IDEAS home Printed from https://ideas.repec.org/a/inm/orited/v18y2017i1p28-36.html
   My bibliography  Save this article

Teaching Use of Binary Variables in Integer Linear Programs: Formulating Logical Conditions

Author

Listed:
  • Scott P. Stevens

    (Computer Information Systems and Business Analytics Department, James Madison University, Harrisonburg, Virginia 22807)

  • Susan W. Palocsay

    (Computer Information Systems and Business Analytics Department, James Madison University, Harrisonburg, Virginia 22807)

Abstract

Binary variables are often needed in linear programming models to indicate whether particular alternatives should be implemented and to impose logical relations among decisions. However, it is usually not obvious to students how to use binary variables to transform conditional statements of logic into linear relations. We propose to address this difficulty with a simple two-step approach. It provides rules for decomposing a conditional requirement into a group of elementary implications and then translating each of these into linear constraints. Pre- and post-test results from a sample of undergraduate business students are presented to support the effectiveness of this pedagogical approach.

Suggested Citation

  • Scott P. Stevens & Susan W. Palocsay, 2017. "Teaching Use of Binary Variables in Integer Linear Programs: Formulating Logical Conditions," INFORMS Transactions on Education, INFORMS, vol. 18(1), pages 28-36, September.
    • Handle: RePEc:inm:orited:v:18:y:2017:i:1:p:28-36
    DOI: 10.1287/ited.2017.0177
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ited.2017.0177
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ited.2017.0177?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. Lynn Gordon & Erhan Erkut, 2004. "Improving Volunteer Scheduling for the Edmonton Folk Festival," Interfaces, INFORMS, vol. 34(5), pages 367-376, October.
    2. Julie Ann Stuart Williams & Maxwell Rankin & Kristine Gallamore & Randall Reid, 2016. "Beyond Model Formulation: Assessment of Novices Graphing, Interpreting, and Writing About Their Model and Solution," INFORMS Transactions on Education, INFORMS, vol. 17(1), pages 13-19, September.
    3. Janice K. Winch & Jack Yurkiewicz, 2014. "Case Article—Class Scheduling with Linear Programming," INFORMS Transactions on Education, INFORMS, vol. 15(1), pages 143-147, September.
    4. Gerald G. Brown & Robert F. Dell, 2007. "Formulating Integer Linear Programs: A Rogues' Gallery," INFORMS Transactions on Education, INFORMS, vol. 7(2), pages 153-159, January.
    5. Alexandra M. Newman & Martin Weiss, 2013. "A Survey of Linear and Mixed-Integer Optimization Tutorials," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 26-38, September.
    6. S G Powell & T R Willemain, 2007. "How novices formulate models. Part I: qualitative insights and implications for teaching," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 983-995, August.
    7. Scott P. Stevens & Susan W. Palocsay, 2004. "A Translation Approach To Teaching Linear Program Formulation," INFORMS Transactions on Education, INFORMS, vol. 4(3), pages 38-54, May.
    8. H. Paul Williams, 2009. "Logic and Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-92280-5, April.
    9. Frederic H. Murphy & Venkat Panchanadam, 1999. "Using Analogical Reasoning and Schema Formation to Improve the Success in Formulating Linear Programming Models," Operations Research, INFORMS, vol. 47(5), pages 663-674, October.
    10. Jeffrey D. Camm & Amitabh S. Raturi & Shigeru Tsubakitani, 1990. "Cutting Big M Down to Size," Interfaces, INFORMS, vol. 20(5), pages 61-66, October.
    11. Plastria, Frank, 2002. "Formulating logical implications in combinatorial optimisation," European Journal of Operational Research, Elsevier, vol. 140(2), pages 338-353, July.
    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. Steven Shechter, 2023. "Case Article—Pediatrician Scheduling at British Columbia Women’s Hospital," INFORMS Transactions on Education, INFORMS, vol. 24(1), pages 35-39, September.
    2. Dries Goossens & Jeroen Beliën, 2023. "Teaching Integer Programming by Scheduling the Belgian Soccer League," INFORMS Transactions on Education, INFORMS, vol. 23(3), pages 164-172, May.

