Download or read book Precedence Constrained Scheduling to Minimize Weighted Completion Time on a Single Machine written by Stanford University. Computer Science Department and published by . This book was released on 1997 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the problem of scheduling a set of jobs on a single machine with the objective of mimizing weighted (average) completion time. The problem is NP-hard when there are precedence constraints between jobs, [12] and we provide a simple and efficient combinatorial 2-approximation algorithm. In contrast to our work, earlier approximation altorithms [9] achieving the same ratio are based on solving a linear programming relaxation of the problem.
Download or read book Single Machine Scheduling with Precedence Constraints written by José Correa and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss the problem of sequencing precedence-constrained jobs on a single machine to minimize the average weighted completion time. This problem has attracted much attention in the mathematical programming community since Sidney's pioneering work in 1975. We look at the problem from a polyhedral perspective and uncover a relation between Sidney's decomposition theorem and different linear programming relaxations. More specifically, we present a generalization of Sidney's result, which particularly allows us to reason that virtually all known 2-approximation algorithms comply with his decomposition. Moreover, we establish a connection between the single-machine scheduling problem and the vertex cover problem. Indeed, in the special case of series-parallel precedence constraints, we prove that the sequencing problem can be seen as a special case of the vertex cover problem. We also argue that this result is true for general precedence constraints if one can show that a certain integer program represents a valid formulation of the sequencing problem. Finally, we give a 3/2-approximation algorithm for two-dimensional partial orders, and we also provide a characterization of the active inequalities of a linear programming relaxation in completion time variables.
Download or read book Integer Programming and Combinatorial Optimization written by Daniel Bienstock and published by Springer Science & Business Media. This book was released on 2004-05-24 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2004, held in New York City, USA in June 2004. The 32 revised papers presented were carefully reviewed and selected from 109 submissions. Among the topics addressed are vehicle routing, network management, mixed-integer programming, computational complexity, game theory, supply chain management, stochastic optimization problems, production scheduling, graph computations, computational graph theory, separation algorithms, local search, linear optimization, integer programming, graph coloring, packing, combinatorial optimization, routing, flow algorithms, 0/1 polytopes, and polyhedra.
Download or read book Machine Scheduling to Minimize Weighted Completion Times written by Nicoló Gusmeroli and published by Springer. This book was released on 2018-04-30 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reviews the most important results regarding the use of the α-point in Scheduling Theory. It provides a number of different LP-relaxations for scheduling problems and seeks to explain their polyhedral consequences. It also explains the concept of the α-point and how the conversion algorithm works, pointing out the relations to the sum of the weighted completion times. Lastly, the book explores the latest techniques used for many scheduling problems with different constraints, such as release dates, precedences, and parallel machines. This reference book is intended for advanced undergraduate and postgraduate students who are interested in scheduling theory. It is also inspiring for researchers wanting to learn about sophisticated techniques and open problems of the field.
Download or read book Encyclopedia of Algorithms written by Ming-Yang Kao and published by Springer Science & Business Media. This book was released on 2008-08-06 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.
Download or read book Integer Programming and Combinatorial Optimization written by Robert E. Bixby and published by Springer. This book was released on 1998-06-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Machine Scheduling to Minimize Weighted Completion Times written by Nicoló Gusmeroli and published by . This book was released on 2018 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reviews the most important results regarding the use of the ?-point in Scheduling Theory. It provides a number of different LP-relaxations for scheduling problems and seeks to explain their polyhedral consequences. It also explains the concept of the ?-point and how the conversion algorithm works, pointing out the relations to the sum of the weighted completion times. Lastly, the book explores the latest techniques used for many scheduling problems with different constraints, such as release dates, precedences, and parallel machines. This reference book is intended for advanced undergraduate and postgraduate students who are interested in scheduling theory. It is also inspiring for researchers wanting to learn about sophisticated techniques and open problems of the field.
Download or read book Stochastic single machine scheduling to minimize the weighted expected flow time and maximum expected lateness subject to precedence constraints given by an OR network written by Matthias Bücker and published by . This book was released on 1989 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Machine Scheduling Problems written by A.H.G. Rinnooy Kan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction.- 2. Problem Formulation.- 2.1. Notations and representations.- 2.2. Restrictive assumptions.- 2.3. Optimality criteria.- 2.3.1. Regular measures.- 2.3.1.1. Criteria based on completion times.- 2.3.1.2. Criteria based on due dates.- 2.3.1.3. Criteria based on inventory cost and utilization.- 2.3.2. Relations between criteria.- 2.3.3. Analysis of scheduling costs.- 2.4. Classification of problems.- 3. Methods of Solution.- 3.1. Complete enumeration.- 3.2. Combinatorial analysis.- 3.3. Mixed integer and non-linear programming.- 3.3.1. [Bowman 1959].- 3.3.2. [Pritsker et al. 1969].
