# Library

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
• ddc:000  (27)
• English  (27)
Source
Keywords
Language
• 1
Unknown
Publication Date: 2020-03-09
Description: In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix $A$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the %LP- and MIP-libraries \Netlib{} and MIPLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 2
Unknown
Publication Date: 2020-08-05
Description: This paper is about {\em set packing relaxations\/} of combinatorial optimization problems associated with acyclic digraphs and linear orderings, cuts and multicuts, and vertex packings themselves. Families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 3
Publication Date: 2020-08-05
Description: This article investigates a certain class of combinatorial packing problems and some polyhedral relations between such problems and the set packing problem.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 4
Unknown
Publication Date: 2020-08-05
Description: We consider an auction of slots to run trains through a railway network. In contrast to the classical setting for combinatorial auctions, there is not only competition for slots, but slots can mutually exclude each other, such that general conflict constraints on bids arise. This turns the winner determination problem associated with such an auction into a complex combinatorial optimization problem. It also raises a number of auction design questions, in particular, on incentive compatibilty. We propose a single-shot second price auction for railway slots, the Vickrey Track Auction (VTA). We show that this auction is incentive compatible, i.e., rational bidders are always motivated to bid their true valuation, and that it produces efficient allocations, even in the presence of constraints on allocations. These properties are, however, lost when rules on the submission of bids such as, e.g., lowest bids, are imposed. Our results carry over to generalized" Vickrey auctions with combinatorial constraints.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Format: application/postscript
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 5
Publication Date: 2020-08-05
Description: Technical restrictions and challenging details let railway traffic become one of the most complex transportation systems. Routing trains in a conflict-free way through a track network is one of the basic scheduling problems for any railway company. This article focuses on a robust extension of this problem, also known as train timetabling problem (TTP), which consists in finding a schedule, a conflict free set of train routes, of maximum value for a given railway network. However, timetables are not only required to be profitable. Railway companies are also interested in reliable and robust solutions. Intuitively, we expect a more robust track allocation to be one where disruptions arising from delays are less likely to be propagated causing delays of subsequent trains. This trade-off between an efficient use of railway infrastructure and the prospects of recovery leads us to a bi-criteria optimization approach. On the one hand we want to maximize the profit of a schedule, that is more or less to maximize the number of feasible routed trains. On the other hand if two trains are scheduled as tight as possible after each other it is clear that a delay of the first one always affects the subsequent train. We present extensions of the integer programming formulation in [BorndoerferSchlechte2007] for solving (TTP). These models can incorporate both aspects, because of the additional track configuration variables. We discuss how these variables can directly be used to measure a certain type of robustness of a timetable. For these models which can be solved by column generation techniques, we propose so-called scalarization techniques, see [Ehrgott2005], to determine efficient solutions. Here, an efficient solution is one which does not allow any improvement in profit and robustness at the same time. We prove that the LP-relaxation of the (TTP) including an additional $\epsilon$-constraint remains solvable in polynomial time. Finally, we present some preliminary results on macroscopic real-world data of a part of the German long distance railway network.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Format: application/pdf
Format: application/postscript
Format: application/postscript
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 6
Unknown
Publication Date: 2020-12-15
Description: The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Format: application/postscript
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 7
Unknown
Publication Date: 2020-08-05
Description: The need to solve {\it transportation problems\/} was and still is one of the driving forces behind the development of the mathematical disciplines of graph theory, optimization, and operations research. Transportation problems seem to occur for the first time in the literature in the form of the four ''River Crossing Problems'' in the book Propositiones ad acuendos iuvenes. The {\it Propositiones\/} ---the oldest collection of mathematical problems written in Latin--- date back to the $8$th century A.D. and are attributed to Alcuin of York, one of the leading scholars of his time, a royal advisor to Charlemagne at his Frankish court. Alcuin's river crossing problems had no impact on the development of mathematics. However, they already display all the characteristics of today's large-scale real transportation problems. From our point of view, they could have been the starting point of combinatorics, optimization, and operations research. We show the potential of Alcuin's problems in this respect by investigating his problem~18 about a wolf, a goat and a bunch of cabbages with current mathematical methods. This way, we also provide the reader with a leisurely introduction into the modern theory of integer programming.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 8
Unknown
Publication Date: 2020-12-15
Description: The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize operating costs, the passengers want to minimize travel times. We propose a n ew multi-commodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. We discuss properties of this model and investigate its complexity. Results with data for the city of Potsdam, Germany, are reported.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Format: application/pdf
Format: application/postscript
Format: application/postscript
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 9
Unknown
Publication Date: 2020-08-05
Description: This article is about the optimal track allocation problem (OPTRA) to find, in a given railway network, a conflict free set of train routes of maximum value. We study two types of integer programming formulations: a standard formulation that models block conflicts in terms of packing constraints, and a new extended formulation that is based on additional configuration' variables. We show that the packing constraints in the standard formulation stem from an interval graph, and that they can be separated in polynomial time. It follows that the LP relaxation of a strong version of this model, including all clique inequalities from block conflicts, can be solved in polynomial time. We prove that the extended formulation produces the same LP bound, and that it can also be computed with this model in polynomial time. Albeit the two formulations are in this sense equivalent, the extended formulation has advantages from a computational point of view, because it features a constant number of rows and is therefore amenable to standard column generation techniques. Results of an empirical model comparison on mesoscopic data for the Hannover-Fulda-Kassel region of the German long distance railway network are reported.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Format: application/postscript
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
• 10
Publication Date: 2020-03-09
Description: {\def\NP{\hbox{$\cal N\kern-.1667em\cal P$}} The {\sl storage assignment problem} asks for the cost minimal assignment of containers with different sizes to storage locations with different capacities. Such problems arise, for instance, in the optimal control of automatic storage devices in flexible manufacturing systems. This problem is known to be $\NP$-hard in the strong sense. We show that the storage assignment problem is $\NP$-hard for {\sl bounded sizes and capacities}, even if the sizes have values $1$ and~$2$ and the capacities value~$2$ only, a case we encountered in practice. Moreover, we prove that no polynomial time $\epsilon$-approximation algorithm exists. This means that almost all storage assignment problems arising in practice are indeed hard.}
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
Others were also interested in ...
Close ⊗