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To try to make the world more sustainable and reduce air pollution, diesel buses are being replaced with electric buses. This leads to challenges in scheduling, as electric buses need recharging during the day. Moreover, buses encounter varying traffic conditions and passenger demands, leading to delays. Scheduling electric buses with these stochastic driving times is also called the Stochastic Vehicle Scheduling Problem. The classical approach to make a schedule more robust against these delays, is to add slack to the driving time. However, this approach doesn't capture the variance of a distribution well, and it doesn't account for dependencies between trips. We use discrete event simulation in order to evaluate the robustness of a schedule. Then, to create a schedule, we use a hybrid approach, where we combine integer linear programming and simulated annealing with the use of these simulations. We show that with the use of our hybrid algorithm, the punctuality of the buses increase, and they also have a more timely arrival. However, we also see a slight increase in operating cost, as we need slightly more buses compared to when we use deterministic driving times.

BACKGROUND: The prevalence of multimorbidity is increasing in recent years, and patients with multimorbidity often have a decrease in quality of life and require more health care. The aim of this study was to explore the evolution of multimorbidity taking the sequence of diseases into consideration. METHODS: We used a Belgian database collected by extracting coded parameters and more than 100 chronic conditions from the Electronic Health Records of general practitioners to study patients older than 40 years with multiple diagnoses between 1991 and 2015 (N = 65 939). We applied Markov chains to estimate the probability of deve

In this paper we consider the integration of the personnel scheduling into planning railway yards. This involves an extension of the Train Unit Shunting Problem, in which a conflict-free schedule of all activities at the yard has to be constructed. As the yards often consist of several kilometers of railway track, the main challenge in finding efficient staff schedules arises from the potentially large walking distances between activities. We present two efficient heuristics for staff assignment. These methods are integrated into a local search framework to find feasible solutions to the Train Unit Shunting Problem with staff requirements. To the best of our knowledge, this is the first algorithm to solve the complete version of this problem. Additionally, we propose a dynamic programming method to assign staff members as passengers to train movements to reduce their walking time. Furthermore, we describe several ILP-based approaches to find a feasible solution of the staff assignment problem with maximum robustness, which solution we use to evaluate the quality of the solutions produced by the heuristics. On a set of 300 instances of the train unit shunting problem with staff scheduling on a real-world railway yard, the best-performing heuristic integrated into the local search approach solves 97% of the instances within three minutes on average.

The general problem of scheduling activities subject to temporal and resource constraints as well as a deadline emerges naturally in numerous application domains such as project management, production planning, and public transport. The schedules often have to be implemented in an uncertain environment, where disturbances cause deviations in the duration, release date or deadline of activities. Since these disruptions are not known in the planning phase, we must have schedules that are robust, i.e., capable of absorbing the disturbances without large deteriorations of the solution quality. Due to the complexity of computing the robustness of a schedule directly, many surrogate robustness measures have been proposed in literature. In this paper, we propose new robustness measures, and compare these and several existing measures with the results of a simulation study to determine which measures can be applied in practice to obtain good approximations of the true robustness of a schedule with deadlines. The experiments are performed on schedules generated for real-world scheduling problems at the shunting yards of the Dutch Railways (NS).

At an airport a series of assignment problems need to be solved before aircraft can arrive and depart and passengers can embark and disembark. A lot of different parties are involved with this, each of which having to plan their own schedule. Two of the assignment problems that the 'Regie' at Amsterdam Airport Schiphol (AAS) is responsible for, are the gate assignment problem (i.e. where to place which aircraft) and the bus assignment problem (i.e. which bus will transport which passengers to or from the aircraft). Currently these two problems are solved in a sequential fashion, the output of the gate assignment problem is used as input for the bus assignment problem. We look at integrating these two sequential problems into one larger problem that considers both problems at the same time. This creates the possibility of using information regarding the bus assignment problem while solving the gate assignment problem. We developed a column generation algorithm for this problem and have implemented a prototype. To make the algorithm efficient we used a special technique called stabilized column generation and also column deletion. Computational experiments with real-life data from AAS indicate that our algorithm is able to compute a planning for one day at Schiphol in a reasonable time.

We consider the single-machine scheduling problem of minimizing the number of late jobs. This problem is well-studied and well-understood in case of deterministic processing times. We consider the problem with stochastic processing times, and we show that for a number of probability distributions the problem can be reformulated as a deterministic problem (and solved by the corresponding algorithm) when we use the concept of minimum success probabilities, which is, that we require that the probability that a job complete on time is `big enough'. We further show that we can extend our approach to the case of machines with stochastic output.