Download or read book Stochastic Local Search written by Holger H. Hoos and published by Morgan Kaufmann. This book was released on 2005 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application.
Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.
Download or read book Scheduling Precedence Constrained Jobs On Two Resources To Minimize The Total Weighted Completion Time written by Rajneesh Rajneesh and published by . This book was released on 2012 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Algorithms for Packing and Scheduling Problems written by José Rafael Correa and published by . This book was released on 2004 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) Finally, in the third chapter, we discuss a standard sequencing problem, namely, scheduling precedence-constrained jobs on a single machine to minimize the sum of weighted completion times. We look at the problem from a polyhedral perspective, obtaining, as one of our main results, a generalization of a classical result by Sidney. This new insight allows us to reason that all known 2-approximation algorithms behave similarly. Furthermore, we present a new integer programming model that suggests a strong connection between the scheduling problem and the vertex cover problem.
Download or read book Time Dependent Scheduling written by Stanislaw Gawiejnowicz and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-dependent scheduling involves problems in which the processing times of jobs depend on when those jobs are started. This book is a comprehensive study of complexity results and optimal and suboptimal algorithms concerning time-dependent scheduling in single-, parallel- and dedicated-machine environments. In addition to complexity issues and exact or heuristic algorithms which are typically presented in scheduling books, the author also includes more advanced topics such as matrix methods in time-dependent scheduling, and time-dependent scheduling with two criteria. The reader should be familiar with basic notions of calculus, discrete mathematics and combinatorial optimization theory, while the book offers introductory material on NP-complete problems, and the basics of scheduling theory. The author includes numerous examples, figures and tables, he presents different classes of algorithms using pseudocode, and he completes the book with an extensive bibliography, and author, symbol and subject indexes. The book is suitable for researchers working on scheduling, problem complexity, optimization, heuristics and local search algorithms.
Download or read book Resource Constrained Project Scheduling written by Christian Artigues and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title presents a large variety of models and algorithms dedicated to the resource-constrained project scheduling problem (RCPSP), which aims at scheduling at minimal duration a set of activities subject to precedence constraints and limited resource availabilities. In the first part, the standard variant of RCPSP is presented and analyzed as a combinatorial optimization problem. Constraint programming and integer linear programming formulations are given. Relaxations based on these formulations and also on related scheduling problems are presented. Exact methods and heuristics are surveyed. Computational experiments, aiming at providing an empirical insight on the difficulty of the problem, are provided. The second part of the book focuses on several other variants of the RCPSP and on their solution methods. Each variant takes account of real-life characteristics which are not considered in the standard version, such as possible interruptions of activities, production and consumption of resources, cost-based approaches and uncertainty considerations. The last part presents industrial case studies where the RCPSP plays a central part. Applications are presented in various domains such as assembly shop and rolling ingots production scheduling, project management in information technology companies and instruction scheduling for VLIW processor architectures.
Download or read book Handbook of Scheduling written by Joseph Y-T. Leung and published by CRC Press. This book was released on 2004-04-27 with total page 1215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook provides full coverage of the most recent and advanced topics in scheduling, assembling researchers from all relevant disciplines to facilitate new insights. Presented in six parts, these experts provides introductory material, complete with tutorials and algorithms, then examine classical scheduling problems. Part 3 explores scheduling models that originate in areas such as computer science, operations research. The following section examines scheduling problems that arise in real-time systems. Part 5 discusses stochastic scheduling and queueing networks, and the final section discusses a range of applications in a variety of areas, from airlines to hospitals.
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Ashish Goel and published by Springer. This book was released on 2008-08-28 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the 11th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2008) and the 12th International Workshop on Randomization and Computation (RANDOM 2008), which took place concurrently at the MIT (M- sachusetts Institute of Technology) in Boston, USA, during August 25–27, 2008. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 11th in the series after Aalborg (1998), Berkeley (1999), Saarbru ̈cken (2000), Berkeley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 12th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). Topics of interest for APPROX and RANDOM are: design and analysis of - proximation algorithms, hardness of approximation, small space, sub-linear time, streaming, algorithms, embeddings and metric space methods, mathematical programming methods, combinatorial problems in graphs and networks, game t- ory, markets, economic applications, geometric problems, packing, covering, scheduling, approximate learning, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and - beddings, error-correcting codes, average-case analysis, property testing, com- tational learning theory, and other applications of approximation and randomness.
