IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v212y2011i3p433-444.html
   My bibliography  Save this article

Dominance rules in combinatorial optimization problems

Author

Listed:
  • Jouglet, Antoine
  • Carlier, Jacques

Abstract

The aim of this paper is to study the concept of a "dominance rule" in the context of combinatorial optimization. A dominance rule is established in order to reduce the solution space of a problem by adding new constraints to it, either in a procedure that aims to reduce the domains of variables, or directly in building interesting solutions. Dominance rules have been extensively used over the last 50 years. Surprisingly, to our knowledge, no detailed description of them can be found in the literature other than a few short formal descriptions in the context of enumerative methods. We are therefore proposing an investigation into what dominance rules are. We first provide a definition of a dominance rule with its different nuances. Next, we analyze how dominance rules are generally formulated and what are the consequences of such formulations. Finally, we enumerate the common characteristics of dominance rules encountered in the literature and in the usual process of solving combinatorial optimization problems.

Suggested Citation

  • Jouglet, Antoine & Carlier, Jacques, 2011. "Dominance rules in combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 212(3), pages 433-444, August.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:3:p:433-444
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00765-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bennett Fox, 1966. "Discrete Optimization Via Marginal Analysis," Management Science, INFORMS, vol. 13(3), pages 210-216, November.
    2. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    3. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    4. Norman Agin, 1966. "Optimum Seeking with Branch and Bound," Management Science, INFORMS, vol. 13(4), pages 176-185, December.
    5. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    6. John D. C. Little & Katta G. Murty & Dura W. Sweeney & Caroline Karel, 1963. "An Algorithm for the Traveling Salesman Problem," Operations Research, INFORMS, vol. 11(6), pages 972-989, December.
    7. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    8. Jouglet, Antoine & Savourey, David & Carlier, Jacques & Baptiste, Philippe, 2008. "Dominance-based heuristics for one-machine total cost scheduling problems," European Journal of Operational Research, Elsevier, vol. 184(3), pages 879-899, February.
    9. R. E. Levitan, 1959. "A Note on Professor Manne's "Dominance" Theorem," Management Science, INFORMS, vol. 5(3), pages 332-334, April.
    10. Carlier, J. & Pinson, E., 1994. "Adjustment of heads and tails for the job-shop problem," European Journal of Operational Research, Elsevier, vol. 78(2), pages 146-161, October.
    11. Egon Balas, 1967. "Discrete Programming by the Filter Method," Operations Research, INFORMS, vol. 15(5), pages 915-957, October.
    12. Frank Proschan & T. A. Bray, 1965. "Optimum Redundancy Under Multiple Constraints," Operations Research, INFORMS, vol. 13(5), pages 800-814, October.
    13. L. G. Mitten, 1970. "Branch-and-Bound Methods: General Formulation and Properties," Operations Research, INFORMS, vol. 18(1), pages 24-34, February.
    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. Bocquillon, Ronan & Jouglet, Antoine, 2017. "Modeling elements and solving techniques for the data dissemination problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 713-728.
    2. Ponboon, Sattrawut & Qureshi, Ali Gul & Taniguchi, Eiichi, 2016. "Branch-and-price algorithm for the location-routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 1-19.
    3. Rasti-Barzoki, Morteza & Hejazi, Seyed Reza, 2013. "Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries for multiple customers in supply chains," European Journal of Operational Research, Elsevier, vol. 228(2), pages 345-357.
    4. Nasini, Stefano & Nessah, Rabia, 2022. "A multi-machine scheduling solution for homogeneous processing: Asymptotic approximation and applications," International Journal of Production Economics, Elsevier, vol. 251(C).
    5. Braune, R. & Zäpfel, G. & Affenzeller, M., 2012. "An exact approach for single machine subproblems in shifting bottleneck procedures for job shops with total weighted tardiness objective," European Journal of Operational Research, Elsevier, vol. 218(1), pages 76-85.
    6. Jacques Carlier & Antoine Jouglet & Eric Pinson & Abderrahim Sahli, 2022. "A data structure for efficiently managing a set of energy functions," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2460-2481, November.
    7. Falq, Anne-Elisabeth & Fouilhoux, Pierre & Kedad-Sidhoum, Safia, 2022. "Dominance inequalities for scheduling around an unrestrictive common due date," European Journal of Operational Research, Elsevier, vol. 296(2), pages 453-464.
    8. Silva, Marco & Poss, Michael & Maculan, Nelson, 2020. "Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 283(1), pages 70-82.
    9. Rico Walter & Alexander Lawrinenko, 2020. "A characterization of optimal multiprocessor schedules and new dominance rules," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 876-900, November.

