Showing papers on "Single-machine scheduling published in 2002"
01 Jan 2002
TL;DR: A general framework for using real time information to improve scheduling decisions is developed, which allows us to trade off the quality of the revised schedule against the production disturbance which results from changing the planned schedule.
Abstract: In many production processes real time information may be obtained from process control computers and other monitoring systems, but most existing scheduling models are unable to use this information to effectively influence scheduling decisions in real time. In this paper we develop a general framework for using real time information to improve scheduling decisions, which allows us to trade off the quality of the revised schedule against the production disturbance which results from changing the planned schedule. We illustrate how our framework can be used to select a strategy for using real time information for a single machine scheduling model and discuss how it may be used to incorporate real time information into scheduling the complex production processes of steel continuous caster planning. 2002 Elsevier Science B.V. All rights reserved.
237 citations
TL;DR: In this paper, a general framework for using real-time information to improve scheduling decisions is developed, which allows us to trade off the quality of the revised schedule against the production disturbance which results from changing the planned schedule.
226 citations
TL;DR: Two simple randomized approximation algorithms are described, which are guaranteed to deliver feasible schedules with expected objective function value within factors of 1.7451 and 1.6853, respectively, of the optimum of two linear programming relaxations of the problem.
Abstract: We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completion-time formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective function value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent $\alpha$-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least $e/(e-1) \approx 1.5819$. Both algorithms may be derandomized; their deterministic versions run in O(n2) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards.
170 citations
TL;DR: This work describes an Ant Colony Optimization (ACO) algorithm having a new feature using look-ahead information in the transition rule that shows an improvement in performance.
Abstract: We compare several heuristics for solving a single machine scheduling problem. In the operating situation modelled, setup times are sequence-dependent and the objective is to minimize total tardiness. We describe an Ant Colony Optimization (ACO) algorithm having a new feature using look-ahead information in the transition rule. This feature shows an improvement in performance. A comparison with a genetic algorithm, a simulated annealing approach, a local search method and a branch-and-bound algorithm indicates that the ACO that we describe is competitive and has a certain advantage for larger problems.
160 citations
TL;DR: It is shown that the robust version of the single machine scheduling problem with sum of completion times criterion (SS) is NP-complete even for very restricted cases.
Abstract: The single machine scheduling problem with sum of completion times criterion (SS) can be solved easily by the Shortest Processing Time (SPT) rule. In the case of significant uncertainty of the processing times, a robustness approach is appropriate. In this paper, we show that the robust version of the (SS) problem is NP-complete even for very restricted cases. We present an algorithm for finding optimal solutions for the robust (SS) problem using dynamic programming. We also provide two polynomial time heuristics and demonstrate their effectiveness.
116 citations
TL;DR: Computational experiments indicate that the performance of the proposed approach to a single machine scheduling problem with distinct due windows to minimize total weighted earliness and tardiness is quite well, especially for the instances of large size.
115 citations
TL;DR: A comparison between the problems with job processing times being decreasing and increasing linear functions of their start times is presented, which shows that the decreasing and increase linear models of job processing time seem to be closely related to each other.
94 citations
TL;DR: The problem is to find a schedule for which the total weighted completion time is minimized and it is proved that the problem is NP-hard.
Abstract: This paper deals with a single machine scheduling problem with start time dependent job processing times. The job processing times are characterized by decreasing linear functions dependent on their start times. The problem is to find a schedule for which the total weighted completion time is minimized. It is proved that the problem is NP-hard. Some properties of special cases of the general problem are also given. Based on these results, two heuristic algorithms are constructed and their performance is compared.
73 citations
TL;DR: This work considers the NP-hard preemptive single-machine scheduling problem to minimize the total weighted completion time subject to release dates, and proves that the competitive ratio of this simple on-line algorithm is precisely 2 and shows that list scheduling in order of random � -points drawn from the same schedule results in an on- line algorithm with competitive ratio 4.
Abstract: SUMMARY We consider the NP-hard preemptive single-machine scheduling problem to minimize the total weighted completion time subject to release dates. A natural extension of Smith’s ratio rule is to preempt the currently active job whenever a new job arrives that has higher ratio of weight to processing time. We prove that the competitive ratio of this simple on-line algorithm is precisely 2. We also show that list scheduling in order of random � -points drawn from the same schedule results in an on-line algorithm with competitive ratio 4 . Since its analysis relies on a well-known integer programming relaxation of the scheduling problem, the relaxation has performance guarantee 4 as well. On the other hand, we show that it is at best an 8 -relaxation. Copyright ? 2002 John Wiley & Sons, Ltd.
