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Customer scheduling with incomplete information. (English) Zbl 1335.90042

Summary: A stochastic scheduling model with linear waiting costs and unknown routing probabilities is considered. Using a Bayesian approach and methods of Bayesian dynamic programming, we investigate the finite-horizon stochastic scheduling problem with incomplete information. In particular, we study an equivalent nonstationary bandit model and show the monotonicity of the total expected reward and of the Gittins index. We derive the monotonicity and well-known structural properties of the (greatest) maximizers, the so-called stay-on-a-winnerproperty and the stopping-property. The monotonicity results are based on a special partial ordering on \(\mathbb{N}^k_0\).

MSC:

90B35 Deterministic scheduling theory in operations research
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[1] DOI: 10.2307/1427064 · Zbl 0557.60082 · doi:10.2307/1427064
[2] Burnetas, Probability in the Engineering and Informational Sciences 7 pp 85– (1993)
[3] Berry, Bandit problems (1985) · doi:10.1007/978-94-015-3711-7
[4] DOI: 10.2307/1427059 · Zbl 0554.60087 · doi:10.2307/1427059
[5] DOI: 10.1007/BF01414030 · Zbl 0819.90047 · doi:10.1007/BF01414030
[6] Gittins, Multi-armed bandit allocation indices (1989) · Zbl 0699.90068
[7] Ross, Introduction to stochastic dynamic programming (1983) · Zbl 0567.90065
[8] DOI: 10.1007/BF02204833 · Zbl 0749.62051 · doi:10.1007/BF02204833
[9] DOI: 10.2307/1426080 · Zbl 0316.90081 · doi:10.2307/1426080
[10] DOI: 10.1093/biomet/65.2.335 · Zbl 0381.62065 · doi:10.1093/biomet/65.2.335
[11] DOI: 10.2307/3213458 · Zbl 0373.90035 · doi:10.2307/3213458
[12] DOI: 10.1287/opre.25.2.248 · Zbl 0372.60137 · doi:10.1287/opre.25.2.248
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