Debtor level collection operations using Bayesian dynamic programming

We consider a non-stationary Bayesian dynamic decision model with general state, action and parameter spaces. It is shown that this model can be reduced to a non-Markovian (resp. Markovian) decision model with completely known transition probabilities. Under rather weak convergence assumptions on the expected total rewards some general results are presented concerning the restriction on deterministic generalized Markov policies, the criteria of optimality and the existence of Bayes policies. These facts are based on the above transformations and on results of Hindererand Schäl.

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Bayesian dynamic programming

Advances in Applied Probability ◽

10.1017/s0001867800046012 ◽

1975 ◽

Vol 7 (02) ◽

pp. 330-348 ◽

Cited By ~ 7

Author(s):

Ulrich Rieder

Keyword(s):

Dynamic Programming ◽

Weak Convergence ◽

Decision Model ◽

Transition Probabilities ◽

General State ◽

Parameter Spaces ◽

State Action ◽

Total Rewards ◽

Bayesian Dynamic Programming ◽

Dynamic Decision Model

We consider a non-stationary Bayesian dynamic decision model with general state, action and parameter spaces. It is shown that this model can be reduced to a non-Markovian (resp. Markovian) decision model with completely known transition probabilities. Under rather weak convergence assumptions on the expected total rewards some general results are presented concerning the restriction on deterministic generalized Markov policies, the criteria of optimality and the existence of Bayes policies. These facts are based on the above transformations and on results of Hindererand Schäl.

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Customer Scheduling with Incomplete Information

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800003855 ◽

1995 ◽

Vol 9 (2) ◽

pp. 269-284 ◽

Cited By ~ 2

Author(s):

Ulrich Rieder ◽

Jürgen Weishaupt

Keyword(s):

Dynamic Programming ◽

Incomplete Information ◽

Bayesian Approach ◽

Stochastic Scheduling ◽

Partial Ordering ◽

Scheduling Problem ◽

Gittins Index ◽

Scheduling Model ◽

Bayesian Dynamic Programming ◽

Monotonicity Results

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 .

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