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Previously in Chapter 6

Previously in Chapter 6. Using binary variables Unintended options Lack of sensitivity analysis. Agenda. Quiz logistics Finish binary variables Traveling salesman problem Nonlinear functions Finishes optimization (Will come back to chapter 5 later.). Quiz Survey.

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Previously in Chapter 6

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  1. Previously in Chapter 6 • Using binary variables • Unintended options • Lack of sensitivity analysis

  2. Agenda • Quiz logistics • Finish binary variables • Traveling salesman problem • Nonlinear functions • Finishes optimization • (Will come back to chapter 5 later.)

  3. Quiz Survey Should I move it? 11 Yes, 3 No Most preferred Acceptable Mon-Tue 4 6 Tue-Wed 4 9 Wed-Thur 3 9 Thur-Fri 3 9 Fri-Sat 1 6

  4. Quiz • Tue 11am to Wed 11am • office hours Mon 4-5 • moving Wed office hours to Tue 4-5

  5. Agenda • Quiz logistics • Finish binary variables • Traveling salesman problem • Nonlinear functions • Finishes optimization • (Will come back to chapter 5 later.)

  6. Traveling Salesman Problem Detroit Chicago Atlanta

  7. Traveling Salesman Problem • Data: Cities and Distances • Goal: minimize travel time to tour all cities (visit each city exactly once)

  8. Traveling Salesman Problem (TSP) • Famous problem • Vehicle Routing • Job Sequencing (p207) • 5 tasks that need to be done on a machine • Setup time for a task depends on the task that just completed

  9. task 2 task 1 start/finish task 3 task 5 task 4 Job Sequencing

  10. Solving TSP • Setup an assignment problem

  11. Solving TSP • Setup an assignment problem • Any subtours (loops of length k<n) ?

  12. Solving TSP • Setup an assignment problem • Any subtours (loops of length k<n) ? • Add subtour constraints • sum of variables ≤ k-1 • now binary variables needed

  13. Solving TSP • Setup an assignment problem • Any subtours (loops of length k<n) ? • Add subtour constraints • sum of variables ≤ k-1 • now binary variables needed • Repeat (go to stop 2) • often you finish quickly (though no guarantees)

  14. Nonlinear functions • product terms • chemical processes • area, volume • variance • log terms • utility functions • entropy

  15. Nonlinear Functions • Sensitivity Analysis • Like a derivative • Sqrt() function • Help the solver by defining it for x<0 • Solution may depend on starting point • Solvers use hill-climbing methods

  16. Nonlinear Example • Given a set of rectangular boxes, how many can you fit into a container?

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