A Benders approach for the constrained minimum break problem

doi:10.1016/J.EJOR.2005.10.063

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A Benders approach for the constrained minimum break problem

Journal Article•DOI•

A Benders approach for the constrained minimum break problem

Rasmus V. Rasmussen¹, Michael A. Trick²•Institutions (2)

Aarhus University¹, Carnegie Mellon University²

16 Feb 2007-European Journal of Operational Research (North-Holland)-Vol. 177, Iss: 1, pp 198-213

TL;DR: A hybrid IP/CP algorithm for designing a double round robin schedule with a minimal number of breaks is presented and is capable of solving a number of previously unsolved benchmark problems for the Traveling Tournament Problem with constant distances.

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About: This article is published in European Journal of Operational Research.The article was published on 2007-02-16 and is currently open access. It has received 79 citations till now. The article focuses on the topics: Constrained optimization.

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Citations

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Integer and Combinatorial Optimization

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Karla Hoffman¹, Ted K. Ralphs²•Institutions (2)

George Mason University¹, Lehigh University²

01 Jan 2013

TL;DR: In today’s changing and competitive industrial environment, the difference between ad hoc planning methods and those that use sophisticated mathematical models to determine an optimal course of action can determine whether or not a company survives.

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Abstract: Integer optimization problems are concerned with the efficient allocation of limited resources to meet a desired objective when some of the resources in question can only be divided into discrete parts. In such cases, the divisibility constraints on these resources, which may be people, machines, or other discrete inputs, may restrict the possible alternatives to a finite set. Nevertheless, there are usually too many alternatives to make complete enumeration a viable option for instances of realistic size. For example, an airline may need to determine crew schedules that minimize the total operating cost; an automotive manufacturer may want to determine the optimal mix of models to produce in order to maximize profit; or a flexible manufacturing facility may want to schedule production for a plant without knowing precisely what parts will be needed in future periods. In today’s changing and competitive industrial environment, the difference between ad hoc planning methods and those that use sophisticated mathematical models to determine an optimal course of action can determine whether or not a company survives.

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1,066 citations

Cites methods from "A Benders approach for the constrai..."

...For example, see Hooker (2007) and Rasmussen and Trick (2007) for some applications that use both Benders decomposition and constraint programming to handle difficult scheduling problems....
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Journal Article•DOI•

Round robin scheduling – a survey

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Rasmus V. Rasmussen¹, Rasmus V. Rasmussen², Michael A. Trick¹, Michael A. Trick²•Institutions (2)

Aarhus University¹, Carnegie Mellon University²

01 Aug 2008-European Journal of Operational Research

TL;DR: A comprehensive survey on the literature considering round robin tournaments, outlining the contributions presented during the last 30 years and discussing directions for future research within the area.

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297 citations

Cites background or methods from "A Benders approach for the constrai..."

...Rasmussen and Trick [39] propose another iterative approach using logic-based Benders decomposition called a pattern generating Benders approach (PGBA)....
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...The constant distance TTP was also considered by Rasmussen and Trick [39] who used the PGBA discussed in Section 4.2 to solve the problem....
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...In an extended version of the paper Rasmussen and Trick also present a new heuristic approach called the circular traveling salesman approach (CTSA) to solve the TTP....
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...Separation constraints ([4, 11, 17, 23, 36, 38, 39, 62]) When we consider tournaments where teams meet more than once and the schedule is non-mirrored, most leagues have a lower bound on the number of slots between two games with the same opponents....
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...The problem is defined as follows: Definition 4 (Rasmussen and Trick [40]) Given a timetable for a double round robin tournament with n teams, a distance matrix specifying the distances between the venues and an upper bound UB on the number of consecutive home and consecutive away games, find a feasible pattern set which minimizes the total distance traveled by all teams....
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Journal Article•

Combinatorial aspects of construction of competition Dutch Professional Football Leagues

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Jan A. M. Schreuder¹•Institutions (1)

University of Twente¹

01 Jan 1990-Memorandum Faculty of Mathematical Sciences

TL;DR: Theoretical and real worid aspects will be demonstrated by the construction of the Dutch Professional Football (US: soccer) Leagues by developing a Home-Away schedule with oriented egde-colourings of complete graphs and assigning the clubs to a clustering algorithm.

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Abstract: Competitions are defined as a set of meetings between a number of clubs at preset dates under preset rules. Such a problem can be divided in two subproblems: firstly developing a Home-Away schedule with oriented egde-colourings of complete graphs and secondly assigning the clubs to the Home-Away patterns with a clustering algorithm. Theoretical and real world aspects will be demonstrated by the construction of the Dutch Professional Football (US: soccer) Leagues.

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98 citations

Journal Article•DOI•

50 years of OR in sport

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Mike Wright¹•Institutions (1)

Lancaster University¹

04 Feb 2009-Journal of the Operational Research Society

TL;DR: This paper reviews about 50 years of activity in OR as applied to sports, presenting four themes: tactics and strategy, scheduling, forecasting and ‘other’.

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Abstract: This paper reviews about 50 years of activity in OR as applied to sports. After some history and an overview, including discussions of what we mean by sport and what we mean by OR, four themes are presented: tactics and strategy, scheduling, forecasting and ‘other’. Within each theme many papers are discussed, showing the wide range of methods used and sports analysed. The issue is then raised of who our clients are and who they ought to be—it is suggested that not nearly enough is done for amateur sport. The paper ends with a conclusion and speculations about the next 50 years.

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97 citations

Cites methods from "A Benders approach for the constrai..."

