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Showing papers on "Single-machine scheduling published in 1995"


Journal ArticleDOI
TL;DR: In this paper, it was shown that the bicriteria single-machine scheduling problem of minimizing total completion time and maximum cost simultaneously is solvable in polynomial time.

82 citations


Journal ArticleDOI
TL;DR: An efficient algorithm for calculating nondominated schedules is proposed that first defines a schedule vector and then a nondominated schedule vector, and reflects the satisfaction level with respect to precedence between two jobs.

76 citations


Journal ArticleDOI
TL;DR: The problem can be formulated as a problem of maximizing a zero-one quadratic function which is a submodular function with a special cost structure and it immediately follows from the cost structure that value of the function for a sequence that minimizes total absolute deviation about a common unrestrictive due date is at most 100% smaller than the one for an optimal sequence for the completion time variance problem.

62 citations


Journal ArticleDOI
TL;DR: A pseudopolynomial algorithm and a branch and bound algorithm in which lower bounds are obtained using the dynamic programming state-space relaxation method is proposed for this general problem of scheduling a single machine to minimize total weighted late work.
Abstract: In the problem of scheduling a single machine to minimize total weighted late work, there are n jobs to be processed for which each has an integer processing time, a weight and a due date. The objective is to minimize the total weighted late work, where the late work for a job is the amount of processing of this job which is performed after its due date. An O(n log n) algorithm is derived for the preemptive total weighted late work problem. For non-preemptive scheduling, efficient algorithms are derived for the special cases in which all processing times are equal and in which all due dates are equal. A pseudopolynomial algorithm is presented for the general non-preemptive total weighted late work problem. Also, a branch and bound algorithm in which lower bounds are obtained using the dynamic programming state-space relaxation method is proposed for this general problem. Computational results with the branch and bound algorithm for problems with up to 700 jobs are given. INFORMS Journal on Computing, ISSN...

56 citations


Journal ArticleDOI
TL;DR: Two dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme that is shown to be NP-hard even for the special case of common parameters.

45 citations


Journal ArticleDOI
TL;DR: Two approximation algorithms with the worst-case performance ratio of 3 2 are given for the case with sequence independent batch setup times and results of computational experiments are provided.

43 citations


Proceedings ArticleDOI
21 Jun 1995
TL;DR: In this paper, the authors provide the solution to the partial differential equations associated with the steady-state joint probability density function of the buffer levels for two part-type, single machine flexible manufacturing systems under a linear switching curve (LSC) policy.
Abstract: Quadratic approximations to the differential cost-to-go function, which yield linear switching curves, have been extensively studied. In this paper, the authors provide the solution to the partial differential equations associated with the steady-state joint probability density function of the buffer levels for two part-type, single machine flexible manufacturing systems under a linear switching curve (LSC) policy. When there are more than two part-types, the authors derive the density functions under a prioritized hedging point (PHP) policy by decomposing the multiple part-type problem into a sequence of single part-type problems. The expressions for the steady-state density functions are independent of the cost function. Therefore, for additive cost functions that are non-linear in the buffer levels, one can compute the optimal PHP policy, or the more general optimal LSC policy for two part-type problems.

26 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider the problem of minimizing the total tardiness of a job set while keeping the number of tardy jobs to its minimum value, and present a simple algorithm to obtain an optimal sequence when the set of Tardy jobs is specified.
Abstract: We consider the scheduling problem to minimize the total tardiness of a job set keeping the number of tardy jobs to its minimum value. A simple algorithm is presented to obtain an optimal sequence when the set of tardy jobs is specified. A set of properties is presented that explores the structure induced by the minimum number of tardy jobs requirement. The general problem is solved optimally by employing an efficient Branch & Bound (B&B) search that takes advantage of the theory developed. We identify special cases where the Moore-Hodgson algorithm can be applied to find the optimal tardy job set. Computational experiments show that the B&B algorithm solves relatively large instances in just a few seconds, on a personal computer.

25 citations


Journal ArticleDOI
TL;DR: In this paper, a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints is proposed, which is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0-1 linear program.
Abstract: We design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0-1 linear program. Also, we show that upon termination of such an ascent direction algorithm we get a dual decomposition of the original problem, which can be exploited to develop approximative and enumerative approaches for it. Computational results exhibit that in our application the ascent direction leads to good Lagrangian lower and upper bounds.