71 citations
TL;DR: A heuristic algorithm for finding a sub-optimal solution of the single machine scheduling problem, where the critical scheduling parameter, that is job value, deteriorates exponentially over time, is presented.
57 citations
TL;DR: The proposed problem is shown to be NP-hard, a heuristic algorithm with computational experiments is provided and an extension with more than one maintenance intervals is considered.
Abstract: This paper considers a single machine scheduling problem with a flexible maintenance, we consider the machine should be stopped to maintain or to reset for a constant time r during the scheduling period. Meanwhile we assume that the maintenance period [s, t] is arranged previously; and the time r would not be longer than the maintenance period [s, t] (i.e. r ≤ t-s). The time s (t) is the earliest (latest) time at which the machine starts (stops) its maintenance. The objective is to minimize the makespan (maximum completion time). This scheduling problem is often occurred in computer center, NC-machine and IC-testing machine for the jobs scheduling and repairmen arrangement. In this paper, the proposed problem is shown to be NP-hard. A heuristic algorithm with computational experiments is provided. An extension with more than one maintenance intervals is also considered.
TL;DR: FLC is used to adaptively regulate the crossover ratio and the mutation ratio of the proposed algorithm and various experiments show that the results of pro-fGA outperform those ofpro-GA.
TL;DR: This work shows that this problem of scheduling a set of nonsimultaneously available jobs on one machine is strongly NP-hard and gives an efficient algorithm that finds an optimal due date and schedule when either the job sequence is predetermined or all jobs have the same processing time.
TL;DR: A new subclass of machine scheduling problems in which due dates are treated as variables and must be assigned to the individual jobs is introduced, and polynomial time algorithms are available though most problems that are intractable under traditional due date definitions remain so.
TL;DR: An iterative heuristic procedure is used to address the notorious combinatorial complexity of a large-scale industrial production scheduling problem and an illustrative example based on industrial data is presented.
TL;DR: The problem of scheduling n jobs to minimize the Total Weighted Late Work (TWLW) is evaluated within the single machine context and various scheduling rules, heuristics and algorithms are empirically evaluated using different parameters to determine the utility of each approach.
TL;DR: This paper studies the single machine scheduling problem for the purpose of minimizing the expected number of tardy jobs, and a dynamic policy based on a myopic approach is developed.
TL;DR: A tabu search algorithm that schedules N jobs to a single machine in order to minimise the maximum lateness of the jobs and obtains much better solutions more quickly than the RHP heuristic suggested by Ovacik and Uzsoy.
Abstract: In this paper, we present a tabu search algorithm that schedules N jobs to a single machine in order to minimise the maximum lateness of the jobs. The release times, due dates, and sequence-dependent set-up times of the jobs are assumed to exist. We modified the original tabu search method to be suitable for the scheduling problem. The proposed tabu search algorithm is composed of two parts: a MATCS (modified apparent tardiness cost with set-ups) rule for finding an efficient initial solution, and the tabu search method to seek a near optimal solution from the initial solution. The experimental results show that the tabu search algorithm obtains much better solutions more quickly than the RHP (rolling horizon procedure) heuristic suggested by Ovacik and Uzsoy.
12 May 2002
TL;DR: In this paper, a scheduling framework based on genetic algorithms for real world scheduling problems, which considers job release times, job due dates and different assembly levels, is presented, based on a decomposition of the job shop scheduling problem into a series of deterministic single machine scheduling problems.
Abstract: This paper starts by presenting a scheduling framework, based on genetic algorithms for the resolution of real world scheduling problems, which considers job release times, job due dates and different assembly levels. This framework is based on a decomposition of the job-shop scheduling problem into a series of deterministic single machine scheduling problem. A coordination mechanism is proposed.
TL;DR: A new procedure that considers the use of inserted idle time to optimally solve the single machine scheduling problem where the objective is to minimize the sum of squares lateness is proposed.
06 Oct 2002
TL;DR: Four heuristics are proposed to determine a good schedule that minimizes the objective function of scheduling processing of jobs and maintenance of machines simultaneously to minimize total tardiness of jobs.
Abstract: This paper considers single machine scheduling with preventive maintenance. In many cases, a machine must be maintained after it continuously works for a period of time. But most papers in the literature ignore non-availability of the machine. For this reason, this paper studies the problem of scheduling processing of jobs and maintenance of machines simultaneously. The objective is to minimize total tardiness of jobs. Four heuristics are proposed to determine a good schedule that minimizes the objective function. Computational experiments are done to evaluate the effectiveness of the algorithms.