...Papers on this topic include Elf et al (2003), who used a branch-and-cut approach; Miyashiro and Matsui (2006), who used semidefinite programming; Rasmussen and Trick (2007), who used integer programming and constraint programming; and Briskorn and Drexl (2007), who used a branch-and-price method....
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...and Matsui (2006), who used semidefinite programming; Rasmussen and Trick (2007), who used integer programming...
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Journal Article•DOI•

A composite-neighborhood tabu search approach to the traveling tournament problem

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Luca Di Gaspero¹, Andrea Schaerf¹•Institutions (1)

University of Udine¹

01 Apr 2007-Journal of Heuristics

TL;DR: This work proposes a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures and shows that the algorithm is competitive with those in the literature.

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Abstract: The Traveling Tournament Problem (TTP) is a combinatorial problem that combines features from the traveling salesman problem and the tournament scheduling problem. We propose a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures. The different neighborhoods have been thoroughly analyzed and experimentally compared. We evaluate the solvers on three sets of publicly available benchmarks and we show a comparison of their outcomes with previous results presented in the literature. The results show that our algorithm is competitive with those in the literature.

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79 citations

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Journal Article•DOI•

Logic-Based Benders Decomposition

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John N. Hooker¹, G. Ottosson²•Institutions (2)

Carnegie Mellon University¹, ILOG²

01 Apr 2003-Mathematical Programming

TL;DR: The aim of this paper is to generalize the linear programming dual used in the classical method to an ``inference dual'' that takes the form of a logical deduction that yields Benders cuts.

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Abstract: Benders decomposition uses a strategy of ``learning from one's mistakes.'' The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an ``inference dual.'' Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logic-based Benders may be to provide a framework for combining optimization and constraint programming methods.

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500 citations

"A Benders approach for the constrai..." refers background or methods in this paper

...The approach is inspired by the work of Hooker and Ottosson [10] in which the concept of logic based Benders decomposition is developed....
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...Instead a logic based Benders decomposition is used, as defined by Hooker and Ottosson [10], where the Benders cuts are obtained from inference duals....
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...Keywords: Timetabling; Hybrid integer programming/constraint programming; Sports scheduling; Logic based Benders cuts...
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Journal Article•DOI•

Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems

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Vipul Jain, Ignacio E. Grossmann¹•Institutions (1)

Carnegie Mellon University¹

01 Sep 2001-Informs Journal on Computing

TL;DR: The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods.

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Abstract: The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

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403 citations

"A Benders approach for the constrai..." refers background in this paper

...Keywords: Timetabling; Hybrid integer programming/constraint programming; Sports scheduling; Logic based Benders cuts...
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Journal Article•DOI•

Scheduling a Major College Basketball Conference

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Hemant K. Bhargava, Ramayya Krishnan, Patrick T. Harker

01 Jan 1998-Operations Research

TL;DR: The focus issue on Manufacturing Logistics as mentioned in this paper was created by pulling together previously accepted papers from all topical areas of the journal and achieved state-of-the-art thinking on manufacturing logistics.

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Abstract: I am pleased to present this Focus Issue on Manufacturing Logistics. Unlike a special issue, where new papers are solicited that deal with a theme, this issue was created by pulling together previously accepted papers from all topical areas of the journal. Thus, this focused issue achieves two goals. First, it creates a volume that presents state-of-the-art thinking on manufacturing logistics. Second, it reduces the backlog of accepted papers thereby reducing the publication delay-i.e., the time from acceptance to publication-which had been as long as 24 months. Our goal is, through the use of this supplement, to reduce the publication delay to 12 months over the next year. I hope that you enjoy this focused issue and I look forward to your comments and suggestions.

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242 citations

"A Benders approach for the constrai..." refers background or methods in this paper

...Nemhauser and Trick [ 18 ] outline examples of...
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...three phase approach used by Nemhauser and Trick [ 18 ] and Henz [8]....
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...cal applications [1,8, 18 ,23] as well as general solution methods [6,7,9,15,20,21,24,25]...
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Book Chapter•DOI•

The Traveling Tournament Problem Description and Benchmarks

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Kelly Easton¹, George L. Nemhauser¹, Michael A. Trick²•Institutions (2)

Georgia Institute of Technology¹, Carnegie Mellon University²

26 Nov 2001

TL;DR: The Traveling Tournament Problem is a sports timetabling problem that abstracts two issues in creating timetables: home/away pattern feasibility and team travel, and one way of modeling it is described.

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Abstract: The Traveling Tournament Problem is a sports timetabling problem that abstracts two issues in creating timetables: home/away pattern feasibility and team travel. Instances of this problem seem to be very difficult even for a very small number of teams, making it an interesting challenge for combinatorial optimization techniques such as integer programming and constraint programming. We introduce the problem, describe one way of modeling it, and give some interesting classes of instances with base computational results.

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229 citations

"A Benders approach for the constrai..." refers background in this paper

...Furthermore, the algorithm is capable of solving a number of previously unsolved benchmark problems for the Traveling Tournament Problem with constant distances....
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Book Chapter•DOI•

Scheduling in Sports

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D. de Werra¹•Institutions (1)

École Polytechnique Fédérale de Lausanne¹

01 Jan 1981-North-holland Mathematics Studies

TL;DR: In this article, the problem of scheduling the games of a hockey or football league is addressed using a graph theoretical model and some constraints related to the alternating pattern of home-games and away-games.

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Abstract: The purpose of this paper is to present the problem of scheduling the games of a hockey or football league. It is shown how a graph theoretical model may be used and how some constraints related to the alternating pattern of home-games and away-games can be handled. Finally some other requirements occurring in practice are also discussed and introduced into the model.

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148 citations