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Showing papers on "Single-machine scheduling published in 1997"


Journal ArticleDOI
TL;DR: It is proved that, when scheduling on parallel machines under the group technology assumption with sequence-independent setup times, minimizing total completion times is NP-hard unless all families contain the same number of jobs.

70 citations


Journal ArticleDOI
TL;DR: This paper introduces a discrete model in which job processing times are discretely controllable, i.e. the possible processing time of a job can only be controlled to be some specified lengths.

60 citations


Posted Content
01 Jan 1997
TL;DR: In this paper, the problem of solving the discrete lotsizing and scheduling problem for one machine with sequence dependent setup times and setup costs is solved as a single machine scheduling problem, which is termed the batch sequencing problem.
Abstract: The discrete lotsizing and scheduling problem for one machine with sequence dependent setup times and setup costs is solved as a single machine scheduling problem, which we term the batch sequencing problem. The relationship between the lotsizing problem and the batch sequencing problem is analyzed. The batch sequencing problem is solved with a brauch & bound algorithm which is accelerated by bounding and dominance rules. The algorithm is compared with recently published procedures for solving variants of the DLSP and is found to be more efficient if the number of items is not large.

50 citations


Journal ArticleDOI
TL;DR: This paper considers a problem of scheduling N jobs on a single machine to minimize the maximum lateness, and proposes a single-batch heuristic in which all jobs of a family form a batch, and a double-batchHeuristics in which each family is partitioned into at most two batches according to the due dates of its jobs.
Abstract: This paper considers a problem of scheduling N jobs on a single machine to minimize the maximum lateness. A partitioning of the jobs into F families is given. A set-up time is required at the start of each batch, where a batch is a largest set of contiguously scheduled jobs from the same family. We propose a single-batch heuristic in which all jobs of a family form a batch, and a double-batch heuristic in which each family is partitioned into at most two batches according to the due dates of its jobs. Both heuristics require O(N log N) time. It is shown that the single-batch heuristic has a worst-case performance ratio of 2 -1/F, whereas a composite heuristic which selects the better of the schedules generated by the single- and double-batch heuristics has a worst-case performance ratio of 5/3 for arbitrary F. Lower bounds are derived and are incorporated in a branch and bound algorithm. This algorithm uses a procedure to reduce the size of the problem, and employs a branching rule which forces pairs of jobs to lie in the same batch or in different batches. Computational tests show that the algorithm is effective in solving problems with up to 50 jobs.

47 citations


Journal ArticleDOI
TL;DR: Four alternative neighbourhood search methods are developed: multi-start descent, simulated annealing, threshold accepting and tabu search, which generate high quality schedules at relatively modest computational expense.
Abstract: Local search heuristics are developed for a problem of scheduling a single machine to minimize the total weighted completion time. The jobs are partitioned into families, and a set-up time is necessary when there is a switch in processing jobs from one family to jobs of another family. Four alternative neighbourhood search methods are developed: multi-start descent, simulated annealing, threshold accepting and tabu search. The performance of these heuristics is evaluated on a large set of test problems, and the results are also compared with those obtained by a genetic algorithm. The best results are obtained with the tabu search method for smaller numbers of families and with the genetic algorithm for larger numbers of families. In combination, these methods generate high quality schedules at relatively modest computational expense.

38 citations


Journal ArticleDOI
TL;DR: The results suggest that the heuristics are effective in generating near-optimal solutions quickly in a problem in which a set of n jobs has to be batched as well as scheduled for processing on a single machine.
Abstract: We study a problem in which a set of n jobs has to be batched as well as scheduled for processing on a single machine. A constant machine set-up time is required before the first job of each batch is processed. A schedule specifies the sequence of batches, where each batch comprises a sequence of jobs. The batch delivery time is defined as the completion time of the last job in a batch. The earliness of a job is defined as the difference between the delivery time of the batch to which it belongs and the job completion time. The objective is to find a number B of batches and a schedule so as to minimize the sum of the total weighted job earliness and mean batch delivery time. The problem is shown to be strongly NP-hard. It remains strongly $NP$-hard if the set-up time is zero and $B\le U$ for any variable $U\ge 2$ or if $B\ge U$ for any constant $U\ge 2$. The problem is proved to be ordinary NP-hard even if the set-up time is zero and $B\le 2$. For the case $B\le U$, a dynamic programming algorithm is presented, which is pseudopolynomial for any constant $U\ge 2$. Algorithms with O(n¹) running times are derived for the cases when all weights are equal or all processing times are equal. For the general problem, a family of heuristics is suggested. Computational experiments on the proposed heuristic algorithm are conducted. The results suggest that the heuristics are effective in generating near-optimal solutions quickly.

