Unit 02 Basics Linear Optim

Unit 02 Basics Linear Optim - Copyright 2002 - 2008 by R.E....

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Unformatted text preview: Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission Unit 2 Basics of Linear Optimization Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission Relation to Ragsdale Our introduction to linear optimization is similar to that in Ragsdale. Specifically, our discussion about algebraic models, graphical solutions, and spreadsheets solvers using Examples 1 and 2 is similar to that given for Howies decision problem in chapter 2 pp 21-36, chapter 3 pp 46-62, and chapter 4 pp 136-146. Example 1: An Assembly Line Copyright 2002 - 2007 by R.E. Wendell. All rights reserved. May not be reproduced without permission What is an assembly line? http://www.youtube.com/watch?v=4wp3m1vg06Q Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission Example 1: Company #1 Assembly Line - Produces Product #1 CAP HRS/WK Profit: $3000 per car Maximum Profit? CAP. UTILIZATION HRS/UNIT 2 hrs. 75 1 hr. 15 7 hrs. 250 2 hrs. 100 Dept 1 Dept 2 Dept 3 Dept 4 Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission Example 1: Company #2 Assembly Line - Produces Product #2 CAP HRS/WK Profit: $4000 per van Maximum Profit? CAP. UTILIZATION HRS/UNIT 3 hr. 285 1 hrs. 240 2 hrs. 300 3 hrs. 255 Dept 1 Dept 2 Dept 3 Dept 4 Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission CAP. UTIL. HRS/UNIT Product #1 $3000/unit Profit Product #2 $4000/unit Profit Capacity: Hrs/Wk Current Solution: 15 units per wk of Product #1(cars) 85 units per wk of Product #2 (vans) profit of $385,000 per week. Best Solution? Example 1: Merged Company 2 hrs. 3 hrs. 330 1 hr. 3 hrs. 300 7 hrs. 1 hr. 490 2 hrs. 2 hrs. 400 Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission Dept. #1 Cap. used Dept. #2 Cap. used Dept. #3 Cap. used Dept. #4 Cap. used Units Product 1 Units Product 2 Dept. #1 Cap. avail. Dept. #2 Cap. avail. Dept. #3 Cap. avail. Dept. #4 Cap. Avail. PROFIT Example 1: Influence Diagram Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission Decision Variables x 1 = units of Product #1 to produce x 2 = units of Product #2 to produce Example 1: Modeling Structure Max Profit s.t. Hrs. Used in Dept. #1 Hrs. Available Hrs. Used in Dept. #2 Hrs. Available Hrs. Used in Dept. #3 Hrs. Available Hrs. Used in Dept. #4 Hrs. Available Copyright 2002 - 2008 by R.E. Wendell. All rights reserved. May not be reproduced without permission...
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This note was uploaded on 12/23/2010 for the course BUSQOM 0050 taught by Professor Glowackia during the Spring '08 term at Pittsburgh.

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Unit 02 Basics Linear Optim - Copyright 2002 - 2008 by R.E....

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