System Planning 2013. Lecture 7: Optimization Appendix A Contents: General about optimization Formulating optimization problems Linear Programming (LP) Mixed Integer Linear Programming (MILP). Optimization – General. Discipline in applied mathematics Used when:
building to achieve an acceptable expected waiting time?
Formulation of optimization problems:
2. Define symbols:
3. Mathematical formulation:
The optimization problem:
Linear Programming problems (LP problems)
New objective function
Theorem (strong duality):
If the primal problem has an optimal solution, then also the dual problem has an optimal solution and the objective values of these solutions are the same.
One dual variable for each constraint!
z = Tb
x1MILP – Example
Split x into two different variables, x1 and x2. Observe that
x1≤ xb. Also note that both x1 and x2 are 0.
Assume that readymade software is used to
solve an LP problem. In which of the following
cases do you get an optimal solution to the LP
problem and in which cases do you have to
reformulate the problem (or correct an error in
a) The problem has no feasible solution.
b) The problem is degenerated.
c) The problem does not have a finite solution.