    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. Thomas L. Morin & Roy E. Marsten, 1974. "Brand-and-Bound Strategies for Dynamic Programming," Discussion Papers 106, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "A Recursive Approach To The Implementation Of Enumerative Methods," Econometric Institute Archives 272202, Erasmus University Rotterdam.
    3. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    4. Tian, Z. J. & Ng, C. T. & Cheng, T. C. E., 2005. "On the single machine total tardiness problem," European Journal of Operational Research, Elsevier, vol. 165(3), pages 843-846, September.
    5. Jiancheng Long & Wai Yuen Szeto, 2019. "Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks," Operations Research, INFORMS, vol. 67(1), pages 167-182, January.
    6. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    7. M. A. Venkataramanan & Kathryn A. Wilson, 1991. "A branch‐and‐bound algorithm for flow‐path design of automated guided vehicle systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 431-445, June.
    8. Rafael Blanquero & Emilio Carrizosa, 2013. "Solving the median problem with continuous demand on a network," Computational Optimization and Applications, Springer, vol. 56(3), pages 723-734, December.
    9. Koulamas, Christos & Kyparisis, George J., 2019. "New results for single-machine scheduling with past-sequence-dependent setup times and due date-related objectives," European Journal of Operational Research, Elsevier, vol. 278(1), pages 149-159.
    10. Shabtay, Dvir & Steiner, George & Zhang, Rui, 2016. "Optimal coordination of resource allocation, due date assignment and scheduling decisions," Omega, Elsevier, vol. 65(C), pages 41-54.
    11. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1994. "Due‐date assignment and early/tardy scheduling on identical parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 17-32, February.
    12. Sankaran, Jayaram K., 1995. "Column generation applied to linear programs in course registration," European Journal of Operational Research, Elsevier, vol. 87(2), pages 328-342, December.
    13. Coşar Gözükırmızı & Metin Demiralp, 2019. "Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic," Mathematics, MDPI, vol. 7(4), pages 1-23, April.
    14. José Berenguel & L. Casado & I. García & Eligius Hendrix, 2013. "On estimating workload in interval branch-and-bound global optimization algorithms," Journal of Global Optimization, Springer, vol. 56(3), pages 821-844, July.
    15. Gueret, Christelle & Jussien, Narendra & Prins, Christian, 2000. "Using intelligent backtracking to improve branch-and-bound methods: An application to Open-Shop problems," European Journal of Operational Research, Elsevier, vol. 127(2), pages 344-354, December.
    16. Kezong Tang & Xiong-Fei Wei & Yuan-Hao Jiang & Zi-Wei Chen & Lihua Yang, 2023. "An Adaptive Ant Colony Optimization for Solving Large-Scale Traveling Salesman Problem," Mathematics, MDPI, vol. 11(21), pages 1-26, October.
    17. Pan, Yunpeng & Shi, Leyuan, 2006. "Branch-and-bound algorithms for solving hard instances of the one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 168(3), pages 1030-1039, February.
    18. Willem E. de Paepe & Jan Karel Lenstra & Jiri Sgall & René A. Sitters & Leen Stougie, 2004. "Computer-Aided Complexity Classification of Dial-a-Ride Problems," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 120-132, May.
    19. S. David Wu & Eui-Seok Byeon & Robert H. Storer, 1999. "A Graph-Theoretic Decomposition of the Job Shop Scheduling Problem to Achieve Scheduling Robustness," Operations Research, INFORMS, vol. 47(1), pages 113-124, February.
    20. Haiyan Wang & Chung‐Yee Lee, 2005. "Production and transport logistics scheduling with two transport mode choices," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 796-809, December.

    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:eee:ejores:v:212:y:2011:i:3:p:433-444. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.