## Dynamic programming (with management applications) |

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### Contents

THE VALUE ITERATION ALGORITHM l | 1 |

DETERMINISTIC APPLICATIONS | 43 |

FINIT E STAGE MARKOV PROGRAMMING | 82 |

Copyright | |

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### Common terms and phrases

Action Trial Value actions and values boats column vector computational corresponds current policy deﬁned denoted Determine deterministic discount factor discounted returns dynamic programming ﬁnd ﬁnding ﬁnite ﬁrst ﬁsh ﬁxed fundamental matrix gain optimal policies gain rate given inﬁnite stage linear simultaneous equations marketing example Markov decision problem Markov process Max r(n maximise mean total return minimises minmax month optimal action optimal path optimal plan optimal process optimal value optimisation overhaul partitioning problem plan is followed planning horizon policy evaluation operation policy improvement routine proﬁt random variable raw material recurrence relation relative bias values return associated return r(i semi-Markov semi-Markov process separability condition shortest path problem shown in Table Slotting Machine Example stage Markov stage return Stage State Action stochastic stochastic matrix stock level summarised terminal values test quantity transition equation transition probability matrix transition returns unichain units value iteration algorithm value iteration method value table zero