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lecture11 - IE170 Algorithms in Systems Engineering Lecture...

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Unformatted text preview: IE170: Algorithms in Systems Engineering: Lecture 11 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University February 9, 2007 Jeff Linderoth IE170:Lecture 11 Taking Stock Last Time Easiest Quiz Ever This Time Intro to Dynamic Programming Jeff Linderoth IE170:Lecture 11 Dynamic Programming Not really an algorithm but a technique. Not really “programming” like Java programming Dynamic Programming in a Nutshell 1 Characterize the structure of an optimal solution 2 Recursively define the value of an optimal solution 3 Compute the value of an optimal solution “from the bottum up” 4 Construct optimal solution (if required) Jeff Linderoth IE170:Lecture 11 Capital Budgeting A company has $5 million to allocate to its three plants for possible expansion. Each plant has submitted different proposals on how it intends to spend the money. Each proposal gives the cost of the expansion c and the total revenue expected r . Investment Possibilities Plant 1 Plant 2 Plant 3 Proposal c 1 r 1 c 2 r 2 c 3 r 3 1 2 1 5 2 8 1 4 3 2 6 3 9-- 4-- 4 12-- Jeff Linderoth IE170:Lecture 11 More Setup Each plant will only be permitted to enact one of its proposals. The goal is to maximize the firm’s revenues resulting from the allocation of the $5 million. Assume that any of the $5 million we don’t spend is lost Solve It! How would you solve this problem? Jeff Linderoth IE170:Lecture 11 Solution Methods One way—Enumeration: only 2 × 3 × 4 = 24 possibilities, and many of these don’t obey the budget constraint This doesn’t scale well. Let’s think of another way: Jeff Linderoth IE170:Lecture 11 Building a Solution Let’s break the problem into three stages : each stage represents the money allocated to a single plant....
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