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Author: Stanford University. Computer Science Department Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
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.
Author: Stanford University. Computer Science Department Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
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.
Author: José Correa Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Daniel Bienstock Publisher: Springer Science & Business Media ISBN: 3540221131 Category : Computers Languages : en Pages : 453
Book Description
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.
Author: Nicoló Gusmeroli Publisher: Springer ISBN: 3319775286 Category : Business & Economics Languages : en Pages : 63
Book Description
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.
Author: Ming-Yang Kao Publisher: Springer Science & Business Media ISBN: 0387307702 Category : Computers Languages : en Pages : 1200
Book Description
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.
Author: Nicoló Gusmeroli Publisher: ISBN: Category : Algorithms Languages : en Pages : 53
Book Description
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.
Author: A.H.G. Rinnooy Kan Publisher: Springer Science & Business Media ISBN: 1461343836 Category : Business & Economics Languages : en Pages : 188
Book Description
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].
Author: Joseph Y-T. Leung Publisher: CRC Press ISBN: 0203489802 Category : Business & Economics Languages : en Pages : 1215
Book Description
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.
Author: Stanford University. Computer Science Department
Author: Stanford University. Computer Science Department
Author: José Correa
Author: Daniel Bienstock
Author: Nicoló Gusmeroli
Author: Ming-Yang Kao
Author: Robert E. Bixby
Author: Nicoló Gusmeroli
Author: A.H.G. Rinnooy Kan
Author: Matthias Bücker
Author: Joseph Y-T. Leung