Robustness in Production Planning

Specialeforsvar ved Uffe Gram Christensen
og Pimin Konstantin Balic Kefaloukos


In this thesis on robust optimization we show how partially robust solutions to problems
with uncertainty can be calculated using genetic algorithms and scenario optimization.

We define a solution with partial robustness rho to be a solution that has a probability of rho to be feasible given a realization of stochastic parameters in an uncertain problem. We use simulation to prove the partial robustness of solutions to uncertain problems, within statistically precise bounds.

We have successfully used our methods to solve the knapsack problem with uncertainty and the capacitated lot-sizing problem with uncertainty. For instances of the capacitated lot-sizing
problem with uncertainty, we are able to find robust solutions that have an added cost of only 0.001%, when compared to the non-robust optimal solution to the deterministic problem.  For
the knapsack problem we are able to find partially robust solutions while losing only 0.04% of the profit of a non-robust optimal solution to a deterministic problem.

Både præsentation og eksamination vil være på dansk og er offentlige
under venlig hensyntagen til eksamenssituationen. Alle er velkomne.

Eksaminator: Martin Zachariasen