IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v272y2019i3p999-1016.html
   My bibliography  Save this article

Analysis of a chance-constrained new product risk model with multiple customer classes

Author

Listed:
  • Fontem, Belleh
  • Smith, Jeremiah

Abstract

We consider the non-convex problem of minimizing a linear deterministic cost objective subject to a probabilistic requirement on a nonlinear multivariate stochastic expression attaining, or exceeding a given threshold. The stochastic expression represents the output of a noisy system featuring the product of mutually-independent, uniform random parameters each raised to a linear function of one of the decision vector’s constituent variables. We prove a connection to (i) the probability measure on the superposition of a finite collection of uncorrelated exponential random variables, and (ii) an entropy-like affine function. Then, we determine special cases for which the optimal solution exists in closed-form, or is accessible via sequential linear programming. These special cases inspire the design of a gradient-based heuristic procedure that guarantees a feasible solution for instances failing to meet any of the special case conditions. The application motivating our study is a consumer goods firm seeking to cost-effectively manage a certain aspect of its new product risk. We test our heuristic on a real problem and compare its overall performance to that of an asymptotically optimal Monte-Carlo-based method called sample average approximation. Numerical experimentation on synthetic problem instances sheds light on the interplay between the optimal cost and various parameters including the probabilistic requirement and the required threshold.

Suggested Citation

  • Fontem, Belleh & Smith, Jeremiah, 2019. "Analysis of a chance-constrained new product risk model with multiple customer classes," European Journal of Operational Research, Elsevier, vol. 272(3), pages 999-1016.
    • Handle: RePEc:eee:ejores:v:272:y:2019:i:3:p:999-1016
    DOI: 10.1016/j.ejor.2018.07.042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718306647
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.07.042?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. Shahbaz, Muhammad & Benkraiem, Ramzi & Miloudi, Anthony & Lahiani, Amine, 2017. "Production function with electricity consumption and policy implications in Portugal," Energy Policy, Elsevier, vol. 110(C), pages 588-599.
    2. repec:bla:econom:v:51:y:1984:i:204:p:401-11 is not listed on IDEAS
    3. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    4. S K Mishra, 2010. "A Brief History of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 6-34, November.
    5. Fakhar, Majid & Mahyarinia, Mohammad Reza & Zafarani, Jafar, 2018. "On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 265(1), pages 39-48.
    6. Abebe Geletu & Michael Klöppel & Hui Zhang & Pu Li, 2013. "Advances and applications of chance-constrained approaches to systems optimisation under uncertainty," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(7), pages 1209-1232.
    7. Zhang, Bangbang & Feng, Gary & Ahuja, Lajpat R. & Kong, Xiangbin & Ouyang, Ying & Adeli, Ardeshir & Jenkins, Johnie N., 2018. "Soybean crop-water production functions in a humid region across years and soils determined with APEX model," Agricultural Water Management, Elsevier, vol. 204(C), pages 180-191.
    8. A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
    9. Thomas M. Humphrey, 1997. "Algebraic production functions and their uses before Cobb-Douglas," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 51-83.
    10. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    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. Wang, Tingsong & Meng, Qiang & Wang, Shuaian & Tan, Zhijia, 2013. "Risk management in liner ship fleet deployment: A joint chance constrained programming model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 1-12.
    2. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    3. G. Pantuso & L. M. Hvattum, 2021. "Maximizing performance with an eye on the finances: a chance-constrained model for football transfer market decisions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 583-611, July.
    4. Yanikoglu, I. & den Hertog, D., 2011. "Safe Approximations of Chance Constraints Using Historical Data," Other publications TiSEM ab77f6f2-248a-42f1-bde1-0, Tilburg University, School of Economics and Management.
    5. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    6. Chen, Zhen & Archibald, Thomas W., 2024. "Maximizing the survival probability in a cash flow inventory problem with a joint service level constraint," International Journal of Production Economics, Elsevier, vol. 270(C).
    7. Maji, Chandi Charan, 1975. "Intertemporal allocation of irrigation water in the Mayurakshi Project (India): an application of deterministic and chance-constrained linear programming," ISU General Staff Papers 197501010800006381, Iowa State University, Department of Economics.
    8. Yongjia Song & Minjiao Zhang, 2015. "Chance‐constrained multi‐terminal network design problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 321-334, June.
    9. 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.
    10. Wang, Tingsong & Tian, Xuecheng & Wang, Yadong, 2020. "Container slot allocation and dynamic pricing of time-sensitive cargoes considering port congestion and uncertain demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    11. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    12. L. Jeff Hong & Zhaolin Hu & Liwei Zhang, 2014. "Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 385-400, May.
    13. Grani A. Hanasusanto & Vladimir Roitch & Daniel Kuhn & Wolfram Wiesemann, 2017. "Ambiguous Joint Chance Constraints Under Mean and Dispersion Information," Operations Research, INFORMS, vol. 65(3), pages 751-767, June.
    14. Xide Zhu & Peijun Guo, 2020. "Bilevel programming approaches to production planning for multiple products with short life cycles," 4OR, Springer, vol. 18(2), pages 151-175, June.
    15. Saldanha-da-Gama, Francisco, 2022. "Facility Location in Logistics and Transportation: An enduring relationship," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 166(C).
    16. Hadi Charkhgard & Mahdi Takalloo & Zulqarnain Haider, 2020. "Bi-objective autonomous vehicle repositioning problem with travel time uncertainty," 4OR, Springer, vol. 18(4), pages 477-505, December.
    17. Bowen Li & Ruiwei Jiang & Johanna L. Mathieu, 2022. "Integrating unimodality into distributionally robust optimal power flow," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 594-617, October.
    18. Shanshan Wang & Jinlin Li & Sanjay Mehrotra, 2021. "Chance-Constrained Multiple Bin Packing Problem with an Application to Operating Room Planning," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1661-1677, October.
    19. Nicol`o Cangiotti & Mattia Sensi, 2020. "A geometric characterization of VES and Kadiyala-type production functions," Papers 2004.09617, arXiv.org.
    20. Qiushi Chen & Lei Zhao & Jan C. Fransoo & Zhe Li, 2019. "Dual-mode inventory management under a chance credit constraint," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 147-178, March.

    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:272:y:2019:i:3:p:999-1016. 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.