    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. Julie Ann Stuart Williams & Randall Reid & Kristine Gallamore & Maxwell Rankin, 2018. "Introducing Troubleshooting for Model Formulation, Spreadsheet Development, and Memo Communication with Feedforward," INFORMS Transactions on Education, INFORMS, vol. 18(2), pages 102-115, January.
    2. Julie Ann Stuart Williams & Randall Reid & Philip E. Billings & Natalie C. Belford, 2023. "Engaging Students in Optimization Modeling: Gaining Business Disruption Insights," INFORMS Transactions on Education, INFORMS, vol. 24(1), pages 85-94, September.
    3. Julie Ann Stuart Williams & Maxwell Rankin & Kristine Gallamore & Randall Reid, 2016. "Beyond Model Formulation: Assessment of Novices Graphing, Interpreting, and Writing About Their Model and Solution," INFORMS Transactions on Education, INFORMS, vol. 17(1), pages 13-19, September.
    4. Alexandra M. Newman & Martin Weiss, 2013. "A Survey of Linear and Mixed-Integer Optimization Tutorials," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 26-38, September.
    5. Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, vol. 216(2), pages 459-468.
    6. Michael R. Miller & Robert J. Alexander & Vincent A. Arbige & Robert F. Dell & Steven R. Kremer & Brian P. McClune & Jane E. Oppenlander & Joshua P. Tomlin, 2017. "Optimal Allocation of Students to Naval Nuclear-Power Training Units," Interfaces, INFORMS, vol. 47(4), pages 320-335, August.
    7. Plastria, F., 2012. "A note towards improved homeland defense," Omega, Elsevier, vol. 40(2), pages 244-248, April.
    8. Ramiro Saltos & Sebastián Maldonado, 2023. "Case Article—School Timetabling Problem: A Scheduling Problem for High-School Institutions," INFORMS Transactions on Education, INFORMS, vol. 24(1), pages 95-99, September.
    9. Braathen, Christian, 2022. "Interview Scheduling: An Integer Programming Approach," Discussion Papers 2022/10, Norwegian School of Economics, Department of Business and Management Science.
    10. R. Alan Bowman, 2021. "Developing Optimal Student Plans of Study," Interfaces, INFORMS, vol. 51(6), pages 409-421, November.
    11. Sperling, Martina & Schryen, Guido, 2022. "Decision support for disaster relief: Coordinating spontaneous volunteers," European Journal of Operational Research, Elsevier, vol. 299(2), pages 690-705.
    12. Gabriel Zayas‐Cabán & Emmett J. Lodree & David L. Kaufman, 2020. "Optimal Control of Parallel Queues for Managing Volunteer Convergence," Production and Operations Management, Production and Operations Management Society, vol. 29(10), pages 2268-2288, October.
    13. Jomon Aliyas Paul & Leo MacDonald, 2015. "A Teaching Supplement on Sensitivity Analysis for Linear Programming in Undergraduate Business Programs," INFORMS Transactions on Education, INFORMS, vol. 16(1), pages 6-14, September.
    14. James Hebden & Fabian Winkler, 2021. "Impulse-Based Computation of Policy Counterfactuals," Finance and Economics Discussion Series 2021-042, Board of Governors of the Federal Reserve System (U.S.).
    15. Mauro Falasca & Christopher Zobel & Cliff Ragsdale, 2011. "Helping a Small Development Organization Manage Volunteers More Efficiently," Interfaces, INFORMS, vol. 41(3), pages 254-262, June.
    16. Ragheb Rahmaniani & Shabbir Ahmed & Teodor Gabriel Crainic & Michel Gendreau & Walter Rei, 2020. "The Benders Dual Decomposition Method," Operations Research, INFORMS, vol. 68(3), pages 878-895, May.
    17. Emily M. Craparo & Mumtaz Karatas & Tobias U. Kuhn, 2017. "Sensor placement in active multistatic sonar networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 287-304, June.
    18. Roe, R.A. & Smeelen, M. & Hoefeld, C., 2005. "Outsourcing and organizational change : an employee perspective," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    19. Moon, Kyungduk & Lee, Kangbok & Chopra, Sunil & Kwon, Steve, 2022. "Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy," European Journal of Operational Research, Elsevier, vol. 300(2), pages 743-754.
    20. Sonia Cafieri & Alberto Costa & Pierre Hansen, 2014. "Reformulation of a model for hierarchical divisive graph modularity maximization," Annals of Operations Research, Springer, vol. 222(1), pages 213-226, November.

    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:orited:v:18:y:2017:i:1:p:28-36. 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.