Duration problem with multiple exchanges
| Autor: | Mitsushi Tamaki, Krzysztof Szajowski, Charles E. M. Pearce |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Control and Optimization
Algebra and Number Theory Applied Mathematics Existential quantification Probability (math.PR) 60G40 62L15 60K99 90A46 Dynamic programming Combinatorics Optimization and Control (math.OC) FOS: Mathematics Optimal stopping Mathematics - Optimization and Control Mathematics - Probability Secretary problem Mathematics |
| Zdroj: | Numerical Algebra, Control and Optimization. 2:333-355 |
| ISSN: | 2155-3289 |
| DOI: | 10.3934/naco.2012.2.333 |
| Popis: | We treat a version of the multiple-choice secretary problem called the multiple-choice duration problem, in which the objective is to maximize the time of possession of relatively best objects. It is shown that, for the $m$--choice duration problem, there exists a sequence (s1,s2,...,sm) of critical numbers such that, whenever there remain k choices yet to be made, then the optimal strategy immediately selects a relatively best object if it appears at or after time $s_k$ ($1\leq k\leq m$). We also exhibit an equivalence between the duration problem and the classical best-choice secretary problem. A simple recursive formula is given for calculating the critical numbers when the number of objects tends to infinity. Extensions are made to models involving an acquisition or replacement cost. 30 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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