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Abstracts presentations phd studentsJoachim Arts Eindhoven University of Technology j.j.arts@tue.nl Supervisor Abstract We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster `emergency' supply source. Unsatisfied demand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason we study a type of base-stock policy known as the dual-index policy (DIP) as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to-levels. Previous work on this policy assumes deterministic lead times and uses simulation to find the optimal order-up-to levels. We provide an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows us to generalize the model to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times. In an additional numerical study we incorporate dual-sourcing in a two-echelon serial network and show the benefits of dual sourcing in a supply chain perspective.
Anoud den Boer CWI A.V.den.Boer@cwi.nl Supervisor Abstract We consider a monopolist firm selling a single product, with unknown parametric demand function. By experimenting with the selling prices the firm tries to learn the value of the optimal price. Since price experimentation can be costly, the firm needs to find a pricing policy that optimally balances between price experimentation and instant revenue maximization. An intuitive pricing policy is to set at each time period the selling price equal to the price that is optimal with respect to the current parameter estimates. This so-called myopic policy is not consistent: for certain parameter values, the price converges with positive probability to a price different from the optimum. Motivated by this we propose another pricing policy, called Controlled Variance Pricing. The key idea of this policy is to enhance the myopic policy with a taboo interval around the average previously chosen prices. This guarantees an optimal balance between exploration and exploitation. We show that Controlled Variance Pricing is consistent, and give asymptotic performance bounds. Numerical comparisons to other pricing policies from the literature indicate that Controlled Variance Pricing performs well, for different demand models and time scales.
Melania Calinescu VU University Amsterdam mcmelania@gmail.com Supervisor Abstract Survey nonresponse remains a problem that appears in every survey despite the development of methods that aim to reduce nonresponse. Statistical techniques help to get most out of the data that is collected from the responses, however, they do not su ciently address the problem of resource allocation in survey designs in which the focus is on the quality of the survey results given that there will be nonresponse. Therefore, we propose a method in which the optimal allocation of resources in uni-mode or mixed-mode surveys can be determined. The method builds on the idea that population units can be grouped together based on common characteristics that are available as a-priori knowledge. For each group, historical data can be used to produce estimates of contact probabilities and response probabilities for both uni-mode and mixed-mode surveys. Moreover, the total expected costs for any given survey can be separated into group-dependent and group-independent costs, each of these also depending on attempt outcomes (contact and cooperation, contact and no cooperation, non-contact). Our algorithm computes per group an optimal schedule of contact attempts for a set of all feasible combinations of survey modes. This is done by maximizing the group quality indicator (e.g., the response rate) given the pre-estimated group contact probabilities and response probabilities per survey mode. The algorithm is expected to lead to an integrated approach of the scheduling algorithm within adaptive survey designs.
Said Dabia Eindhoven University of Technology S.Dabia@tue.nl Supervisor Abstract In this paper, we consider the Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW). Travel times are time-dependent, meaning that depending on the departure time from a customer a different travel time is incurred. Because of time-dependency, vehicles' dispatch times from the depot are crucial as road congestion might be avoided. Due to its complexity, all existing solutions to the TDVRPTW are based on (meta-) heuristics and no exact methods are known for this problem. In this paper, we propose the first exact method to solve the TDVRPTW. The MIP formulation is decomposed into a master problem that is solved by means of column generation, and a pricing problem. To insure integrality, the resulting algorithm is embedded in a Branch and Cut framework. We aim to determine the set of routes with the least total travel time. Furthermore, for each vehicle, the best dispatch time from the depot is calculated.
Twan Dollevoet Erasmus University dollevoet@ese.eur.nl Supervisor Abstract Every regular train passenger will recognize the frustration of missing a transfer to a connecting train or bus when the incoming train has a small delay. Missing a crucial connection can easily increase the passenger's travel time by half an hour or more. Delay management is the field in railway operations that controls these connections between trains. When a train arrives at a station with a small delay, it might be beneficial to delay a departing train as well, to allow passengers to transfer from the arriving to the departing train. However, as a consequence, passengers in the departing train will be delayed as well. This might cause missed connections at subsequent stations, which makes delay management a very complex problem. For dense railway networks, like the one in the Netherlands, there can be many possibilities to travel from one station to the next. In recent literature, delay management models have been developed that take these re-routing options into account. As the delay management problem should be solved in a real-time setting, these models need to be solved very fast. However, straightforward integer programming techniques give rise to long computation times. We therefore propose several approaches to find good solutions to the delay management problem in a reasonable amount of time. We compare both the quality and the computation time of these solution methods on real-life instances from Netherlands Railways.
