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

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

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. Each formulation in the family is based on a partition of the roster. Intuitively, finer partitions give rise to a formulation with fewer variables, but possibly more constraints. Coarser partitions lead to more variables, but might allow to incorporate many of the constraints implicitly. 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, and use it to compare the strength of the formulations empirically. Both the theoretical and computational results demonstrate the importance of choosing a suitable formulation. In particular, for practical instances of Netherlands Railways, stronger lower bounds are obtained, and more than 90% of the roster constraints can be modeled implicitly

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

An adjustable robust optimization approach for periodic timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing a periodic timetable that can easily be adjusted in case of small periodic disturbances. 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 defines 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-off between the efficiency and robustness of a timetable can be analyzed using our solution method

Visit Allocation Problems in Multi-Service Settings: Policies and Worst-Case Bounds

Problem definition: We consider a resource allocation problem faced by health and humanitarian organizations deploying mobile outreach teams to serve marginalized communities. These teams can provide a single service or an assortment of services during each visit. Combining services is likely to increase operational efficiency but decrease the relative benefit per service per visit, as operations are no longer tailored to a single service. The aim of this study is to analyze this benefit-efficiency trade-off. Academic/practical relevance: Increased operational efficiency will enable organizations to serve more people using fewer resources. This is important given the increasing funding gap organizations are facing. Our work adds to the literature on resource allocation problems and visit allocation problems specifically, where the focus has been primarily on single services. Methodology: We analyze a general visit allocation problem incorporating demand distribution (where to go) and return time (how frequently to go). We derive analytical bounds for the benefit-efficiency trade-off, and propose visit allocation policies with worst-case optimality guarantees. Results: Our results show the benefit-efficiency trade-off can be assessed based on high level parameters. We show demand alignment is a key driver of this trade-off. We apply our results to Praesens Care, a social enterprise start-up developing mobile diagnostic laboratories, and verify our insights using real-world data. Managerial Implications: Our research contributes to the discussion on innovation and increased efficiency in health and humanitarian aid delivery by quantifying operational trade-offs in offering assortments of services. Specifically, our results help assess the potential of integrated models for health and humanitarian aid delivery and provide organizations with easy-to-implement methods to determine close-to-optimal visiting policies. Importantly, our methods remain applicable in case of limited data, making them suitable for strategic decision-making

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

Equity in Health and Humanitarian Logistics:A Beneficiary Perspective

In recent years, academics and health and humanitarian organizations are calling for ‘people-centered’ approaches, making beneficiaries’ preferences central to decisions making. While substantial progress has been made in capturing beneficiaries’ needs in resource allocation models, the approach to equity remains essentially ‘top-down’. That is, while diversity in needs is captured, the diversity in equity perceptions is not acknowledged. In this article, we argue there is a need for a complementary ‘bottom up’ view on equity, taking the perspective of the beneficiary. This will help academics and organizations to better account for the diversity in culture, experience, and social status present in most beneficiary populations. We present the 3P framework (People, Past, and Present) to help systematically think of drivers of beneficiaries’ distributional preferences. Furthermore, we illustrate how these preferences can be integrated into utility-based modeling and why accounting for preferences is important

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