This paper deals with large-scale crew scheduling problems arising at the Dutch railway operator, Netherlands Railways (NS). NS operates about 30,000 trains a week. All these trains need a driver and a certain number of guards. Some labor rules restrict the duties of a certain crew base over the...

This paper deals with large-scale crew scheduling problems arising at the Dutch railway operator, Netherlands Railways (NS). NS operates about 30,000 trains a week. All these trains need a driver and a certain number of conductors. No available crew scheduling algorithm can solve such huge...

In this paper, we discuss the dynamic vehicle and crew scheduling problem and we propose a solution approach consisting of solving a sequence of optimization problems. Furthermore, we explain why it is useful to consider such a dynamic approach and compare it with a static one. Moreover, we...

When tracks are out of service for maintenance during a certain period, trains cannot be operated on those tracks. This leads to a modified timetable, and results in infeasible rolling stock and crew schedules. Therefore, these schedules need to be repaired. The topic of this paper is the...

In this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is...

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach...

We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a min-sum or min-max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results...

In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right--hand side...