15 citations


Journal ArticleDOI
TL;DR: A powerful decomposition mechanism, based on a precedence relation concept, is presented that easily handles problems of the size n = 50 and 100 where the processing times and penalties are independently drawn from a uniform distribution.
Abstract: This paper deals with scheduling n jobs on a single machine in order to minimize the weighted sum of squared waiting times of the jobs. We present a powerful decomposition mechanism, based on a precedence relation concept, that easily handles problems of the size n = 50 and 100 where the processing times and penalties are independently drawn from a uniform distribution. This mechanism is incorporated along with new branching rules in a branch-and-bound scheme that efficiently handles tough problems of the size 20 and 50.

13 citations


Book ChapterDOI
01 Jan 1995
TL;DR: This paper designs and analyzes two on-line algorithms which make scheduling decisions without knowing about jobs that will arrive in future and studies the nonpreemptive single machine scheduling of independent jobs with arbitrary release dates to minimize the total completion time.
Abstract: An increasingly significant branch of computer science is the study of on-line algorithms. In this paper, we apply the theory of on-line algorithms to job scheduling. In particular, we study the nonpreemptive single machine scheduling of independent jobs with arbitrary release dates to minimize the total completion time. We design and analyze two on-line algorithms which make scheduling decisions without knowing about jobs that will arrive in future.

Journal ArticleDOI
TL;DR: This work considers a single-machine scheduling problem in which every job has a given target start time and a due-date, and shows that the problem is NP-complete in the strong sense.

Journal ArticleDOI
TL;DR: In this article, a one-machine scheduling problem to minimize the sum of the total earliness and total tardiness penalties with respect to a common due date, which is a decision variable, is considered.
Abstract: This note deals with a one-machine scheduling problem to minimize the sum of the total earliness and total tardiness penalties with respect to a common due date, which is a decision variable. We show that the V-shaped property holds for a general case. This result is also true if the common due date is a prespecified value.

Journal ArticleDOI
TL;DR: In this paper, the problem of scheduling n jobs on a single machine is studied, where each job is assigned a processing-plus-wait due date, which is an affine-linear function of its processing time.
Abstract: We study the problem of schedulingn jobs on a single machine. Each job is assigned a processing-plus-wait due date, which is an affine-linear function of its processing time. The objective is to minimize the symmetric earliness and tardiness costs. We analyze a combined decision model which includes computing both the optimal job sequence and optimal due date parameters. For the quadratic objective function, we propose a heuristic solution based on a bicriterion approach. Additionally, we provide computational results to compare this model with two simpler models. For the maximum objective function, we show that it is efficiently solved by the shortest processing time sequence.

Proceedings ArticleDOI
10 Oct 1995
TL;DR: A tabu-search-based heuristic procedure is proposed to find the sequence which allows one to reach a value of the cost function as close as possible to the global minimum as part of a single machine scheduling problem with ready times.
Abstract: We consider the minimisation of the mean completion time and the makespan in the single machine scheduling problem with ready times. A tabu-search-based heuristic procedure is proposed to find the sequence which allows one to reach a value of the cost function as close as possible to the global minimum. Computational tests have been carried out to compare the performances of the tabu search procedure with those of a branch and bound algorithm which gives the optimal solution for problems that are not too large. A comparison has also been made with three heuristics, recently presented by Liu-MacCarthy, which have given good outcomes both in terms of mean completion time and response time. Our comparisons have been made both in terms of mean completion time and makespan. The tabu search response time has been considered to asses the reliability of the method. Computational tests show that, with respect to the completion time, the tabu search yields excellent sequences.

01 Jan 1995
TL;DR: A branch-and-bound algorithm is developed that solves almost all instances with up to about 40 jobs to optimality of the NP-hard problem of scheduling n independent jobs with release dates, due dates, and family setup times on a single machine to minimize the maximum lateness.
Abstract: We address the NP-hard problem of scheduling n independent jobs with release dates, due dates, and family setup times on a single machine to minimize the maximum lateness. This problem arises from the constant tug-of-war going on in manufacturing between efficient production and delivery performance, between maximizing machine utilization by batching similar jobs and maximizing customers’ satisfaction by completing jobs before their due dates. We develop a branch-and-bound algorithm, and our computational results show that it solves almost all instances with up to about 40 jobs to optimality. The main algorithmic contribution is our lower bounding strategy to deal with family setup times. The key idea is to see a setup time as a setup job with a specific processing time, release date, due date, and precedence relations. We develop several sufficient conditions to derive setup jobs. We specify their parameters and precedence relations such that the optimal solution value of the modified problem obtained by ignoring the setup times, not the setup jobs, is no larger than the optimal solution value of the original problem. One lower bound for the modified problem proceeds by allowing preemption. Due to the agreeable precedence structure, the preemptive problem is solvable in O(n logn )t ime.

