colonies finding the shortest path from their nest to food by exchanging information via pheromones along their way (Song et al. (2012)). In RCSP literature, this approach is almost exclusively applied by research on real cases in China, either in long-distance passenger transportation (Shi/Zhu/Tian (2015), Song et al. (2012), Tian/Song (2013), Zhu et al. (2014)) or in the urban rail context (Zhou et al. (2016)). Huang/ Yang/Wang (2011) discuss a variant of ACO for the Taiwanese railway transportation. In recent years, some researchers explored alternative meta-heuristics. Fuentes/Ca- darso/Mar´ın (2015) and Yaghini/Karimi/Rahbar (2015) combine neighborhood search with mathematical programming. For larger instances, Fuentes/Cadarso/ Mar´ın (2015) additionally divide the set of trips into smaller, overlapping clusters. Building on a similar trip clustering strategy, Fuentes/Cadarso/Mar´ın (2019) de- velop a fix-and-relax algorithm for their NFP formulation, aiming for providing a frame- work to integrate other planning tasks. Elizondo et al. (2010) propose an evolutionary algorithm to improve the initial solution by crossover operations with two sets, a set of elite duties and a random set. Simulated evolution algorithm is applied by Guo/Zhou/ Li (2014) and Zhao/Zhen (2007). The procedure starts with a randomly generated initial solution. Then, individual duties are eliminated based on their fitness evaluation and released trips are re-combined to new duties. For a multi-dimensional assignment problem of trains, crews and engines, Kuznetsov et al. (2016) suggest a simulated annealing algorithm. Also Hanafi/Kozan (2014) develop a hybrid approach with a constructive heuristic to generate the initial solution and a simulated annealing heuristic for improvement steps. Garc´ıa et al. (2018) explore the use of unsupervised learning methods based on k-means clustering techniques in combination with a cuckoo search algorithm.
3.6 Conclusion and further research opportunities
In this paper, we gave a structured and comprehensive overview of RCSP literature published since 2000. It was shown that most papers (almost 80% of the literature considered) discuss the planning step of crew scheduling separately from other planning steps. In particular in passenger transportation only few articles present integrated approaches, i.e. planning crew schedules simultaneously with rolling stock units or crew rosters. Note that the cost structure of railway operations differs from, for instance, the bus industry. In the latter, personnel cost account for a relatively higher share of total cost which makes integrative approaches more attractive regarding the potential cost savings. As a result, integrating crew scheduling with other planning tasks has been studied by several research groups. In contrast, the cost effect of integrated planning of
crew scheduling in railways is not comprehensively studied and might build a possible larger research stream for future studies.
While cost reduction remains the main motivation for research in crew scheduling, ro- bustness as a means to improve the customer service level and reduce regulatory penalties will play an increasingly important role in near future. New methods or concepts, e.g., based on historical schedule information, could be developed to achieve more robust crew schedules. However, crew schedules become more often subject to change for a defined period of time, e.g., due to large and frequent railway network maintenance projects. In extreme cases, the schedule of the same workday is different each week. This is true in particular for freight transportation with last minute customer orders but applies as well to passenger transportation. Hence, further research is needed to develop RCSP models and methods that are able to adapt to and plan with changed circumstances easily and quickly. This implies a thorough investigation of the impact on schedule cost and em- ployee and customer satisfaction. Likewise, research on real-time (re-)scheduling could lead to higher customer satisfaction in a fast moving world with information available instantly.
As especially in the developed countries labor markets become more competitive, rail- way operators will aim to make their jobs more appealing. This includes, besides payment and company culture, a satisfying and sustainable work schedule. We showed that crew rostering plays an important role by assigning duties to crews. However, specific aspects that affect duty popularity and fairness are determined by the schedule. As employee satisfaction seems not thoroughly investigated in RCSP, research could support oper- ators to investigate different policies for crew scheduling and their effect on employee satisfaction, also as integrated step with crew rostering.
We presented the potential of heuristics, column generation, and meta-heuristics to achieve high quality solutions in reasonable time. Also, acceleration techniques and problem size management strategies were investigated in the past. However, given the complexity and size of RCSP, research to solve even very large-scale instances close to optimality in a reasonable time could continue in the following years. The increasing competition in the private railway sector and public pressure on state-owned companies demand close to optimal solutions. Also, with faster solution methods operators can conveniently test and verify different input parameters. Also, the information obtained could provide recommendations to change the operating model and to improve railway transportation with respect to satisfying the needs of customers, operators and employees equally. Additionally, with the advances of algorithms that are able to recognize patterns in large data sets, e.g., machine learning techniques, new insights to crew scheduling could be found in historical data.