37 citations


Journal ArticleDOI
TL;DR: It is shown that the static deterministic single machine scheduling problem with a common due window can be formulated as an assignment problem and thus can be solved with well-known algorithms.
Abstract: A static deterministic single machine scheduling problem with a common due window is considered. Job processing times are controllable to the extent that they can be reduced, up to a certain limit, at a cost proportional to the reduction. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, its size, processing time reduction as well as job earliness and tardiness. We show that the problem can be formulated as an assignment problem and thus can be solved with well-known algorithms.

36 citations


Book
01 Mar 1997
TL;DR: The paper considers the single machine due date assignment and scheduling problems with n jobs in which the due dates are to be obtained from the processing times by adding a positive slack q and designs fast algorithms for their solution under a wide range of assumptions.
Abstract: The paper considers the single machine due date assignment and scheduling problems with n jobs in which the due dates are to be obtained from the processing times by adding a positive slack q. A schedule is feasible if there are no tardy jobs and the job sequence respects given precedence constraints. The value of q is chosen so as to minimize a function ϕ(F,q) which is non-decreasing in each of its arguments, where F is a certain non-decreasing earliness penalty function. Once q is chosen or fixed, the corresponding scheduling problem is to find a feasible schedule with the minimum value of function F. In the case of arbitrary precedence constraints the problems under consideration are shown to be NP-hard in the strong sense even for F being total earliness. If the precedence constraints are defined by a series-parallel graph, both scheduling and due date assignment problems are proved solvable in time, provided that F is either the sum of linear functions or the sum of exponential functions. The running time of the algorithms can be reduced to if the jobs are independent. Scope and purpose We consider the single machine due date assignment and scheduling problems and design fast algorithms for their solution under a wide range of assumptions. The problems under consideration arise in production planning when the management is faced with a problem of setting the realistic due dates for a number of orders. The due dates of the orders are determined by increasing the time needed for their fulfillment by a common positive slack. If the slack is set to be large enough, the due dates can be easily maintained, thereby producing a good image of the firm. This, however, may result in the substantial holding cost of the finished products before they are brought to the customer. The objective is to explore the trade-off between the size of the slack and the arising holding costs for the early orders.

34 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined a stochastic scheduling model with n jobs and a single machine, where the processing times of the jobs are random variables with arbitrary distributions, and the machine is subject to stochastically breakdowns.

28 citations


Journal ArticleDOI
TL;DR: This paper derives general conditions for the earliness and tardiness cost structure and repair and breakdown processes under which the equivalent cost function is quasi-convex and shows that a V-shaped schedule may fail to be optimal if the property does not apply.
Abstract: In this paper we consider single machine scheduling problems with a common due-date for all jobs, arbitrary monotone earliness and tardiness costs and arbitrary breakdown and repair processes. We show that the problem is equivalent to a deterministic one without breakdowns and repairs and with an equivalent cost function of a job's completion time. A V-shaped schedule without idle times is shown to be optimal, if this equivalent cost function is quasi-convex. Conversely, we show that a V-shaped schedule may fail to be optimal if the property does not apply. We derive general conditions for the earliness and tardiness cost structure and repair and breakdown processes under which the equivalent cost function is quasi-convex. When a V-shaped schedule is optimal, an efficient though pseudo-polynomial algorithm can be used to compute an optimal schedule.

