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Optimization of Multitype Branching Processes

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  • Stanley R. Pliska

    (Northwestern University)

Abstract

We consider either a discrete time or an age-dependent branching process where the population consists of k types of individuals. Each time an individual is born, an action is chosen, for him which affects his lifetime, the number and types of his offspring, and the reward received. The problem of maximizing the expected reward is shown to be equivalent to a generalized Markov decision problem where the (k \times k) transition, matrices are non-negative but not necessarily substochastic. It is shown that this branching process decision model can account for immigration, that it can be viewed as a controlled population process or infinite particle system, and that it has a number of applications including marketing and biology.

Suggested Citation

  • Stanley R. Pliska, 1976. "Optimization of Multitype Branching Processes," Management Science, INFORMS, vol. 23(2), pages 117-124, October.
    • Handle: RePEc:inm:ormnsc:v:23:y:1976:i:2:p:117-124
    DOI: 10.1287/mnsc.23.2.117
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    Cited by:

    1. Kousha Etessami & Alistair Stewart & Mihalis Yannakakis, 2020. "Polynomial Time Algorithms for Branching Markov Decision Processes and Probabilistic Min(Max) Polynomial Bellman Equations," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 34-62, February.
    2. Eugene A. Feinberg & Jefferson Huang, 2019. "On the reduction of total‐cost and average‐cost MDPs to discounted MDPs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 38-56, February.

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