IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v48y2000i1p73-79.html
   My bibliography  Save this article

Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs

Author

Listed:
  • Raymond K.-M. Cheung

    (Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong)

  • Warren B. Powell

    (Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544)

Abstract

We consider the problem of approximating the expected recourse function for two-stage stochastic programs. Our problem is motivated by applications that have special structure, such as an underlying network that allows reasonable approximations to the expected recourse function to be developed. In this paper, we show how these approximations can be improved by combining them with sample gradient information from the true recourse function. For the case of strictly convex nonlinear approximations, we prove convergence for this hybrid approximation. The method is attractive for practical reasons because it retains the structure of the approximation.

Suggested Citation

  • Raymond K.-M. Cheung & Warren B. Powell, 2000. "Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 73-79, February.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:1:p:73-79
    DOI: 10.1287/opre.48.1.73.12452
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.48.1.73.12452
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.48.1.73.12452?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. Stephen M. Robinson, 1996. "Analysis of Sample-Path Optimization," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 513-528, August.
    2. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    3. Raymond K. Cheung & Warren B. Powell, 1996. "An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management," Operations Research, INFORMS, vol. 44(6), pages 951-963, December.
    4. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    5. Andrzej Ruszczyński, 1987. "A Linearization Method for Nonsmooth Stochastic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 32-49, February.
    6. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, 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. Tao Lu & Jan C. Fransoo & Chung-Yee Lee, 2017. "Carrier Portfolio Management for Shipping Seasonal Products," Operations Research, INFORMS, vol. 65(5), pages 1250-1266, October.
    2. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    3. Fan, Wei & Machemehl, Randy, 2004. "A Multi-stage Monte Carlo Sampling Based Stochastic Programming Model for the Dynamic Vehicle Allocation Problem," 45th Annual Transportation Research Forum, Evanston, Illinois, March 21-23, 2004 208244, Transportation Research Forum.
    4. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    5. ZhenFang Liu & GuoHe Huang, 2009. "Dual-Interval Two-Stage Optimization for Flood Management and Risk Analyses," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(11), pages 2141-2162, September.
    6. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    7. Zhou, Shaorui & Zhang, Hui & Shi, Ning & Xu, Zhou & Wang, Fan, 2020. "A new convergent hybrid learning algorithm for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 283(1), pages 33-46.
    8. Song, Haiqing & Huang, Huei-Chuen, 2008. "A successive convex approximation method for multistage workforce capacity planning problem with turnover," European Journal of Operational Research, Elsevier, vol. 188(1), pages 29-48, July.

    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. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    2. Z. L. Chen & W. B. Powell, 1999. "Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 497-524, September.
    3. Gregory D. Glockner & George L. Nemhauser, 2000. "A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure," Operations Research, INFORMS, vol. 48(2), pages 233-242, April.
    4. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    5. Song, Haiqing & Cheung, Raymond K. & Wang, Haiyan, 2014. "An arc-exchange decomposition method for multistage dynamic networks with random arc capacities," European Journal of Operational Research, Elsevier, vol. 233(3), pages 474-487.
    6. Raymond K. Cheung & Chuen-Yih Chen, 1998. "A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem," Transportation Science, INFORMS, vol. 32(2), pages 142-162, May.
    7. Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    8. Ann Melissa Campbell & Martin W. P. Savelsbergh, 2005. "Decision Support for Consumer Direct Grocery Initiatives," Transportation Science, INFORMS, vol. 39(3), pages 313-327, August.
    9. Riis, Morten & Andersen, Kim Allan, 2005. "Applying the minimax criterion in stochastic recourse programs," European Journal of Operational Research, Elsevier, vol. 165(3), pages 569-584, September.
    10. Cosmin Petra & Mihai Anitescu, 2012. "A preconditioning technique for Schur complement systems arising in stochastic optimization," Computational Optimization and Applications, Springer, vol. 52(2), pages 315-344, June.
    11. Martin Šmíd & Václav Kozmík, 2024. "Approximation of multistage stochastic programming problems by smoothed quantization," Review of Managerial Science, Springer, vol. 18(7), pages 2079-2114, July.
    12. Zhou, Shaorui & Zhang, Hui & Shi, Ning & Xu, Zhou & Wang, Fan, 2020. "A new convergent hybrid learning algorithm for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 283(1), pages 33-46.
    13. Ankur Kulkarni & Uday Shanbhag, 2012. "Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms," Computational Optimization and Applications, Springer, vol. 51(1), pages 77-123, January.
    14. Chang, Tsung-Sheng, 2009. "Decision support for truckload carriers in one-shot combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 522-541, June.
    15. Adarsh Vaderobli & Dev Parikh & Urmila Diwekar, 2020. "Optimization under Uncertainty to Reduce the Cost of Energy for Parabolic Trough Solar Power Plants for Different Weather Conditions," Energies, MDPI, vol. 13(12), pages 1-17, June.
    16. Alexander S. Estes & Michael O. Ball, 2021. "Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 785-807, May.
    17. Raghu Pasupathy, 2010. "On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization," Operations Research, INFORMS, vol. 58(4-part-1), pages 889-901, August.
    18. Joel A. Shapiro & Warren B. Powell, 2006. "A Metastrategy for Large-Scale Resource Management Based on Informational Decomposition," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 43-60, February.
    19. Bojovic, Nebojsa J., 2002. "A general system theory approach to rail freight car fleet sizing," European Journal of Operational Research, Elsevier, vol. 136(1), pages 136-172, January.
    20. Warren B. Powell & Joel A. Shapiro & Hugo P. Simão, 2002. "An Adaptive Dynamic Programming Algorithm for the Heterogeneous Resource Allocation Problem," Transportation Science, INFORMS, vol. 36(2), pages 231-249, May.

    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:48:y:2000:i:1:p:73-79. 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.