MIE376 Lec 12 DP - Dynamic Programming Introduction...

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MIE 376 Mathematical Programming 1 Dynamic Programming Introduction Framework Application to an Inventory Problem No return to Excel Onto Formulations…
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MIE 376 Mathematical Programming 2 Dynamic Programming Introduction Framework Application to an Inventory Problem No return to Excel Onto Formulations…
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MIE 376 Mathematical Programming 3 Introduction ± DP is driven by Richard Bellman’s Principle of Optimality ± This principle basically states that ² If an optimization objective is a sum (or product) over Stages ² At each Stage the system can be described by State variables ² The State at the next Stage is a function of the Decision at the current Stage ± Independent of the path by which the system arrived to the current State and Stage . ² If the optimal path traverses a particular State and Stage ² Æ The “future” optimal decisions are independent of the “past” decisions ± DP Formulations Æ Develop Bellman Recursive Equation
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MIE 376 Mathematical Programming 4 Dynamic Programming Introduction Framework Application to an Inventory Problem No return to Excel Onto Formulations…
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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. x
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MIE376 Lec 12 DP - Dynamic Programming Introduction...

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