previously in chapter 6
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
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
Quiz
• Tue 11am to Wed 11am
• office hours Mon 4-5
• moving Wed office hours to Tue 4-5
Agenda
• Quiz logistics
• Finish binary variables– Traveling salesman problem
• Nonlinear functions– Finishes optimization– (Will come back to chapter 5 later.)
Traveling Salesman Problem
Chicago
Detroit
Atlanta
Traveling Salesman Problem
• Data: Cities and Distances
• Goal: minimize travel time to tour all cities(visit each city exactly once)
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
Job Sequencing
task 1 task 2
task 3
task 4task 5
start/finish
Solving TSP
1. Setup an assignment problem
Solving TSP
1. Setup an assignment problem
2. Any subtours (loops of length k<n) ?
Solving TSP
1. Setup an assignment problem
2. Any subtours (loops of length k<n) ?
3. Add subtour constraints• sum of variables ≤ k-1• now binary variables needed
Solving TSP
1. Setup an assignment problem2. Any subtours (loops of length k<n) ?3. Add subtour constraints
• sum of variables ≤ k-1• now binary variables needed
4. Repeat (go to stop 2)• often you finish quickly
(though no guarantees)
Nonlinear functions
• product terms– chemical processes– area, volume– variance
• log terms– utility functions– entropy
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
Nonlinear Example
• Given a set of rectangular boxes, how many can you fit into a container?