Book ChapterDOI
01 Jan 1995
TL;DR: This chapter will present algorithms for single machine scheduling problems which are polynomial or pseudopolynomial, and shows that the optimal objective value does not improve if preemption is allowed.
Abstract: The single machine case has been the subject of extensive research ever since the early work of Jackson [1955] and Smith [1956]. In this chapter, we will present algorithms for single machine scheduling problems which are polynomial or pseudopolynomial. It is useful to note the following general result which holds for single machine problems: if all r j = 0 and if the objective function is a monotone function of the finish times of the jobs, then only schedules without preemption and without idle time need to be considered. This follows from the fact that the optimal objective value does not improve if preemption is allowed. To see this, consider a schedule in which some job i is preempted, i.e.

01 Jun 1995
TL;DR: This paper explores the reuse of components of known good schedules in new scheduling problems by accumulating a case-base of good quality schedules, retrieving a case (or cases) similar to a new scheduling problem and building a new schedule from components of the retrieved cases.
Abstract: In this paper we explore the reuse of components of known good schedules in new scheduling problems. This involves accumulating a case-base of good quality schedules, retrieving a case (or cases) similar to a new scheduling problem and building a new schedule from components of the retrieved cases. Two CBR solutions to a single machine scheduling problem with schedule dependent setup times are described. These are evaluated by comparing them with two more conventional alternative techniques – simulated annealing and myopic search. Both CBR techniques are shown to provide good quality solutions and significant time improvements over simulated annealing.

Journal ArticleDOI
TL;DR: The Simulated Annealing algorithm (SA) consistently provides very high quality solutions to the Single Machine Scheduling Problem and attests to its robustness as an effective solution procedure for combinatorial optimization problems.
Abstract: The Single Machine Scheduling Problem (SMSP) involves the sequencing of JV jobs which arrive simultaneously at time zero to be processed on a continuously available machine. The object is to find that schedule which minimizes the sum of linear sequence dependent setup costs and linear delay penalties. A series of 2k factorial experiments is used to obtain a set of‘ good’ values for the parameters of the SA algorithm for the SMSP. Using these parameter seuings, the Simulated Annealing algorithm (SA) consistently provides very high quality solutions to the SM SP. Results suggest that the performance of SA in solving the SMSP depends heavily upon the type of neighborhood search employed. Results are compared with those of Tabu Search ( TS)and SA matches the performance of TS in 22 of the 25 problems investigated. The performance of SA in the case of the SMSP attests to its robustness as an effective solution procedure for combinatorial optimization problems.

01 Jan 1995
TL;DR: In this article, a branch-and-cut algorithm based on facet inducing inequalities was proposed for minimizing the total weighted completion time on a single machine subject to release dates. But this algorithm is not suitable for single-machine scheduling problems.
Abstract: In Van den Akker, Van Hoesel, and Savelsbergh [1994], we have studied a time-indexed formulation for single-machine scheduling problems and have presented a complete characterization of all facet inducing inequalities with right-hand sides 1 and 2 of the convex hull of the monotone extension of the set of feasible schedules. In this paper, we discuss the development of a branch-and-cut algorithm based on these facet inducing inequalities. We describe separation algorithms for each class of these inequalities, and elaborate on various other important components of the branch-and-cut algorithm, such as branching strategies, cut generation schemes, and primal heuristics. We present our computational experiences with the algorithm for the problem of minimizing the total weighted completion time on a single machine subject to release dates.

Journal ArticleDOI
TL;DR: A comparison of different heuristics to schedule the multi-item, single-machine problem with stochastic, time-varying demands shows how the performance of one of them, the Enhanced Dynamic Cycle Lengths heuristic, can be improved and thus dominate all the otherHeuristics in all the various test cases simulated.
Abstract: A comparison of different heuristics to schedule the multi-item, single-machine problem with stochastic, time-varying demands was previously performed by Gascon, Leachman and Lefran90is. In this note, we show how the performance of one of these heuristics, the Enhanced Dynamic Cycle Lengths heuristic, can be improved and thus dominate all the other heuristics in all the various test cases simulated.

Proceedings ArticleDOI
22 Oct 1995
TL;DR: A distributed simulation technique for on-line scheduling is expanded to encompass several machines or workcells so that the simulation better reflects scheduling demands in manufacturing environments.
Abstract: On-line scheduling has traditionally been restricted to a single machine or workcell. In this paper, a distributed simulation technique for on-line scheduling is expanded to encompass several machines or workcells. Additional machines introduce several difficulties, however, the simulation better reflects scheduling demands in manufacturing environments.