Theresia van Essen University of Twente J.T.vanEssen@ewi.utwente.nl Supervisor Abstract Hospitals aim to deliver high quality of care. One aspect in this context is to schedule emergency surgeries as quick as possible. Postponing these surgeries may increase a patient's risk of complications and morbidity. Reserving capacity in the Operating Rooms (ORs) for emergency surgeries can be done in two ways: (1) dedicating an entire OR to emergency surgeries or (2) scheduling the emergency surgeries in one of the elective ORs. Previous literature has shown that the second option is the best one in terms of waiting time, staff overtime, and OR utilization. In this situation, emergency patients are operated once an ongoing elective surgery is finished. These moments in time are denoted by 'break-in-moments' (BIMs). The waiting time of emergency surgeries can be reduced even further by spreading these BIMs as evenly as possible over the day. This can be achieved by sequencing the surgeries in their assigned OR, such that the maximum distance between two consecutive BIMs is minimized. In this presentation, we discuss several exact and heuristic solution methods for this problem. These methods concern the off-line planning. However, in practice, emergency surgeries arrive during the day, which will disrupt the initial schedule. The remaining BIMs of the OR in which the emergency is scheduled will be shifted to the right, which may increase the maximum distance between two BIMs. Therefore, we also consider on-line rescheduling techniques. In order to test these techniques, we conduct a simulation study.
Lanah Evers TNO lanah.evers@tno.nl Supervisor Abstract Unmanned Areal Vehicles (UAVs) can provide great contributions to information gathering in military missions. UAVs can be used to capture both motion and still imagery of specific target locations within the area of interest. In order to improve the effectiveness of a reconnaissance mission, it is important to visit the largest number of interesting target locations possible, taking into consideration operational constraints like flying times between target locations, weather conditions and endurance of the UAV. In this presentation we will show that this planning problem can be modeled as the well-known orienteering problem (OP), which is a generalization of the traveling salesman problem. Given the uncertainty in the military operational environment, robust planning solutions are needed. As such, our model takes into account uncertainty in the fuel usage between targets (due for instance to weather conditions) as well as uncertainty in the importance of visiting specific target locations. We will present preliminary results using different uncertainty sets that specify the degree of uncertainty against which any feasible solution will be protected. We also compare the probability that a solution is feasible for the (globalized) robust solution on one hand and the solution found with average fuel usage and expected value of information on the other. Finally, we also present the impact of the different sizes and shapes of the uncertainty sets on the quality and reliability of the robust planning solution.
Murat Firat Eindhoven University of Technology m.firat@tue.nl Supervisor Abstract In this study, we introduce the concept of stability in multi-skill workforce scheduling. In our analysis, a schedule is said to be stable if it does not contain a blocking pair, extending the notion of instability in the Marriage Model of Gale-Shapley. Skill efficiency is chosen as the criterion in the preference structure. We show that finding stable schedules is NP-Hard. In some special cases, stable schedules can be constructed in polynomial time. Finally, we define a set of inequalities that must be satisfied by all stable schedules. This set of inequalities is also a certificate to check whether stability can be attained in an instance of multi-skill workforce scheduling.
Maria Frolkova CWI M.Frolkova@cwi.nl Supervisor Abstract ALOHA-type algorithms are intended to govern star/hub networks in which multiple clients machines send data packets to the hub machine at the same frequency, thus collisions of simultaneous transmissions are possible. A packet which has participated in a collision is supposed to be retransmitted after some waiting time. Such algorithms are widely used in WiFi, mobile telephone networks and satellite communications. We consider an ALOHA-type random multiple access protocol where users are allowed to abandon the system before transmission completion.We study fluid limits for the workload process of the latter model focusing on the scenario which would lead to overload in the absence of impatience of customers. Under mild assumptions we show that the fluid limit for the system workload exists and coincides almost surely with the unique solution to a certain system of integral equations. We also show that the fluid limits for distinct initial conditions converge to the same value as time tends to infinity.
