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MIE376 Lec 12 DP.page05 - x n(s n or x n or x Decision...

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MIE 376 Mathematical Programming 5 Framework – Notation is key Describes the immediate consequence of making a decision x n at stage n, given the system is in state s n h n (s n , x n ) Immediate Return Describes what state the system will be in the next stage (n+1) given that it is at a given state s n, and we make decision x n at stage n s n+1 =g n (s n , x n ) Transition Relation The set of all the feasible decisions that could be made in given stage and state, so that x n X n (s n ) X n (s n ) or X n or X Set of Feasible Decisions The decision that needs to be made at each stage n, given that the system is in state s n . Alternate notations vary with context.
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Unformatted text preview: x n (s n ) or x n or x. Decision Variable The set of all the feasible states that a system could be in at a given stage so that s n ∈ S n S n Set of Feasible States The state at each stage is the only system information we need to know at each stage to be able to decide on what to do next. How the system arrived to the current state is irrelevant to the next decision. s n State Variable All DP problems have stages, which must be identified in the problem description n=1,…,N Stages Comment Notation Concept...
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