| Project/Area Number |
10680439
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
社会システム工学
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| Research Institution | Aichi University |
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Principal Investigator |
TAMAKI Mitsuhi Aichi University, Dept. of Business Administration, Professor, 経営学部, 教授 (40121876)
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| Co-Investigator(Kenkyū-buntansha) |
OHNO Katsuhisa Nagoya Institute of Technology, Dept. of Engineering, Professor, 工学部, 教授 (50026118)
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| Project Period (FY) |
1998 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | secretary problem / best choice problem / optimal stopping / relative rank / dynamic programming / multiple choice / rank minimization / probability maximization / optimal selection / urn problem / ballot problem / random walk / multiple choril / optiomal selection / optiomal stopping / rdativl rank |
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| Research Abstract |
In 1998 and 1999, we mainly studied the secretary problem with rank-dependent rejection probability. The main result is summarized in Section 2.6. The rank minimization problem with refusal is considered in Section 2.7. The problem considered in Section 2.5 also falls into the category of the problem with refusal. Boyce's urn problem, a model of bond-selling problem, is modified as a problem of stopping on the maximum of the trajectory with maximum probability. This is analyzed in Section 2.12. The versions of the so called duration problem, which is concerned with maximizing the expected duration of keeping the relatively best applicant, are considered in Sections 2.2 and 2.3. A multiple-choice secretary problem with a random number of applicants is considered in Section 2.4..
In 2000, the problems we considered are probabilistic interpretation of an identity related to the Stirling number of the first kind and an optimal stopping problem related to the random walk. The results are given in Sections 2.8 and 2.10 respectively.
In 2001, Bruss odds theorem is generalized to cover the case with uncertain selection. A multiple-choice secretary problem with partial recall whose objective is to minimize the total expected ranks of the applicants chosen is still under consideration. However, its partial result is given in Section 7 of the survey paper given in Section 2.14. Sections 2.1,2.9 and 2.13 are devoted to some related problems.
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