Alwin Haensel VU University Amsterdam ahaensel@few.vu.nl Supervisor Abstract A stochastic programming approach for a network revenue management problem with flexible capacities is presented. The study focuses on a car rental network, which has the special property that the fleet distribution between rental stations in the network can easily be adjusted at determined costs. Our method simultaneously optimizes the fleet distribution on the network and the capacity controls at station level. A two-stage stochastic program is considered, where the demand uncertainty in the second stage is approximated by a finite number of scenarios. The performance of the proposed stochastic method is tested by simulation on a small car rental network and compared with the results of a deterministic program.
Ruben Hoeksma University of Twente r.p.hoeksma@utwente.nl Supervisor Abstract The price of anarchy measures by how much the performance of a system deteriorates due to the lack of central coordination. We address the classical uniformly related machine scheduling problem, assuming that jobs may choose the machine on which they are processed. When jobs seek to minimize their own completion time, the utilitarian social choice function is to minimize the average job completion time. In this setting we analyze the price of anarchy for the natural coordination mechanism where jobs are sequenced shortest first per machine. We show that the price of anarchy is bounded from below by e/(e-1)>1.58 and from above by 2. This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem by Cole et al. and Correa et al. Moreover, as Nash equilibria correspond one-to-one to SPT schedules, the same bounds hold for the SPT heuristic on uniformly related machines. Thereby, our work also fills a gap in the literature.
Kristel Hoen Eindhoven University of Technology K.M.R.Hoen@tue.nl Supervisor Abstract Over the last few decades (and especially the last few years) global warming has received increasing attention, which has resulted amongst others in the establishment of the Kyoto protocol and the corresponding Kyoto targets. As a means to reach these targets, a carbon emission trading scheme (ETS) has been initiated by the European Union. To date no regulations exist which restrict carbon emissions resulting from transport, however aviation is being included in the ETS. Research by the European Commission has indicated that the emissions resulting from transport are still increasing and expected to continue to increase due to increased demand for transport. It is therefore required that emission reduction opportunities for transport are being identified. We focus on transport mode selection as a way to reduce emissions generated during transport. A trade-off exists in mode selection because slower transport modes typically generate fewer emissions at a cost of higher inventories (or lower service levels) to meet the demand during lead time. In general, it is hard to determine the actual emissions associated with transport because transport activities are outsourced to a third party. In our research we use the NTM methodology (Network for Transport and Environment) to estimate emissions for outsourced transport. We investigate the effect of an emission cost (which represents several emission regulation alternatives) on the selected transport mode and the corresponding costs and emissions.
Dongshuang Hou University of Twente D.Hou@ewi.utwente.nl Supervisor Abstract The Bertrand Oligopoly problem with Shubik’s demand functions is considered as a cooperative TU game. In this paper, we study the general situation in which firms operate with different marginal costs. For the purpose to determine the worth of any coalition in the Bertrand Oligopoly Game we solve two optimization problems. Under some conditions, the Bertrand Oligopoly Game reduces to a specific TU game in which the worth of a coalition resembles the variance of the marginal costs of members of that coalition. Furthermore, this Bertrand Oligopoly Game is shown to be totally balanced, but fails to be convex unless all the firms have the same marginal costs. Under the complementary conditions, the Bertrand Oligopoly Game is shown to be convex and in addition, we calculate its Shapley value on the basis of linearity applied to a decomposition of the Oligopoly Game into four types of games, namely two additive games, one symmetric game, and the square of one of these additive games. Although it concerns the difference of two convex games, it is shown that the Bertrand Oligopoly Game is convex too.
Evelien van der Hurk Erasmus University EHurk@rsm.nl Supervisor Abstract Disruption management in public transport is traditionally focused on resources. However, the contemporary view is that public transport is a service provided to passengers. Consequently public transport operators have become more focused on service. As a result, emphasis in disruption management is shifting from resources to passengers. For passenger oriented disruption management, information is needed on passenger movements and behavior in case of a disruption. The introduction of ticketing through smart cards offers a new source of data on time, origin and destination of journeys. We show how this new data source can be used for passenger oriented disruption management. We argue that the value of smart card data for disruption management is twofold. For one, it can be used to predict passenger flows through the network in far more detail then traditional data sources could. Knowing the flows of passengers is important information for capacity planning and possible rerouting of trains when focused on the comfort of passengers in case of a disruption. Secondly, smart card data can be used for system evaluation. Because it contains origin-destination pairs of all journeys including starting and ending time, one can assess the delay experienced by passengers as well as analyze the chosen or a different disruption management strategy. We will show the value of smart card data at the hand of a case study based on the situation at Dutch Railways (NS), the largest passenger railway operator in the Netherlands. We present ongoing research.