Proceedings ArticleDOI
28 Jun 1995
TL;DR: The WCPM (weighted critical path method) is advanced which optimizes the typical CPM and obtains a more satisfactory scheduling result and has been used to implement a job-shop scheduling system for use in a Japanese factory producing flexible circuit boards.
Abstract: This paper presents an approach for scheduling jobs on machine cells with some processing constraints. A machine cell is a group of some machines. It is a managing unit in a shop. The shop managers assign the personnel and jobs to every cell. The components of cells can be changed with the demands of processed products and managers, which brings about great convenience in the management of semiautomatic manufacturing shops. However, it also increases the complexity of the scheduling problem in such shop. There are various types of cells in a shop. The authors give different scheduling approaches to different types of cells. As to the scheduling algorithm, they advance the WCPM (weighted critical path method) which optimizes the typical CPM and obtains a more satisfactory scheduling result. This approach has been used to implement a job-shop scheduling system for use in a Japanese factory producing flexible circuit boards.

Journal Article
TL;DR: The problem of determining optimal schedules for the static, single machine scheduling problem with the aid of CON and SLK due date determination methods is considered and the numerical example confirms considerations about the structural similarity of the two methods.
Abstract: The problem of determining optimal schedules for the static, single machine scheduling problem with the aid of CON and SLK due date determination methods is considered. The objective is to minimize the total weighted earliness and tardiness penalty in the case when weights are proportional to the processing times of the respective jobs. For each method, an optimization algorithm has been developed, by means of which the set of all optimal sequences is provided. The numerical example, presented after the theoretical foundation, confirms considerations about the structural similarity of the two methods.

Proceedings ArticleDOI
Rodolfo A. Milito1
13 Dec 1995
TL;DR: New results for the problem of scheduling K stochastic jobs in a single machine are derived based on the examination of a necessary condition for optimality in the transform domain.
Abstract: New results for the problem of scheduling K stochastic jobs in a single machine are derived based on the examination of a necessary condition for optimality in the transform domain.

07 Jul 1995
TL;DR: In this paper, the authors consider the problem of finding the optimal schedule for jobs on a single machine when there are penalties for both late and early arrivals, and they point out that if attention is paid to how certain parameters are measured, then a change of scale of measurement might lead to the anomalous situation where a schedule is optimal if these parameters were measured in one way, but not if they are measured in a different way that seems equally acceptable.
Abstract: We consider the problem of finding the optimal schedule for jobs on a single machine when there are penalties for both late and early arrivals. We point out that if attention is paid to how certain parameters are measured, then a change of scale of measurement might lead to the anomalous situation where a schedule is optimal if these parameters are measured in one way, but not if they are measured in a different way that seems equally acceptable. We discuss conditions under which this anomaly is avoided.

01 Jul 1995
TL;DR: In this paper, a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints is proposed, which is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0-1 linear program.
Abstract: textWe design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0–1 linear program. Also, we show that upon termination of such an ascent direction algorithm we get a dual decomposition of the original problem, which can be exploited to develop approximative and enumerative approaches for it. Computational results exhibit that in our application the ascent direction leads to good Lagrangian lower and upper bounds.

01 Jul 1995
TL;DR: A fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints is designed.
Abstract: textWe design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0–1 linear program. Also, we show that upon termination of such an ascent direction algorithm we get a dual decomposition of the original problem, which can be exploited to develop approximative and enumerative approaches for it. Computational results exhibit that in our application the ascent direction leads to good Lagrangian lower and upper bounds.

Proceedings ArticleDOI
10 Oct 1995
TL;DR: A parallel algorithm is proposed, which allows one to solve the scheduling problem in polylogarithmic time using polynomial number of parallel processors.
Abstract: Considers a scheduling problem, where n jobs are to be processed on a single machine, precedence constraints among the jobs are given and preemption is allowed. For each job i, there is known a release date r/sub i/ representing the earliest possible starting time of the job and a processing time p/sub i/. Moreover, precedence constraints are given among the jobs. The precedence constraints are described by a digraph. The problem considered is polynomially solvable. In this paper, a parallel algorithm is proposed, which allows one to solve the problem in polylogarithmic time using polynomial number of parallel processors.

01 Jan 1995
TL;DR: This work considers the problem of common due-date to of simultaneously available jobs and sequencing them on a that a number of the jobs are tardy, and finds the optimal combination of the commonDue-date and job sequence that minimizes the total absolute lateness.
Abstract: We consider the problem of common due-date to of simultaneously available jobs and sequencing them on a that a number of the jobs are tardy. The optimal combination of the common due-date and job sequence that minimizes the total absolute lateness. A simple to achieve this. Effectively three independent procedures : one to the nnT,nn<>1 sequence; a second to the optimal due date and a third to formula for the associated minimum nan""'T"