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Page 1: 0DUNHWLQJ0DQDJHPHQW6XSSRUW LQ6ODXJKWHU3LJ3URGXFWLRQ · 2012. 11. 16. · uhfrpphqgdwlrqvduhw\slfdoo\vxssolhge\wkh’dqlvk6odxjkwhu+rxvhv vhhh j 5dvpxvvhq ˝˙˝˚)OHPLQ 8GHVHQ ˝˝

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A minimization function is specified as:

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Given an instance of the model (GSP� '30RGHO) and a state (VW� 6WDWH), the problem is tominimize the objective function (REMIFW) with respect to all complete policies (S�DOOBSRO �GSP�):

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In other words the goal is to find a solution function, VROXWLRQ, that satisfies the specification:

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The state space is defined as the total set of states (except goal states) in the model and thedecision space as the total set of valid decisions in a given state:

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5.2.3 Bellman’s Principle of Optimality

The derivation of a solution function will be based on Bellman's Principle of Optimality:

The Principle of Optimality. An optimal policy has the property, thatwhatever the initial state and initial decision are, the remaining decisionsmust constitute an optimal policy with regard to the state resulting fromthe first decision.

Bellman (1957)

Referring to the introduced data model, a proposition stating this principle may be formulated as:

Proposition 1:

GSP�'30RGHO� VW�6WDWH� S �DOOBSRO �GSP��

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which (because it is satisfied for ~VW�GRP GSP� implies:

Proposition 2:

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