Ayse Gonul Karaarslan Eindhoven University of Technology A.G.Karaarslan@tue.nl Supervisor Abstract We consider a single item assembled from two components. One of the components has a long leadtime, high holding cost and short review period as compared to the other one. We assume that net stocks are reviewed periodically, customer demand is stochastic and unsatisfied demand is back ordered. We analyze the system under two different policies and show how to determine the policy parameters minimizing average holding and backorder costs. First, we consider a pure base stock policy, where orders for each component are placed such that the inventory position is raised up to a given order-up-to level. In contrast to this, only the orders for one component follow this logic while the other orders are synchronized in case of a balanced base stock policy. Through mathematical analysis, we come up with the exact long-run average cost function and we show the optimality conditions for both policies. In a numerical study the policies are compared and the results suggest that the balanced base stock policy works better than the pure base stock policy under low service levels and when there is a big difference in the holding costs of the components.
Frank Karsten Eindhoven University of Technology F.J.P.Karsten@tue.nl Supervisor Abstract We study a situation where several independent service providers collaborate by pooling their resources into a joint service system. These service providers may represent such diverse things as hospital departments that pool intensive care beds and ambulances, airline companies that share spare engine components, or call centers that pool their telephone operators. We model the service systems as Erlang loss systems that face a fixed cost rate per server and penalty costs for lost customers. We examine the allocation of costs of the pooled system amongst the participants by formulating a cooperative cost game in which each coalition optimizes the number of servers. We identify a cost allocation that is in the core of this game, i.e., that gives no subset of players an incentive to split off and form a separate pooling group. To obtain this result, we define a new extension of the classic Erlang loss function to a non-integral number of servers, and establish several of its structural properties.
Guus Regts CWI G.Regts@cwi.nl Supervisor Abstract A polyhedron P has the Integer Carathéodory Property if the following holds. For any positive integer k and any integer vector w in kP, there exist affinely independent integer vectors x_1,...,x_t in P and positive in- tegers n_1,...,n_t such that n_1+...+n_t = k and w = n_1x1+...+n_tx_t. In this talk we will discuss the relation between the integer Carathéodory property, Carathéodory's theorem from convex geometry and the integer decomposition property. We will give a sufficient condition for a rational polyhedron to have the integer Carathéodory property. Using this con- dition it follows that if P is a (poly)matroid base polytope or if P is defined by a TU matrix, then P and projections of P have the integer Carathéodory property. For the matroid base polytope this answers a question by Cunningham from 1984.
Mathijn Retel Helmrich Erasmus University retelhelmrich@ese.eur.nl Supervisor Abstract There is a growing tendency to not only focus on costs in the production process, but also on environmental implications, in particular emissions of pollutants, such as carbon dioxide. This shift towards a more environmentally friendly production process can be caused by legal restrictions or by a company's desire to pursue a "greener" image by reducing its carbon footprint. For these reasons, the classic economic lot-sizing problem has been extended. In addition to the usual financial costs, there are also emission parameters associated with production, keeping inventory and setting up the production process. The lot-sizing model that we consider minimises the (financial) costs under an emission constraint. This constraint can be seen as one global restriction over all periods. We show that this problem is NP-complete and propose several solution methods. First, we present a Lagrangian heuristic to provide an upper and lower bound for the problem. Next, we give a (1 + ε) approximation scheme. Further, we suggest mixed integer programming formulations based on a standard lot-sizing formulation and based on a shortest path reformulation of the problem.