27 citations


Journal ArticleDOI
Jinxing Xie1
TL;DR: The single machine scheduling problem with multiple financial resource constraints can be reduced to the two machine flow shop scheduling problem if the financial resources arrive uniformly over time, and the LPT (Largest Processing Time) rule generates an optimal solution to the problem.

Journal ArticleDOI
TL;DR: In this article, the problem of scheduling a set of n jobs on a single machine to minimize weighted absolute deviation of completion times from a common due date is studied. But it is assumed that weights of jobs are proportional to their processing times, and it is shown that the problem can be solved efficiently for a sufficiently large due date.

Journal ArticleDOI
TL;DR: This article has derived two dominance criteria and used them in the development of a new pseudopolynomial algorithm, an implicit enumeration scheme based on a binary branching strategy, which is superior to those of De, Ghosh and Wells and Kubiak in terms of computational complexity.

Journal ArticleDOI
TL;DR: A scheduling problem in which n jobs are grouped into F groups and are to be processed on a single machine to find an optimal commonDue date and an optimal sequence of jobs to minimize the sum of the cost of tardy jobs and the cost related to the common due date.

Journal ArticleDOI
TL;DR: A dynamic programming algorithm for the single machine scheduling problem with ready times and deadlines to minimize total weighted completion time is proposed and it is shown that the algorithm is polynomial if time window length is bounded by a constant and times are integer-valued.
Abstract: We propose a dynamic programming algorithm for the single machine scheduling problem with ready times and deadlines to minimize total weighted completion time. Weights may be positive or negative and the cost function may be non-regular. This problem appears as a subproblem in the Dantzig-Wolfe decomposition of the job-shop scheduling problem. We show that the algorithm is polynomial if time window length is bounded by a constant and times are integer-valued. We present computational results for problems with up to 200 jobs.

Journal ArticleDOI
TL;DR: The problem of maximizing the weighted number of on-time jobs on a single machine with time windows (STW) is shown to be strongly NP-hard and an efficient heuristic is presented for STW.


Journal ArticleDOI
TL;DR: A heuristic algorithm in O(n2) time is developed to minimize the weighted earliness subject to a maximum tardiness for each job.

Journal ArticleDOI
TL;DR: This paper transforms the initial problem into a reduced problem, where all jobs with deadlines are eliminated, and gives an opportunity to propose O(n log n) algorithms for some special cases of the considered problems.
Abstract: In this paper we consider a single machine preemptive scheduling problem to minimize the weighted number of late jobs. There are given n jobs and for each job we have a release date, a processing time and a due date. It is assumed that certain specified jobs have to be completed on time. The due dates for these jobs are considered as deadlines. while for the other jobs due dates may be violated. For the case of similarly ordered release and due dates (when there is no advantage to preemption) as well as for the case of embedded release and due date intervals and preemption allowed, we transform the initial problem into a reduced problem, where all jobs with deadlines are eliminated. It gives an opportunity to propose O(n log n) algorithms for some special cases of the considered problems.

Proceedings ArticleDOI
09 Sep 1997
TL;DR: A new mixed-integer linear programming formulation for the minimization of the number of late jobs on a single machine is presented, which allows the same lower bound to be determined faster, but can readily be extended to the weighted case.
Abstract: A new mixed-integer linear programming formulation for the minimization of the number of late jobs on a single machine is presented. The general problem is considered, i.e., when release dates and due dates can be different. This formulation is compared to one that was investigated in a previous work, and is shown to be much more interesting. The new modeling, not only allows the same lower bound to be determined faster, but can readily be extended to the weighted case. Some powerful cuts are also proposed, that were not valid in the previous formulation, which improve the quality of the bound. Some computational experiments are presented.

Journal ArticleDOI
TL;DR: A tabu search approach is proposed for solving the single machine mean tardiness scheduling problem and results indicate that the proposed approach provides a much better solution than the other three approaches.
Abstract: In this paper, a tabu search approach is proposed for solving the single machine mean tardiness scheduling problem. Simulation experiment results obtained from the tabu search approach and three other heuristics are compared. Although computation time is increased, the results indicate that the proposed approach provides a much better solution than the other three approaches.