TL;DR: The relation of time indexed formulations of nonpreemptive single machine scheduling problems to the node packing problem is established and then used to provide simple and intuitive alternate proofs of validity and maximality for previously known results on the facial structure of the scheduling problem.
Abstract: The relation of time indexed formulations of nonpreemptive single machine scheduling problems to the node packing problem is established and then used to provide simple and intuitive alternate proofs of validity and maximality for previously known results on the facial structure of the scheduling problem. Previous work on the facial structure has focused on describing the convex hull of the set of feasible partial schedules, schedules in which not all jobs have to be started. The equivalence between the characteristic vectors of this set and those of the set of feasible node packings in a graph whose structure is determined by the parameters of the scheduling problem is established. The main contribution of this paper is to show that the facet inducing inequalities for the convex hull of the set of feasible partial schedules that have integral coefficients and right hand side 1 or 2 are the maximal clique inequalities and the maximally and sequentially lifted 5-hole inequalities of the convex hull of the set of feasible node packings in this graph respectively.
TL;DR: The paper deals with the single machine scheduling problem where both total and maximum tardiness musl be mimmized, and the e-constraint approach is adopted to search for all the Pareto-optima.
TL;DR: A generic model developed in real vector space is used for understanding the structural relationship between the optimal schedule and the location of the due dates and is found to produce near optimal solutions efficiently, which makes it more scalable and practical compared to the branch and bound algorithm.
Abstract: Reducing the variance of part completion times about promised due dates is an important element of Just-In-Time production because it reduces the work-in-process inventory and tardiness simultaneously. Scheduling models and algorithms are developed to minimize the Mean Squared Deviation (MSD) of completion times about due dates on a single machine. A generic model is developed in real vector space for understanding the structural relationship between the optimal schedule and the location of the due dates. Geometric insights gained from this vector space model are used to relate the shortest and longest processing time sequences to the level of difficulty of the MSD optimization problem. The vector space model is used to develop dominance conditions for a branch and bound algorithm and to analytically synthesize parameters for a continuous variable feedback control algorithm for distributed scheduling. The control algorithm lends itself to massively parallel / distributed computation and is found to produce near optimal solutions efficiently, which makes it more scalable and practical compared to the branch and bound algorithm. Computational experiments with both approaches are presented.
TL;DR: Experiments performed for various instances of the single machine scheduling problems with earliness costs and multiple due dates show the potential of the relative pheromone evaluation method.
Abstract: In this paper the relative pheromone evaluation method for Ant Colony Optimization is investigated.We compare this method to the standard pheromone method and the summation method. Moreover we propose a new variant of the relative pheromone evaluation method. Experiments performed for various instances of the single machine scheduling problems with earliness costs and multiple due dates show the potential of the relative pheromone evaluation method.
TL;DR: This work considers a single-machine environment in which the processing times of individual jobs are uncertain and the performance measure of interest is the criteria of the total flow time, and model the robust scheduling problems and properly incorporate relative robust schedules problem into fractional programming problems.
Abstract: Uncertainty can be found in numerous parts of the manufacturing environments. The uncertain processing time is one of the most prevalent. We consider a single-machine environment in which the processing times of individual jobs are uncertain and the performance measure of interest is the criteria of the total flow time. The processing times uncertainty can be realized in a specified range or a discrete number of distinct processing times in each job. Confronted with the uncertainty, the concept of robust optimization was introduced. The measures of deviation and relative robustness are used to tackle the uncertainty. We model the robust scheduling problems and properly incorporate relative robust schedules problem into fractional programming problems. Bisection searches based on parametric approach are prepared for the relative robust scheduling problem.
TL;DR: A pseudo-polynomial DP solution and a polynomial heuristic for general instance are proposed for a non-preemptive single-machine job sequencing problem where the objective is to minimize the sum of squared deviation of completion times of jobs from a common due date.
Journal Article•
TL;DR: A relationship matrix is developed that allows a branch-and-bound algorithm to eliminate a high percentage of infeasible solutions in a single-machine scheduling problem with weighted earliness and tardiness penalties.
Abstract: In this paper, a single-machine scheduling problem with weighted earliness and tardiness penalties is considered. Idle time between two adjacent jobs is permitted and due dates of jobs could be unequal. The dominance rules are utilized to develop a relationship matrix, which allows a branch-and-bound algorithm to eliminate a high percentage of infeasible solutions. After combining this matrix with a branching strategy, a procedure to solve the problem is proposed. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 760–780, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10039