Johan M. M. van Rooij Utrecht University johanvr@cs.uu.nl Supervisor Abstract Graph decompositions are important tools for solving NP-hard graph problems. While these problems are hard on general graph, they often become polynomial time solvable on graphs given with a graph decomposition corresponding to a bounded decomposition parameter such as the treewidth, branchwidth or cliquewidth. These decomposition based algorithms play an important role in problems like probabilistic inference, constraint satisfaction, query optimisation, and matrix decomposition. In this talk, we will consider the running time of graph decomposition based algorithms as a function of the decomposition parameter k. We will focus on algorithms on tree decomposition of treewidth k, but the ideas extend to branch decompositions and graphs of bounded cliquewidth as well. We will show that one can solve the Dominating Set problem on tree decompositions in O*(3^k) time, and that one can count the number of perfect matchings on a tree decomposition in O*(2^k) time. The O* notation here is a variant of the usual big-O notation that suppresses all polynomial factors in both the treewidth k and in the size of the graph n. These results can be generalised to solve the [rho,sigma]-domination problems in O*(s^k) where s is the natural number of states to represent a partial solution, and to solve various clique covering, packing and partitioning problems like Partition into Triangles, of Cover by l-Cliques in O*(2^k) time. These [rho,sigma]-domination problems include a large series of vertex subset problems like Independent Set, Dominating Set, Total Dominating Set, Perfect Code, and Induced Bounded Degree Subgraph. A recent result by Lokshtanov et al. shows that some of our algorithms have exponentially optimal running times under the strong exponential time hypothesis.
Alex Roubos VU University Amsterdam aroubos@few.vu.nl Supervisor Abstract An important aspect of call center modeling is the presence of impatient customers. In this paper we show that we can realistically model the patience distribution by the hyperexponential distribution. Since the hyperexponential distribution is a mixture of exponential distributions, an exact Markov chain analysis is possible. A framework is developed in order to compute all kinds of practical service levels. This framework utilizes the recursive relation between the queue lengths at successive service completion epochs. Our approach shows overall better performance compared to current algorithms. Moreover, the computation times are short and our approach can therefore readily be applied in practice.
Cyriel Rutten Maastricht University c.rutten@maastrichtuniversity.nl Supervisor Abstract We consider a stochastic scheduling problem which generalizes traditional stochastic scheduling by introducing parameter uncertainty. In traditional stochastic scheduling, parameters of the distribution of jobs' processing requirements are assumed to be known for certain. We extend this setting by introducing uncertainty regarding these parameters. Such a setting is applicable when a product line is being extended with an additional product and no production is available yet on this new product. Two classes of independent jobs have to be processed by a single machine so as to minimize the sum of expected completion times. The processing times of the jobs are assumed to be exponentially distributed with parameters $\vartheta$ and $\mu$, depending on the class of the job. We adopt a Bayesian framework in which $\mu$ is assumed to be known, whereas the value of $\vartheta$ is unknown. However, the scheduler has specific beliefs about the parameter $\vartheta$. By processing jobs from the corresponding class, the scheduler can update his beliefs about this parameter yielding better future decision making. For the traditional stochastic scheduling variant, in which the parameters are known, the policy that always processes a job with shortest expected processing time (SEPT) is an optimal policy. We show that in the Bayesian framework the performance of SEPT is at most a factor $2$ away from the performance of an optimal policy. Furthermore, we construct instances with non-degenerately distributed processing times for which this bound is tight. To our knowledge, this latter result is unique within stochastic scheduling. Finally, we remark that SEPT is asymptotically optimal when the number of jobs of one class tends to infinity, given a fixed number of jobs of the second class.
Julia Katharina Sponsel University of Groningen j.k.sponsel@rug.nl Supervisor Abstract In this talk we present an algorithm to approximate the projection of a matrix A onto the copositive cone C with arbitrary precision. The matrix is projected onto a sequence of polyhedral inner and outer approximations of C which are based on simplicial partitions of the standard simplex. As the partitions get finer, the sequences of approximations converge to the copositive cone. We show that in this case, the sequences of projections onto the inner respectively outer approximations converge to the projection of A onto C. Furthermore we consider the projection of a matrix onto the completely positive cone, which is the dual cone of C, and we discuss an application.
