Crew Planning at Netherlands Railways: Improving Fairness, Attractiveness, and Efficiency

The development and improvement of decision support voor crew planning at Netherlands Railways (NS

Is Equality always desirable?

In this paper, we analyze the trade-off between perceived fairness and perceived attractiveness in crew rostering. First, we introduce the Fairness-oriented Crew Rostering Problem. In this problem, attractive cyclic rosters have to be constructed, while respecting a pre-specified fairness level. Then, we propose a flexible mathematical formulation, able to exploit problem specific knowledge, and develop an exact Branch-Price-and-Cut solution method. The solution method combines Branch-and-Bound with column generation, where profitable columns are separated by solving resource constrained shortest path problems with surplus variables. We also derive a set of valid inequalities to tighten the formulation. Finally, we demonstrate the benefit of our approach on practical instances from Netherlands Railways, the largest passenger railway operator in the Netherlands. We are able to construct the explicit trade-off curve between fairness and attractiveness and show that a sequential approach can lead to suboptimal results. In particular, we show that focusing solely on fairness leads to rosters that are disproportionally less attractive. Furthermore, this decrease in attractiveness is heavily skewed towards the most exible employees. Thus, in order to generate truly fair rosters, the explicit trade-off between fairness and attractiveness should be considered

Analysis of FPTASes for the Multi-Objective Shortest Path Problem

We propose a new FPTAS for the multi-objective shortest path problem. The algorithm uses elements from both an exact labeling algorithm and an FPTAS proposed by Tsaggouris and Zaroliagis (2009). We analyze the running times of these three algorithms both from a the- oretical and a computational point of view. Theoretically, we show that there are instances for which the new FPTAS runs an arbitrary times faster than the other two algorithms. Fur- thermore, for the bi-objective case, the number of approximate solutions generated by the proposed FPTAS is at most the number of Pareto-optimal solutions multiplied by the number of nodes. By performing a set of computational tests, we show that the new FPTAS performs best in terms of running ti

Analyzing a Family of Formulations for Cyclic Crew Rostering

In this paper, we analyze a family of formulations for the Cyclic Crew Rostering Problem (CCRP), in which a cyclic roster has to be constructed for a group of employees. We derive analytical results regarding the relative strength of the different formulations, which can serve as a guideline for formulating a given problem instance. Furthermore, we propose a column generation approach, which we use to develop an exact Branch-and-Price method, and a heuristic which aims at exploiting the information obtained from the linear relaxation. We conclude by applying our proposed solution method to practical instances from Netherlands Railways. In particular, we show that the computation time depends heavily on the selected formulation, and that the column generation approach outperforms a commercial solver on hard instances

A Column Generation Approach for the Integrated Crew Re-Planning Problem

In this paper, we propose a column generation approach for crew re-planning, i.e., the construction of new duties and rosters for the employees, given changes in the timetable and rolling stock schedule. In the current practice, the feasibility of the new rosters is `assured' by allowing the new duties to deviate only slightly from the original ones. In the Integrated Crew Re-Planning Problem (ICRPP), we loosen this requirement and allow more exibility: The ICRPP considers the re-scheduling of crew for multiple days simultaneously, thereby explicitly taking the feasibility of the rosters into account, and hence allowing arbitrary deviations from the original duties. We propose a mathematical formulation for the ICRPP and develop a column generation approach to solve the problem. We apply our solution approach to practical instances from NS, and show the benefit of integrating the re-scheduling process

An Adjustable Robust Optimization Approach for Periodic Timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing an adjustable robust periodic timetable. We develop a solution method for a parametrized class of uncertainty regions. This class relates closely to uncertainty regions known in the robust optimization literature, and naturally denes a metric for the robustness of the timetable. The proposed solution method combines a linear decision rule with well-known reformulation techniques and cutting-plane methods. We show that the RPTP can be solved for practical-sized instances by applying the solution method to practical cases of Netherlands Railways (NS). In particular, we show that the trade-o between the e- ciency and robustness of a timetable can be analyzed using our solution method

Genome-wide analyses identify common variants associated with macular telangiectasia type 2

Idiopathic juxtafoveal retinal telangiectasis type 2 (macular telangiectasia type 2; MacTel) is a rare neurovascular degenerative retinal disease. To identify genetic susceptibility loci for MacTel, we performed a genome-wide association study (GWAS) with 476 cases and 1,733 controls of European ancestry. Genome-wide significant associations (P < 5 × 10−8) were identified at three independent loci (rs73171800 at 5q14.3, P = 7.74 × 10−17; rs715 at 2q34, P = 9.97 × 10−14; rs477992 at 1p12, P = 2.60 × 10−12) and then replicated (P < 0.01) in an independent cohort of 172 cases and 1,134 controls. The 5q14.3 locus is known to associate with variation in retinal vascular diameter, and the 2q34 and 1p12 loci have been implicated in the glycine/serine metabolic pathway. We subsequently found significant differences in blood serum levels of glycine (P = 4.04 × 10−6) and serine (P = 2.48 × 10−4) between MacTel cases and controls