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Optimal Sequential Assignments with Random Arrival Times

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  • S. Christian Albright

    (Indiana University)

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    Abstract

    A problem is considered where jobs arrive at random times and assume random values, or importance. These must be assigned to a fixed set of men whose qualities are different but known. As each job arrives, its value is observed and the decision-maker must decide which man, if any, to assign to this job. If a job arrives at time t and its value is observed to be x, then by assigning man i with quality p i, a reward r(t)p ix is received, where r(t) is a discount function. The object is to find an assignment policy which maximizes the expected reward from the available men. The problem is analyzed for different arrival distributions and for different discount functions, but in all cases, the optimal policies are shown to have fairly simple forms, independent of the actual qualities of the men, the p i's. Other interpretations of the model, besides the men and jobs interpretation, are also given. The paper concludes with a similar model which does not, however, include time as an explicit parameter.

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    File URL: http://dx.doi.org/10.1287/mnsc.21.1.60
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 21 (1974)
    Issue (Month): 1 (September)
    Pages: 60-67

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    Handle: RePEc:inm:ormnsc:v:21:y:1974:i:1:p:60-67

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    Cited by:
    1. Dirk Bergemann & Maher Said, 2010. "Dynamic Auctions: A Survey," Levine's Working Paper Archive 661465000000000035, David K. Levine.
    2. Gershkov, Alex & Moldovanu, Benny, 2012. "Dynamic allocation and pricing: A mechanism design approach," International Journal of Industrial Organization, Elsevier, vol. 30(3), pages 283-286.
    3. Sofronov, Georgy, 2013. "An optimal sequential procedure for a multiple selling problem with independent observations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 332-336.
    4. Moldovanu, Benny & Dizdar, Deniz & Gershkov, Alex, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society, vol. 6(2), May.
    5. Anna Krasnosielska-Kobos & Elżbieta Ferenstein, 2013. "Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem," Dynamic Games and Applications, Springer, vol. 3(2), pages 220-235, June.
    6. Francis Bloch & Nicolas Houy, 2009. "Optimal Assignment of Durable Objects to Successive Agents," Working Papers hal-00435385, HAL.
    7. Gershkov, Alex & Moldovanu, Benny, 2007. "The Dynamic Assignment of Heterogenous Objects: A Mechanism Design Approach," CEPR Discussion Papers 6439, C.E.P.R. Discussion Papers.
    8. David, Israel & Levi, Ofer, 2004. "A new algorithm for the multi-item exponentially discounted optimal selection problem," European Journal of Operational Research, Elsevier, vol. 153(3), pages 782-789, March.
    9. Alex Gershkov & Benny Moldovanu, 2007. "Dynamic Assignment of Heterogeneous Objects: A Mechanism Design Approach," Levine's Working Paper Archive 843644000000000381, David K. Levine.
    10. David, Israel & Levi, Ofer, 2001. "Asset-selling problems with holding costs," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 317-321, May.
    11. Hak Chun, Young, 1996. "Selecting the best choice in the weighted secretary problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 135-147, July.
    12. Gershkov, Alex & Moldovanu, Benny, 2010. "Efficient sequential assignment with incomplete information," Games and Economic Behavior, Elsevier, vol. 68(1), pages 144-154, January.

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