IDEAS home Printed from https://ideas.repec.org/a/spr/opsear/v57y2020i4d10.1007_s12597-020-00454-9.html
   My bibliography  Save this article

Chance constrained programming with some non-normal continuous random variables

Author

Listed:
  • D. K. Mohanty

    (Indian Institute of Technology, Kharagpur)

  • Avik Pradhan

    (Indrashil Institute of Science and Technology, Gujarat Technological University)

  • M. P. Biswal

    (Indian Institute of Technology, Kharagpur)

Abstract

Stochastic or probabilistic programming is a branch of mathematical programming that deals with some situations in which an optimal decision is desired under random uncertainty of some parameters. In this paper, we consider some chance constrained linear programming problems where the right hand side parameters of the chance-constraints follow some non-normal continuous distributions such as power function distribution, triangular distribution and trapezoidal distribution. To find the solution of the stated problems, we first convert the problems in to equivalent deterministic models. Then standard linear programming techniques are used to solve the equivalent deterministic models. Some numerical examples are presented to illustrate the methodology.

Suggested Citation

  • D. K. Mohanty & Avik Pradhan & M. P. Biswal, 2020. "Chance constrained programming with some non-normal continuous random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1281-1298, December.
    • Handle: RePEc:spr:opsear:v:57:y:2020:i:4:d:10.1007_s12597-020-00454-9
    DOI: 10.1007/s12597-020-00454-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12597-020-00454-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12597-020-00454-9?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
    ---><---

    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. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    2. Sun, Wei & Huang, Guo H. & Lv, Ying & Li, Gongchen, 2013. "Inexact joint-probabilistic chance-constrained programming with left-hand-side randomness: An application to solid waste management," European Journal of Operational Research, Elsevier, vol. 228(1), pages 217-225.
    3. R. Jagannathan, 1974. "Chance-Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 22(2), pages 358-372, April.
    4. Powell, Mark R. & Wilson, James D., 1997. "Risk Assessment for National Natural Resource Conservation Programs," Discussion Papers 10859, Resources for the Future.
    5. Biswal, M. P. & Biswal, N. P. & Li, Duan, 1998. "Probabilistic linear programming problems with exponential random variables: A technical note," European Journal of Operational Research, Elsevier, vol. 111(3), pages 589-597, December.
    6. Bilsel, R. Ufuk & Ravindran, A., 2011. "A multiobjective chance constrained programming model for supplier selection under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1284-1300, September.
    7. Miguel A. Lejeune & François Margot, 2016. "Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities," Operations Research, INFORMS, vol. 64(4), pages 939-957, August.
    8. Powell, Mark & Wilson, James, 1997. "Risk Assessment for National Natural Resource Conservation Programs," RFF Working Paper Series dp-97-49, Resources for the Future.
    9. Avik Pradhan & M. P. Biswal, 2017. "Multi-choice probabilistic linear programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 122-142, March.
    10. N. H. Agnew & R. A. Agnew & J. Rasmussen & K. R. Smith, 1969. "An Application of Chance Constrained Programming to Portfolio Selection in a Casualty Insurance Firm," Management Science, INFORMS, vol. 15(10), pages 512-520, June.
    Full references (including those not matched with items on IDEAS)

    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. Rashed Khanjani-Shiraz & Salman Khodayifar & Panos M. Pardalos, 2021. "Copula theory approach to stochastic geometric programming," Journal of Global Optimization, Springer, vol. 81(2), pages 435-468, October.
    2. Alwynelle (Nell) S. AM, 1999. "Invited Editorial: Risk Assessment Challenges at USDA," Risk Analysis, John Wiley & Sons, vol. 19(3), pages 323-326, June.
    3. Ümit Sakallı & Ömer Baykoç & Burak Birgören, 2011. "Stochastic optimization for blending problem in brass casting industry," Annals of Operations Research, Springer, vol. 186(1), pages 141-157, June.
    4. Cooper, W. W. & Hemphill, H. & Huang, Z. & Li, S. & Lelas, V. & Sullivan, D. W., 1997. "Survey of mathematical programming models in air pollution management," European Journal of Operational Research, Elsevier, vol. 96(1), pages 1-35, January.
    5. Ozgoc-Caglar, C. Derya & Farnsworth, Richard L., 2008. "A Multiple Criteria Decision System to Improve Performance of Federal Conservation Programs," 2008 Conference (52nd), February 5-8, 2008, Canberra, Australia 5986, Australian Agricultural and Resource Economics Society.
    6. Johan René van Dorp & Salvador Cruz Rambaud & José García Pérez & Rafael Herrerías Pleguezuelo, 2007. "An Elicitation Procedure for the Generalized Trapezoidal Distribution with a Uniform Central Stage," Decision Analysis, INFORMS, vol. 4(3), pages 156-166, September.
    7. Xiao Liu & Simge Küçükyavuz, 2018. "A polyhedral study of the static probabilistic lot-sizing problem," Annals of Operations Research, Springer, vol. 261(1), pages 233-254, February.
    8. Michel Minoux & Riadh Zorgati, 2019. "Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems," Journal of Global Optimization, Springer, vol. 75(3), pages 735-766, November.
    9. Sun, Xuting & Chung, Sai-Ho & Choi, Tsan-Ming & Sheu, Jiuh-Biing & Ma, Hoi Lam, 2020. "Combating lead-time uncertainty in global supply chain's shipment-assignment: Is it wise to be risk-averse?," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 406-434.
    10. Xiaodi Bai & Jie Sun & Xiaojin Zheng, 2021. "An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1056-1069, July.
    11. Sun, X.T. & Chung, S.H. & Chan, Felix T.S. & Wang, Zheng, 2018. "The impact of liner shipping unreliability on the production–distribution scheduling of a decentralized manufacturing system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 242-269.
    12. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    13. Aigner, Kevin-Martin & Clarner, Jan-Patrick & Liers, Frauke & Martin, Alexander, 2022. "Robust approximation of chance constrained DC optimal power flow under decision-dependent uncertainty," European Journal of Operational Research, Elsevier, vol. 301(1), pages 318-333.
    14. Zhiping Chen & Shen Peng & Jia Liu, 2018. "Data-Driven Robust Chance Constrained Problems: A Mixture Model Approach," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1065-1085, December.
    15. Zheng, Xiaojin & Wu, Baiyi & Cui, Xueting, 2017. "Cell-and-bound algorithm for chance constrained programs with discrete distributions," European Journal of Operational Research, Elsevier, vol. 260(2), pages 421-431.
    16. Johansson, Robert C. & Claassen, Roger & Peters, Mark, 2002. "New Conservation Initiatives In The 2002 Farm Bill," 2002 Annual meeting, July 28-31, Long Beach, CA 19760, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    18. Borodin, Valeria & Dolgui, Alexandre & Hnaien, Faicel & Labadie, Nacima, 2016. "Component replenishment planning for a single-level assembly system under random lead times: A chance constrained programming approach," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 79-86.
    19. Patrice Gaillardetz & Saeb Hachem, 2019. "Risk-Control Strategies," Papers 1908.02228, arXiv.org.
    20. Atwood, Jay D. & Knight, Lynn & Cattaneo, Andrea & Smith, Peter F., 2003. "Benefit Cost Analysis Of The 2002 Eqip Farm Bill Provisions," 2003 Annual meeting, July 27-30, Montreal, Canada 21992, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    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:spr:opsear:v:57:y:2020:i:4:d:10.1007_s12597-020-00454-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.