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 preferredAcceptable Mon-Tue46 Tue-Wed49 Wed-Thur39 Thur-Fri39 Fri-Sat16

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 4 task 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 problem 2.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?