Skip to main content
Springer Nature Link
Log in

Triply stochastic sequential assignment problem with the uncertainty in worker survival

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

The Sequential Stochastic Assignment Problem (SSAP), introduced by Derman et al. [1], lies in non-anticipatively assigning workers with given success rates to sequentially arriving jobs to maximize the total expected reward over all assignments; every job’s value follows a given distribution and remains unknown until the job presents itself to the workers. The problem’s variations have practical significance in multiple applications, such as in healthcare (organ allocation) and military operations (target assignment). This paper formulates and solves the Triply Stochastic Sequential Assignment Problem (3SSAP): a generalized SSAP, where (1) the job values, (2) the number of jobs yet to arrive, and (3) the future worker availability - all experience stochasticity. To this end, the paper relies on a decision analysis logic and explains what variations of 3SSAP can be solved with simple threshold policies and why. Closed-form 3SSAP optimal assignment policies are presented, accompanied by illustrative numerical examples of policy application.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Derman, Cyrus, Lieberman, Gerald J., Ross, Sheldon M.: A Sequential Stochastic Assignment Problem. Management Science 18(7), 349–355 (1972)

    Article  MathSciNet  Google Scholar 

  2. Nikolaev, Alexander G., Jacobson, Sheldon H., Mclay, Laura A.: A sequential stochastic security system design problem for aviation security. Transportation Science 41(2), 182–194 (2007)

    Article  Google Scholar 

  3. David, Israel, Yechiali, Uri: One-Attribute Sequential Assignment Match Processes in Discrete Time. Operations Research 43(5), 879–884 (1995)

    Article  MathSciNet  Google Scholar 

  4. Alexander, G., Nikolaev and Sheldon, H. Jacobson.: Stochastic sequential decision-making with a random number of jobs. Operations Research, 58(4 PART 1):1023–1027, (2010)

  5. Christian Albright, S.: A Markov-Decision-Chain Approach to a Stochastic Assignment Problem. Operations Research 22(1), 61–64 (1974)

    Article  MathSciNet  Google Scholar 

  6. Christian Albright, S.: Optimal Sequential Assignments with Random Arrival Times. Management Science 21(1), 60–67 (1974)

    Article  MathSciNet  Google Scholar 

  7. Righter, Rhonda: The stochastic sequential assignment problem with random deadlines. Probability in the Engineering and Informational Sciences 1(2), 189–202 (1987)

    Article  MathSciNet  Google Scholar 

  8. Albright, Christian S.: Bayesian Approach To a Generalized House Selling Problem. Management Science 24(4), 432–440 (1977)

    Article  Google Scholar 

  9. Xuanming, Su., Zenios, Stefanos A.: Patient choice in kidney allocation: A sequential stochastic assignment model. Operations Research 53(3), 443–455 (2005)

    Article  MathSciNet  Google Scholar 

  10. Kennedy, D.P.: Optimal Sequential Assignment. Mathematics of Operations Research 11(4), 619–626 (1986)

    Article  MathSciNet  Google Scholar 

  11. Nakai, Toru: Sequential Stochastic Assignment Problem in a Partially Observable Markov Chain. Mathematics of Operations Research 11(2), 230–240 (1986)

    Article  MathSciNet  Google Scholar 

  12. Righter, Rhonda: Resource allocation problem in a random environment. Operations Research 37(2), 329–338 (1989)

    Article  MathSciNet  Google Scholar 

  13. Khatibi, Arash, Baharian, Golshid, Kone, Estelle R., Jacobson, Sheldon H.: The sequential stochastic assignment problem with random success rates. IIE Transactions (Institute of Industrial Engineers) 46(11), 1169–1180 (2014)

    Google Scholar 

  14. Baharian, Golshid, Khatibi, Arash, Jacobson, Sheldon H.: Sequential stochastic assignment problem with time-dependent random success rates. Journal of Applied Probability 53(4), 1052–1063 (2016)

