@misc{Tesch, author = {Tesch, Alexander}, title = {Exact Energetic Reasoning in O(n^2 log^2 n)}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60367}, abstract = {In this paper, we address the Energetic Reasoning propagation rule for the Cumulative Scheduling Problem (CuSP). An energetic reasoning propagation algorithm is called exact, if it computes the maximum possible energetic reasoning propagation for all the jobs. The currently best known exact energetic reasoning algorithm has complexity O(n^3). In this paper, we present a new exact energetic reasoning propagation algorithm with improved complexity of O(n^2 \log^2 n).}, language = {en} } @misc{Tesch, type = {Master Thesis}, author = {Tesch, Alexander}, title = {Compact MIP Models for the Resource-Constrained Project Scheduling Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60208}, abstract = {In the Resource-Constrained Project Scheduling Problem (RCPSP) a set of jobs is planned subject to resource- and precedence constraints. The objective is to minimize the makespan, that is the time when all jobs have been completed. There exist several Mixed-Integer-Programming (MIP) models in order to solve the problem. Most common models are based on time-discretization. In this case, the scheduling horizon is split into unit size intervals and each job gets assigned a unique starting interval. The drawback of time-discrete models is the computational intractability for large scheduling horizons or fine discretizations. In this connection, this thesis deals with compact MIP models where the model size is independent of the scheduling horizon. In addition to two compact models from the literature, we present two new compact models. We investigate their induced polyhedra and deduce an inclusion hierarchy via linear transformations. Moreover, we give a combinatorial interpretation of these transformations. Furthermore, we study a class of valid cutting planes for the compact models, which are known as cover inequalities. In order to strengthen these cutting planes we introduce a lifting algorithm that is independent of the model size. Subsequently, we examine lower bounds for the RCPSP from linear programming. Based on a linear transformation, we reveal a connection between two approaches from the literature. For one model we generate strong cutting planes that are obtained from a primal-dual relation between the models. Two cutting plane algorithms are derived. Likewise, we show that similar cutting planes can be transferred to the compact MIP models. Our models have been implemented, tested and evaluated on the instances of the PSPLIB problem library.}, language = {en} } @misc{GilgKlugMartienssenetal., author = {Gilg, Brady and Klug, Torsten and Martienssen, Rosemarie and Paat, Joseph and Schlechte, Thomas and Schulz, Christof and Seymen, Sinan and Tesch, Alexander}, title = {Conflict-Free Railway Track Assignment at Depots}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63843}, abstract = {Managing rolling stock with no passengers aboard is a critical component of railway operations. In particular, one problem is to park the rolling stock on a given set of tracks at the end of a day or service. Depending on the parking assignment, shunting may be required in order for a parked train to depart or for an incoming train to park. Given a collection of tracks M and a collection of trains T with fixed arrival-departure timetable, the train assignment problem (TAP) is to determine the maximum number of trains from T that can be parked on M according to the timetable and without the use of shunting. Hence, efficiently solving the TAP allows to quickly compute feasible parking schedules that do not require further shunting adjustments. In this paper, we present two integer programming models for solving the TAP. To our knowledge, this is the first integrated approach that considers track lengths along with the three most common types of parking tracks. We compare these models on a theoretical level. We also prove that a decision version of the TAP is NP-complete, justifying the use of integer programming techniques. Using stochastic and robust modelling techniques, both models produce parking assignments that are optimized and robust according to random train delays. We conclude with computational results for both models, observing that they perform well on real timetables.