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Machine Scheduling Problem (machine + scheduling_problem)

Distribution by Scientific Domains
Mathematics and Statistics60%

Selected Abstracts

Tight bounds for the identical parallel machine scheduling problem

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2006
Mohamed Haouari
Abstract We address the problem of minimizing makespan on identical parallel machines. We propose new lower bounding strategies and heuristics for this fundamental scheduling problem. The lower bounds are based on the so-called lifting procedure. In addition, two optimization-based heuristics are proposed. These heuristics require iteratively solving a subset-sum problem. We present the results of computational experiments that provide strong evidence that the new proposed lower and upper bounds consistently outperform the best bounds from the literature. [source]

Minimizing Total Tardiness: A Case Study in an Autoparts Factory

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 4 2002
Leandro Kiyuzato
The application of heuristic procedures for solving a real scheduling problem that arises in an autoparts factory is reported in this paper. Due to the characteristics of the environment, the measure of performance considered is the minimization of the total tardiness of the jobs. The original problem is reduced to the single machine scheduling problem, and the dispatching rules EDD (earliest due date), SPT (shortest processing time), and the PSK algorithm are used to obtain approximate solutions. Computational tests and a comparison with the usual schedule are presented. [source]

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2003
Stéphane Dauzère-Pérès
This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed-integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003 [source]

On-line algorithms for minimizing makespan on batch processing machines

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2001
Gouchuan Zhang
Abstract We consider problem of scheduling jobs on-line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on-line algorithms with worst-case ratio (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst-case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on-line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241,258, 2001 [source]

Metaheuristics for the vehicle routing problem with loading constraints

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2007
Karl F. Doerner
Abstract We consider a combination of the capacitated vehicle routing problem and a class of additional loading constraints involving a parallel machine scheduling problem. The work is motivated by a real-world transportation problem occurring to a wood-products retailer, which delivers its products to a number of customers in a specific region. We solve the problem by means of two different metaheuristics algorithms: a Tabu Search and an Ant Colony Optimization. Extensive computational results are given for both algorithms, on instances derived from the vehicle routing literature and on real-world instances. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 49(4), 294,307 2007 [source]