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An Inventory Instance (cont’d)The simplest situation (From backward)01,?2,?3,?4,????I 3最优解 :最优值 :最优解 :最优值 :x( I 4)f( I 4)x( I 3)fRelation?( I 3)May 20, 2011
An Inventory InstanceLetft(i) : the minimum cost of meeting demands for months t,t+1, …, 4, if i units are on hand at the beginning of month t.☼ Here you can understand i units on hand as an input inventoryfrom previous stage).1,?2,?3,?4,?0????Let x t (i): a production level during month t thatminimizes the total cost during months t, t + 1, …,4 if i units are on hand at the beginning of month t.May 20, 2011
Page 1 and 2: Lecture 22. Dynamic Programming (2)
Page 3 and 4: An Inventory ExampleA company know
Page 5: An Inventory Instance (cont’d)Dyn
Page 9 and 10: t=4During month 4, the firm will pr
Page 11 and 12: An Inventory InstanceRecursion form
Page 13 and 14: t=30000i x (1/2)(i+x-2)+c(x) f 4(i+
Page 15 and 16: t=2i x (1/2)(i+x-3)+c(x) f 3(i+x-3)
Page 17 and 18: t=1i x (1/2)(i+x-1)+c(x) f 3(i+x-1)
Page 19 and 20: An Inventory Problem (Cont’d)3. E
Page 21 and 22: General Resource Allocation Problem
Page 23 and 24: Dynamic Programming ProcedureDefine
Page 25 and 26: Lot-size ModelAn inventory model:-
Page 27 and 28: Wagner-Whitin lemmaLemma1 : Given a
Page 29 and 30: Wagner-Whitin AlgorithmRecursive fo
Page 31 and 32: The silver-meal HeuristicIn extensi
Page 33: The End

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