35(2), pages 143-151, April.
    14. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Other publications TiSEM ed1f8fce-da76-41a6-9a9e-9, Tilburg University, School of Economics and Management.
    15. Sung, C. S. & Choung, Y. I., 2000. "Minimizing makespan on a single burn-in oven in semiconductor manufacturing," European Journal of Operational Research, Elsevier, vol. 120(3), pages 559-574, February.
    16. Melouk, Sharif & Damodaran, Purushothaman & Chang, Ping-Yu, 2004. "Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing," International Journal of Production Economics, Elsevier, vol. 87(2), pages 141-147, January.
    17. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    18. Chang, Yung-Chia & Lee, Chung-Yee, 2004. "Machine scheduling with job delivery coordination," European Journal of Operational Research, Elsevier, vol. 158(2), pages 470-487, October.
    19. Bo Chen & Xiaotie Deng & Wenan Zang, 2004. "On-Line Scheduling a Batch Processing System to Minimize Total Weighted Job Completion Time," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 85-95, March.
    20. Beat Gfeller & Leon Peeters & Birgitta Weber & Peter Widmayer, 2009. "Single machine batch scheduling with release times," Journal of Combinatorial Optimization, Springer, vol. 17(3), pages 323-338, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:49:y:2001:i:1:p:52-65. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.