lecture13 - Assembly Line Balancing Uncapacitated Lot...

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Unformatted text preview: Assembly Line Balancing Uncapacitated Lot Sizing IE170: Algorithms in Systems Engineering: Lecture 13 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University February 21, 2007 Jeff Linderoth IE170:Lecture 13 Assembly Line Balancing Uncapacitated Lot Sizing Taking Stock Last Time Assembly Line Balancing (Intro to) Lot Sizing Knapsack Problem This Time: DP + Ilyas Favorite Algorithm Lot Sizing Greedy Algorithm Jeff Linderoth IE170:Lecture 13 Assembly Line Balancing Uncapacitated Lot Sizing Uncapacitated Lot Sizing Lot sizing is the canonical production planning problem Given a planning horizon T = { 1 , 2 , . . . , T } You must meet given demands d t for t T You can meet the demand from a combination of production ( x t ) and inventory ( s t- 1 ) Production cost: c ( x t ) = K + cx t if x t > if x t = 0 Inventory cost: I ( s t ) = h t s t Jeff Linderoth IE170:Lecture 13 Assembly Line Balancing Uncapacitated Lot Sizing Lets Solve it with DP What should our stages be? Hint: Typically stages have type from beginning until now (like S ij ) or from now until end (like in capital budgeting) Stage Let f t ( s ) : be the minimum cost of meeting demands from t, t + 1 , . . . T if s units are in inventory at the beginning of period t Jeff Linderoth IE170:Lecture 13 Assembly Line Balancing Uncapacitated Lot Sizing Lets Solve an Example T = 3 d = [2 , 1 , 2] h = [1 , 1 , 0] K = 2 , c = 1 Busy Going Backwards f 3 (0) = 2 + 2(1) = 4 f 3 (1) = 2 + 1(1) = 3 f 3 (2) = 0 Jeff Linderoth IE170:Lecture 13 Assembly Line Balancing Uncapacitated Lot Sizing In General A General Recursive Relationship f t ( s ) = min x , 1 , 2 ,... { c t ( x ) + h t ( s + x- d t ) + f t +1 ( s + x- d t ) } . Lets do a couple by hand....
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This note was uploaded on 08/06/2008 for the course IE 170 taught by Professor Ralphs during the Spring '07 term at Lehigh University .

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lecture13 - Assembly Line Balancing Uncapacitated Lot...

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