    Article  MathSciNet  Google Scholar 

  15. Baharian, Golshid, Jacobson, Sheldon H.: Stochastic sequential assignment problem with threshold criteria. Probability in the Engineering and Informational Sciences 27(3), 277–296 (2013)

    Article  MathSciNet  Google Scholar 

  16. Baharian, Golshid, Jacobson, Sheldon H.: Limiting behavior of the target-dependent stochastic sequential assignment problem. Journal of Applied Probability 51(4), 943–953 (2014)

    Article  MathSciNet  Google Scholar 

  17. Khatibi, Arash, Jacobson, Sheldon H.: Generalized Sequential Stochastic Assignment Problem. Stochastic Systems 8(4), 293–306 (2018)

    Article  MathSciNet  Google Scholar 

  18. Khatibi, Arash, Jacobson, Sheldon H.: Doubly Stochastic Sequential Assignment Problem. Naval Research Logistics 63(2), 124–137 (2016)

    Article  MathSciNet  Google Scholar 

  19. Yu, G., Jacobson, S.H., Kiyavash, N.: Asymptotic analysis for multi-objective sequential stochastic assignment problems. Stochastics 92(2), 223–264 (2020)

    Article  MathSciNet  Google Scholar 

  20. David, Israel, Yechiali, Uri: Sequential assignment match processes with arrivals of candidates and offers. Probability in the Engineering and Informational Sciences 4(4), 413–430 (1990)

    Article  Google Scholar 

  21. Zenios, Stefanos A.: Modeling the transplant waiting list: A queueing model with reneging. Queueing Systems 31(3–4), 239–251 (1999)

    Article  MathSciNet  Google Scholar 

  22. Paret, Kyle E., Mayorga, Maria E., and Lodree. Emmett J.: Assigning spontaneous volunteers to relief efforts under uncertainty in task demand and volunteer availability. Omega (United Kingdom), 99:102228, (2021)

  23. Mayorga, Maria E., Lodree, Emmett J., Wolczynski, Justin: The optimal assignment of spontaneous volunteers. Journal of the Operational Research Society 68(9), 1106–1116 (2017)

    Article  Google Scholar 

  24. Paciarotti, Claudia, Cesaroni, Angela, Bevilacqua, Maurizio: The management of spontaneous volunteers: A successful model from a flood emergency in Italy. International Journal of Disaster Risk Reduction 31, 260–274 (2018)

    Article  Google Scholar 

  25. Gallant, Brian: Managing the Spontaneous Volunteer. EVAN M, BERMAN (2008)

    Book  Google Scholar 

  26. Mazlan, Nurulhasanah, Ahmad, Sharifah Sakinah Syed., Kamalrudin, Massila: Volunteer selection based on crowdsourcing approach. Journal of Ambient Intelligence and Humanized Computing 9(3), 743–753 (2018)

    Article  Google Scholar 

  27. Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. Cambridge University Press (1952)

Download references

Author information

Authors and Affiliations

  1. MedStar Health Research Institute, Hyattsville, MD, USA

    Siddhartha Nambiar

  2. University at Buffalo (SUNY), Buffalo, NY, USA

    Alexander Nikolaev

  3. AFRL Munitions Directorate, Air Force Research Laboratory, Eglin, FL, USA

    Eduardo Pasiliao

Authors
  1. Siddhartha Nambiar
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Alexander Nikolaev
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Eduardo Pasiliao
    View author publications

    You can also search for this author inPubMed Google Scholar

Ethics declarations

Conflicts of interest

This work was funded in part by the 2015 U.S. Air Force Summer Faculty Fellowship (granted to the second author by the Air Force Office of Scientific Research), and in part, by the Mathematical Modeling and Optimization Institute at the University of Florida.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nambiar, S., Nikolaev, A. & Pasiliao, E. Triply stochastic sequential assignment problem with the uncertainty in worker survival. Optim Lett 16, 2469–2482 (2022). https://doi.org/10.1007/s11590-021-01820-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-021-01820-2

Keywords