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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 Howie’s 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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Unit 02 Basics Linear Optim - Copyright © 2002 2008 by R.E...

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