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THE VALUE ITERATION ALGORITHM
FINITE STAGE MARKOV PROGRAMMING
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Action Trial Value Action Value actions and values bias quantity boats calculations Stage column vector computational corresponds current policy denoted Determine deterministic discount factor discounted returns dynamic programming Figure function fundamental matrix gain optimal policies gain rate given linear simultaneous equations marketing example Markov decision problem Markov process maximise Mean return mean total return minimises minmax month number of stages 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 Prob random variable raw material recurrence relation relative bias values return associated semi-Markov semi-Markov process separability condition shortest path problem shown in Table Slotting Machine Example solution stage return Stage State Action stochastic stochastic matrix stock level suboptimality test summarised terminal values test quantity transition equation transition probability matrix transition return units value iteration algorithm value iteration method value table zero