}, language = {en} } @masterthesis{Tesch, type = {Bachelor Thesis}, author = {Tesch, Alexander}, title = {Optimization of Large-Scale Conference Schedules}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49506}, abstract = {Scientific conferences play an important role in almost all areas of today's science and research. They offer a wide platform for international researchers and developers for communication and scientific exchange of current problems, experiences and knowledge in nearly all fields of research. Such conferences usually consist of talks about different topics that are given by authorized speakers. The planning process of a conference includes the creation of a scientific program schedule, that means a local and temporal allocation of all available talks. As the number of talks can grow into thousands for large-scale conferences, the conference scheduling becomes a complex challenge. Furthermore there exist a great bandwidth on various and individual requirements on the allocation of the talks. In this thesis we discuss the major problems that occur during the development of a conference schedule and provide a framework how proper conference schedules can be generated computationally. For that, we use Mixed-Integer-Programming techniques to find sched- ules that respect the difficult range of additional constraints. The basis of this thesis was the development of an optimized conference schedule of the International Symposium on Mathematical Programming 2012 (ISMP 2012) in Berlin, Germany. The ISMP is one of the largest conferences in the field of applied mathematics and mathematical optimization and constitutes a great attraction for in- ternational mathematicians and researchers. We will present our results based on the problem instance that we used for the ISMP 2012.}, language = {en} } @misc{Tesch, author = {Tesch, Alexander}, title = {Improved Compact Models for the Resource-Constrained Project Scheduling Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62891}, abstract = {In this article, we study compact Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP). Compared to the classical time-indexed formulation, the size of compact models is strongly polynomial in the number of jobs. In addition to two compact models from the literature, we propose a new compact model. We can show that all three compact models are equivalent by successive linear transformations. For their LP-relaxations, however, we state a full inclusion hierarchy where our new model dominates the previous models in terms of polyhedral strength. Moreover, we reveal a polyhedral relationship to the common time-indexed model. Furthermore, a general class of valid cutting planes for the compact models is introduced and finally all models are evaluated by computational experiments.}, language = {en} } @misc{Tesch, author = {Tesch, Alexander}, title = {A Nearly Exact Propagation Algorithm for Energetic Reasoning in O(n^2 log n)}, issn = {1438-0064}, doi = {10.1007/978-3-319-44953-1_32}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59332}, abstract = {In constraint programming, energetic reasoning constitutes a powerful start time propagation rule for cumulative scheduling problems (CuSP). In this paper, we first present an improved time interval checking algorithm that is derived from a polyhedral model. In a second step, we extend this algorithm to an energetic reasoning propagation algorithm with complexity O(n^2 log n) where n denotes the number of jobs. The key idea is based on a new sweep line subroutine that efficiently evaluates the relevant time intervals for all jobs. In particular, our algorithm yields at least one possible energetic reasoning propagation for each job. Finally, we show that on the vast number of relevant time intervals our approach yields the maximum possible propagation according to the energetic reasoning rule.}, language = {en} } @misc{BrettHobergPachecoetal.2015, author = {Brett, Charles and Hoberg, Rebecca and Pacheco, Meritxell and Smith, Kyle and Bornd{\"o}rfer, Ralf and Euler, Ricardo and Gamrath, Gerwin and Grimm, Boris and Heismann, Olga and Reuther, Markus and Schlechte, Thomas and Tesch, Alexander}, title = {G-RIPS 2014 RailLab - Towards robust rolling stock rotations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53475}, year = {2015}, abstract = {The Graduate-Level Research in Industrial Projects (G-RIPS) Program provides an opportunity for high-achieving graduate-level students to work in teams on a real-world research project proposed by a sponsor from industry or the public sector. Each G-RIPS team consists of four international students (two from the US and two from European universities), an academic mentor, and an industrial sponsor. This is the report of the Rail-Lab project on the definition and integration of robustness aspects into optimizing rolling stock schedules. In general, there is a trade-off for complex systems between robustness and efficiency. The ambitious goal was to explore this trade-off by implementing numerical simulations and developing analytic models. In rolling stock planning a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects, have to be considered in an integrated model. General hypergraphs provide the modeling power to tackle those requirements. Furthermore, integer programming approaches are able to produce high quality solutions for the deterministic problem. When stochastic time delays are considered, the mathematical programming problem is much more complex and presents additional challenges. Thus, we started with a basic variant of the deterministic case, i.e., we are only considering hypergraphs representing vehicle composition and regularity. We transfered solution approaches for robust optimization from the airline industry to the setting of railways and attained a reasonable measure of robustness. Finally, we present and discuss different methods to optimize this robustness measure.