Journal ArticleDOI
TL;DR: This work studies preemptive single machine scheduling problems where the buffer capacity is finite, and presents a complexity classification for various problems, either by deriving an efficient algorithm, or by proving that such an algorithm is unlikely to exist.
Abstract: In many scheduling problems, an arriving job is stored in an input buffer until it starts to be processed. Also, it may be necessary to hold a partially completed preempted job in an input buffer until processing of this job resumes. In the scheduling literature, most problems have been studied using the implicit assumption that the buffer has infinite capacity. We study preemptive single machine scheduling problems where the buffer capacity is finite. In this scheduling environment, jobs may be lost either because of insufficient input buffer capacity, or because due date requirements cannot be met. We examine problems where the objective is to minimize the weighted or unweighted number of lost jobs. Various assumptions about the generality of the data are examined. We present a complexity classification for various problems, either by deriving an efficient algorithm, or by proving that such an algorithm is unlikely to exist.


Proceedings ArticleDOI
04 Jun 1997
TL;DR: The utility of receding horizon optimal control for scheduling of manufacturing systems is explored and cost function approximations are used to reduce the computational burden.
Abstract: The utility of receding horizon optimal control for scheduling of manufacturing systems is explored. Both online and off-line computations of the optimal policy are considered. Cost function approximations are used to reduce the computational burden. The results are demonstrated on a re-entrant line and transfer line.

01 Jan 1997
TL;DR: This work presents the theoretical characterization of the solution of a production system comprising a multi-item single machine with piecewise deterministic demands and establishes the rate of convergence of the discrete solution toward the original continuous solution.
Abstract: In this work we study the optimization of a production system comprising a multi-item single machine with piecewise deterministic demands. Demands can only take a finite number of values and the demand changes are described by Poisson processes. We present the theoretical characterization of the solution and a numerical procedure to solve it. We establish the rate of convergence of the discrete solution toward the original continuous solution.

Journal ArticleDOI
TL;DR: A single machine scheduling problem where the resource consumed depends on the release times of jobs is investigated and the objective is to minimize the total consumption subject to a constraint on the makespan or the total completion time.

Book ChapterDOI
01 Jan 1997
TL;DR: It appears that some problems with job release dates and technological precedence constraints among jobs are NP-complete even for the some models of release dates for all jobs.
Abstract: Single machine scheduling problems with job release dates and technological precedence constraints among jobs are considered. It is assumed that job release dates depend on continuously-divisible resources such as: energy, fuel, catalyzer, row materials, financial outlay. The following optimization criteria are considered: makespan, total resource consumption and both simultaneously. Detailed computational complexity analysis of the considered problems and their special cases were conducted. It appears that some problems are NP-complete even for the some models of release dates for all jobs. Several special cases with polynomial time algorithms are found.

Journal ArticleDOI
TL;DR: In this article, the one-machine scheduling problem with the objective of minimizing the mean tardiness subject to maintaining a prescribed number of tardy jobs is analyzed and an algorithm for solving this problem is presented.
Abstract: In this paper the one-machine scheduling problem with the objective of minimizing the mean tardiness subject to maintaining a prescribed number of tardy jobs is analysed. An algorithm for solving this problem is presented. It is proved that the schedule generated by the proposed algorithm is indeed optimal.

Journal ArticleDOI
TL;DR: Several properties of the optimal solution and a lower bound of the ideal lateness are developed to construct a branch-and-bound algorithm in the search of an optimal schedule and the effectiveness of the proposed algorithm is empirically evaluated.
Abstract: Standard scheduling problems bear the assumption that each job has a constant setup time and thus this setup time can be included in the processing time of a job. However, many realistic production...

Journal ArticleDOI
TL;DR: A heuristic batching and sequencing algorithm which is based on a repetitive schedule to minimize the total production cost is proposed which is superior to the well known lot sizing (Economic Order Quantity) rule for the problem.