Train dispatchers play a vital role for safe and efficient railway operations. Their role includes several tasks, such as controlling train movements, maneuvering railway infrastructures (e.g., switches and signals), communicating with train crew and maintenance contractors. Dispatching centers operate around the clock, resulting in a high risk of fatigue for dispatchers, especially during night shifts. Moreover, dispatchers’ cognitive performance deteriorates when workload levels are too high. Although workload is a subjective measure, it is correlated with task load, i.e., the number of tasks executed in a given period of time. A preventive approach against too high workload levels is to account for the task load already during the scheduling phase. Currently, shifts are scheduled manually, which is a very complex task that cannot guarantee a satisfying quality both in terms of high efficiency and balanced workload levels.

The aim of this thesis is to create a scheduling framework, based on mathematical optimization models, that supports shift planners in their work. The framework helps in automatizing the scheduling process and improves the quality of the resulting shifts. Our initial approach is to use our models to figure out the required staffing levels and produce baseline schedules, and then improve these by increasing their attractiveness. To achieve this goal, we conduct three related studies considering the case of Malm¨o dispatching center. The studies result in different optimization models for shift scheduling of train dispatchers. We present the complete results in the following three papers:

In the first paper, we build an optimization model for one-day shift scheduling, where the objective function is to minimize the number of needed dispatchers. Moreover, we analyze the impact on the computation time of different parameters, such as the number of geographical areas and how these are combined. The results of the experiments are obtained within acceptable run times for real-world size instances. In the second paper, we suggest a stronger formulation of the previous model; in addition, we focus on improving the quality of the shifts. The improvements consider avoiding undesirable start times (between 00 and 05 am) and too short shifts (shorter than 6h). Our major contribution in this paper is giving four approaches for defining and modeling area-dispatcher-assignment switches, called handovers,  which occur when a dispatcher changes the assigned controlled areas during a shift. Two of these approaches gave promising results for solving real-world size instances to optimality within acceptable run times.

In the third paper, we increase the time horizon from one day to a week. We do this by combining the resulting shifts from some instances in the second paper where we consider a list of legal constraints, such as resting time between shifts, weekly rest and the total weekly working hours. In addition, we analyze the impact of the variability in shift lengths on the quality of the weekly schedules. 

We consider the problem of creating weekly shift schedules for train dispatchers, which conform to a variety of operational constraints, in particular, several work and rest time restrictions. We create the schedules in a two-stage process. First, using a previously presented IP model, we create a set of feasible daily shifts, which takes care of minimum-rest and shift-length requirements, taskload bounds, and combinability of dispatching areas. We then formulate an IP model to combine these daily shifts into weekly schedules, enforcing that each daily shift is covered by some dispatcher every day of the week, while ensuring that the weekly schedules comply with various restrictions on working hours from a union agreement. With this approach, we aim to identify "good" sets of daily shifts for the longer schedules. We run experiments for real-world sized input and consider different distributions of the daily shifts w.r.t. shift length and ratio of night shifts. Daily shifts with shift-length variability, relatively few long shifts, and a low ratio of night shifts generally yield better weekly schedules. The runtime for the second stage with the best daily-shift pattern is below three hours, which - together with the runtime for stage 1 of ca. 2 hours per run - can be feasible for real-world use.

Train dispatchers monitor and control train traffi c from a dispatching center, which isresponsible for a certain region in the railway network. This region is divided into subareas, where each train dispatcher controls one or several subareas at any time. Giventhe high safety concerns of their profession, dispatchers’ working shifts should fulfi lseveral legal and operational constraints, such as bounds on the length of shifts andon the resting periods between shifts. To construct shift schedules for train dispatchers is a complex and time-consuming process that is currently done manually. In thispaper, we present an optimization framework to automate this process, based on amodel for single-day shifts. Here, we focus on the objective of minimizing the numberof dispatchers as a baseline for future objectives. We present experimental results forreal-world sized data (number of geographical areas and train movements in the orderof magnitude as for one dispatching center in Sweden, covering the southern partof the country). We study the impact on the run time for diff erent input parameters,namely: the total number of geographical areas, the maximum number of geographical areas that can be assigned to a dispatcher in any period, changes in adjacencybetween the geographical areas, and the number of geographical areas that eachdispatcher is qualifi ed to monitor. The run time for the instances is between 19 and305 seconds