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An Inventory ProblemAn inventory problem with the following characteristics can beshown to be solved by using a dynamic programmingapproach.Time is divided into periods, At the beginning of period 1, thedemand during each period is known.At the beginning of each period, the firm must determine howmany units should be produced. Production capacity duringeach period is limited.May 20, 2011
An Inventory Problem (Cont’d)3. Each period's demand must be met on time from inventory orcurrent production. During any period in which productiontakes place, a fixed cost of production as well as a variableper-unit cost is incurred.4. The firm has limited storage capacity. This is reflected by alimit on end-of-period inventory. A per-unit holding cost isincurred on each period's ending inventory.5. The firm's goal is to minimize the total cost of meeting ontime the demands for periods 1, 2, …, T.This is a periodic review model (the firm's inventory position is reviewedat the end of each period, and then the production decision is made).May 20, 2011
Page 1 and 2: Lecture 22. Dynamic Programming (2)
Page 3 and 4: An Inventory ExampleA company know
Page 5 and 6: An Inventory Instance (cont’d)Dyn
Page 7 and 8: An Inventory InstanceLetft(i) : the
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: t=1i x (1/2)(i+x-1)+c(x) f 3(i+x-1)
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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