Scheduling problems are central in combinatorial optimization, and there exists a hugeliterature describing both problems and algorithms. Master surgery scheduling (MSS),where one must assign surgery teams in hospitals to different rooms at different times,is a specialization of the assignment problem, which can be solved using mixed integerprogramming (MIP).If not all parameters to an optimization problem are known beforehand, we mayuse robust optimization to find solutions which are both feasible and good, even if theparameters are not as expected. In particular, we assume such parameters to varyin a given set of possible ”realizations”. The more realistic assumptions, the bettersolutions.In this thesis we model MSS with the aim of minimizing the expected queue lengthsin hospitals. The model is made robust by considering the demand to be uncertain, butbelonging to a simple polytope. It can be modeled as a bilevel program. The masterprogram looks for feasible schedules minimizing queue lengths, while the slave programlooks for feasible demands maximizing queue lenghts.In order to solve this bilevel program, we use an iterative cutting plane approach.We find a solution with the best possible behaviour for the worst case parameters, bysplitting the problem in two. In particular, we implemented the so-called ”implementor/adversary” scheme (I-A), recently proposed by Bienstock in the context of portfoliooptimization (see [7, 8]). The implementor finds an optimum schedule with respect toa restricted set of feasible parameter vectors. The adversary finds a new vector (notincluded in the restricted set) which maximizes queues with respect to the currentschedule. The new vector is included in the restricted set and the method is iterated.When the adversary is not able to find a new parameter realization which is worseningthe value of the current schedule, we are finished. In our experiments on realisticinstances we need at most a few hundred of iteration before convergence is reached.For comparison, we also make a non-robust model of MSS as a reference solution,where we only consider a single demand vector.Testing shows that I-A is indeed a very effective algorithm, solving large probleminstances in reasonable time. Moreover, the solutions were in general found to beconsiderably better than the non-robust reference solution, even in cases where thedemand did not belong to the polytope we assumed. The algorithm also gives us goodintermediate solutions with provable bounds on optimality, which can be used even ifconvergence is not reached.We believe I-A both offers more flexibility and yields better results compared to theother robust approaches, when applied to the right problems, MSS only being one ofthese.