Duygu Tas Eindhoven University of Technology D.Tas@tue.nl Supervisor Abstract The vehicle routing problem is to find the set of feasible routes with the minimum total cost to serve a number of customers in respect of the constraints which are related to the vehicles and the customers. This problem turns into the vehicle routing problem with time windows if each customer is introduced to the problem with a time interval which specifies the allowed times for the deliveries. In the case that the delivery time constraints are built by hard time windows, deliveries must be received by the customers within the interval of the time windows. In the presence of soft time windows, the services before or after the limits set by the time windows are possible; after all, these situations cause penalties to the carrier companies. Most literature studies the vehicle routing problem and the vehicle routing problem with time windows by assuming that the travel times are deterministic. However; one of the first things that should be included is the uncertainty in the travel times especially when the delivery reliability is considered for the routing problems. In addition, the carrier companies and the customers have different concerns during the operations. From the perspective of the carrier companies, the goal is to deliver the goods to different customers as efficiently as possible. From the customers' point of view, the main concern is to receive the deliveries on-time. Therefore, this study focuses on the vehicle routing problem with time windows where time windows are defined as soft time windows and stochastic travel times are considered to construct the systems which are reliable for the customers and effective for the carrier companies. We develop a model which considers the transportation costs resulting from the total traveled distance, number of vehicles used by the solution and the total expected overtime of the drivers working on each route. Furthermore, the service costs evolved out of the early and late arrivals are also being included by the model in terms of the reliability. By considering the stochasticity of the problem, we generate an algorithm to find the initial feasible solution and develop a tabu search method to improve this solution. Results of the computational experiments that are conducted for the well-known problem instances are presented.
Philippe Uyttendaele Maastricht University philippe.uyttendaele@maastrichtuniversity.nl Supervisor Abstract We present two models of evolutionary games, driven by replicator dynamics, in which the fitness matrix changes in time. The motivation of such models is that most of the evolutionary games explored are based on invariant payoff matrices, whereas in real populations the actions taken usually have an impact on the world that the population is living in, or the world is just changing and the population has to adapt in order to survive. In one model the fitnesses are time dependent in a cyclical way and the population has to adjust accordingly. In the other model the population affects the `state of the world’ in a more drastic way, i.e. based on the population distribution the complete fitness matrix may suddenly change and the population is confronted with new circumstances. In the latter model we combine the traditional approach of evolutionary games with that of stochastic games. Each of these models will be presented by a small example in which the population seems to converge to a stable orbit rather than a stable point.
Luuk Veelenturf Erasmus University LVeelenturf@rsm.nl Supervisor Abstract In passenger railway operations unforeseen events like infrastructure malfunctions, accidents or rolling stock breakdowns can make parts of the railway infrastructure temporarily unavailable. Then, within minutes, or even better, seconds, a new timetable and new resource (rolling stock and crew) schedules must be constructed. Although these schedules are interdependent, the rescheduling is carried out sequentially in practice due to the limited time available and its complexity. In this research we make an start with integrating the rescheduling of the rolling stock and the timetable. A disruption does also affect the passengers. However, for railway operators without a seat reservation system it is difficult to reschedule the passengers. The passengers will make their new travel plan by themselves. If they had planned to take a train which is now canceled, they will cancel their trip or they will reroute themselves. By the changed passenger flows, the disruption has caused changes in the demand for capacity. In response to that, the railway operator has to arrange additional capacity on the alternative routes. Therefore, a rolling stock rescheduling approach to handle a disruption must take the modified passenger flows into account dynamically and not the flows of a regular day. Sometimes the modified flows ask for a lot of additional capacity on a certain regional station. One way to handle this is to increase the capacity of certain regional trains, but another option is to let some intercity trains make an additional stop at that regional station. Such an additional stop will delay the intercity train with a few minutes. As a consequence, the original passengers of the intercity train will get an additional delay in favor of reducing the delay of the passengers at the regional station. A small delay of the train can, however, lead to a large delay for the passengers if they miss their transfer by it. The railway operator has to make trade-offs between the different consequences for the passengers. In this research we propose a disruption management approach which integrates the reschedul- ing of rolling stock and the adaptation of stopping patterns. This approach makes decisions on the rolling stock schedule and the stopping patterns by looking at the passenger flows. If passenger flows require it, more capacity is assigned to certain trains or intercity trains will make additional stops. So far, the approach has only been tested in a situation where the stopping patterns of the trains are not modified. The promising solution quality and computation time give us confidence that natural extensions, such as the incorporation of stopping pattern decisions, will still be computationally tractable on realistic problem instances. We believe that the approach proposed in this research can significantly help to improve the quality of the railway rolling stock rescheduling process in case of major disruptions.
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