}, language = {en} } @misc{SagnolSchmidtgenanntWaldschmidtTesch, author = {Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel and Tesch, Alexander}, title = {The Price of Fixed Assignments in Stochastic Extensible Bin Packing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68415}, abstract = {We consider the stochastic extensible bin packing problem (SEBP) in which \$n\$ items of stochastic size are packed into \$m\$ bins of unit capacity. In contrast to the classical bin packing problem, bins can be extended at extra cost. This problem plays an important role in stochastic environments such as in surgery scheduling: Patients must be assigned to operating rooms beforehand, such that the regular capacity is fully utilized while the amount of overtime is as small as possible. This paper focuses on essential ratios between different classes of policies: First, we consider the price of non-splittability, in which we compare the optimal non-anticipatory policy against the optimal fractional assignment policy. We show that this ratio has a tight upper bound of \$2\$. Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule yielding a tight approximation ratio of \$1+1/e \approx 1.368\$ under a reasonable assumption on the distributions of job durations. Furthermore, we prove that the price of fixed assignments, which describes the loss when restricting to fixed assignment policies, is within the same factor. This shows that in some sense, LEPT is the best fixed assignment policy we can hope for.}, language = {en} } @misc{Tesch, author = {Tesch, Alexander}, title = {A Polyhedral Study of Event-Based Models for the Resource-Constrained Project Scheduling Problem}, issn = {1438-0064waoa}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68485}, abstract = {We consider event-based Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP) that represent an alternative to the common time-indexed model (DDT) of Pritsker et al. (1969) for the case where the underlying time horizon is large or job processing times are subject to huge variations. In contrast to the time-indexed model, the size of event-based models does not depend on the time horizon. For two event-based formulations OOE and SEE of Kon{\´e} et al. (2011) we present new valid inequalities that dominate the original formulation. Additionally, we introduce a new event-based model: the Interval Event-Based Model (IEE). We deduce linear transformations between all three models that yield the strict domination order IEE > SEE > OOE for their linear programming (LP) relaxations, meaning that IEE has the strongest linear relaxation among the event-based models. We further show that the popular DDT formulation can be retrieved from IEE by certain polyhedral operations, thus giving a unifying view on a complete branch of MIP formulations for the RCPSP. In addition, we analyze the computational performance of all presented models on test instances of the PSPLIB (Kolisch and Sprecher 1997).}, language = {en} } @misc{Tesch, author = {Tesch, Alexander}, title = {Improving Energetic Propagations for Cumulative Scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69331}, abstract = {We consider the Cumulative Scheduling Problem (CuSP) in which a set of \$n\$ jobs must be scheduled according to release dates, due dates and cumulative resource constraints. In constraint programming, the CuSP is modeled as the cumulative constraint. Among the most common propagation algorithms for the CuSP there is energetic reasoning (Baptiste et al., 1999) with a complexity of O(n^3) and edge-finding (Vilim, 2009) with O(kn log n) where k <= n is the number of different resource demands. We consider the complete versions of the propagators that perform all deductions in one call of the algorithm. In this paper, we introduce the energetic edge-finding rule that is a generalization of both energetic reasoning and edge-finding. Our main result is a complete energetic edge-finding algorithm with a complexity of O(n^2 log n) which improves upon the complexity of energetic reasoning. Moreover, we show that a relaxation of energetic edge-finding with a complexity of O(n^2) subsumes edge-finding while performing stronger propagations from energetic reasoning. A further result shows that energetic edge-finding reaches its fixpoint in strongly polynomial time. Our main insight is that energetic schedules can be interpreted as a single machine scheduling problem from which we deduce a monotonicity property that is exploited in the algorithms. Hence, our algorithms improve upon the strength and the complexity of energetic reasoning and edge-finding whose complexity status seemed widely untouchable for the last decades.}, language = {en} }