Showing papers on "Flow shop scheduling published in 1977"
TL;DR: In this paper, the authors survey and extend the results on the complexity of machine scheduling problems and give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity.
Abstract: We survey and extend the results on the complexity of machine scheduling problems. After a brief review of the central concept of NP-completeness we give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity. The problems for which a polynomial-bounded algorithm is available are listed and NP-completeness is established for a large number of other machine scheduling problems. We finally discuss some questions that remain unanswered.
1,881 citations
TL;DR: Three previously unreported heuristics are included in the study, one of which turns out to be superior to the other ten heuristic tested and is presented in this paper.
Abstract: This paper presents computational experience with eleven flow shop sequencing heuristics. Included in the study are three previously unreported heuristics, one of which turns out to be superior to the other ten heuristics tested. The comparisons were made on a variety of problem sizes, up to fifty jobs and fifty operations.
512 citations
TL;DR: This paper surveys the deterministic scheduling of jobs in job-shop and multIprogramming environments, flow-shop schedules, and multiprocessor schedules in terms of optimal constructive algorithms and suboptimal heuristics.
Abstract: This paper surveys the deterministic scheduling of jobs m uniprocessor, multiprocessor, and job-shop environments. The survey begins with a brief introduction to the representation of task or job sets, followed by a discussion of classification categories. These categories include number of processors, task interruptlbility, job periodicity, deadlines, and number of resources. Results are given for single-processor schedules in job-shop and multIprogramming environments, flow-shop schedules, and multiprocessor schedules. They are stated in terms of optimal constructive algorithms and suboptimal heuristics. In most cases the latter are stated in terms of performance bounds related to optimal results. Annotations for most of the references are provided in the form of a table classifying the referenced studies m terms of various parameters.
215 citations
TL;DR: In this paper, a general bounding approach is developed which includes all previously presented lower bounds as special cases, and the strongest bound obtained in this way is combined with two enumeration schemes, the relative merits of which are discussed.
Abstract: The classical combinatorial optimization problem of minimizing maximum completion time in a general job-shop has been the subject of extensive research. In this paper we review and extend this work. A general bounding approach is developed which includes all previously presented lower bounds as special cases. The strongest bound obtainable in this way is combined with two enumeration schemes, the relative merits of which are discussed. The results of some computational experiments and a large bibliography are included as well.
187 citations
TL;DR: An algorithm is presented for solving a single-machine job shop scheduling problem in which penalties occur for jobs that either commence before their target start times or are completed after their due dates, generalized to cover the case in which the machine is available for only a limited time span.
Abstract: We consider a single-machine job shop scheduling problem in which penalties occur for jobs that either commence before their target start times or are completed after their due dates. The objective is to minimize the maximum penalty, subject to restrictive assumptions on the target start times, the due dates, and the penalty functions. We present an algorithm for solving this problem, along with a method for generating alternative optima. The algorithm is generalized to cover the case in which the machine is available for only a limited time span.
170 citations
TL;DR: In this article, the authors focus on methods for generating useful solution standards for large combinatorial problems, in particular, several procedures that provide point estimates of the value of the optimum solution are suggested and tested.
Abstract: This study focuses attention on methods for generating useful solution standards for large combinatorial problems. In particular, several procedures that provide point estimates of the value of the optimum solution are suggested and tested. These concepts are applied to a representative combinatorial problem: flow shop sequencing. Detailed computational results are presented.
74 citations
TL;DR: In this paper, a number of objective criteria for optimal maintenance scheduling of thermal generators are discussed, based on generation operating cost, reliability indices, deviations from a desired schedule and/or constraints violation penalties.
Abstract: A number of objective criteria for optimal maintenance scheduling of thermal generators is discussed. The criteria are based on generation operating cost, reliability indices, deviations from a desired schedule and/or constraints violation penalties. A comparison of the performance of all these criteria is presented by maintenance scheduling a realistic 30 thermal-unit system. Also, the relationships between the several realibility indices are dicussed.
49 citations
TL;DR: In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination.
Abstract: The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. A multi-pass heuristic program, which has proven effective in earlier research, is applied to the up-dated static scheduling problem at each review time. A procedure is proposed for implementing priorities on the shop floor between review times. The procedure is expressly designed to integrate the scheduling of newly arriving jobs to modify the schedule. In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination. Comparison with another procedure that gives the centralized schedule precedence over new arrivals indicates the importance of the implementation procedure when periodic centralized scheduling is used in a dynamic situation.
46 citations
TL;DR: This paper considers a model of a computing system with several independent but identical processors, each with a private memory of limited, and possibly different, storage capacity, and an optimal preemptive algorithm is given to find the shortest schedule for a task set with no precedence constraints.
Abstract: This paper considers a model of a computing system with several independent but identical processors, each with a private memory of limited, and possibly different, storage capacity. The tasks are assumed to have known resource demands expressed as processing times and memory requirements. Several scheduling strategies are evaluated by worst-case performance bounds and simulation results. Both preemptive and nonpreemptive scheduling are considered. An optimal preemptive algorithm is given to find the shortest schedule for a task set with no precedence constraints.
46 citations
TL;DR: In this article, the authors examined all known special cases of the mXn flow shop problem and provided solution procedures to three new special cases along with the optimality proofs, based on the critical path concept.
Abstract: The paper examines all known special cases of the mXn flow-shop problem. It provides solution procedures to three new special cases along with the optimality proofs. The theory of the new special cases is based on the critical path concept.
39 citations
TL;DR: In this paper, the authors identify classes of problems that are efficiently solvable because of special patterns of 0's in the 0-1 constraint matrices, and identify several interesting idle-time scheduling problems are shown to be solvable as finite and bounded series of network flow or matching problems.
Abstract: Integer linear programs with 0-1 constraint matrices arise frequently in scheduling and staffing models For many such problems it is natural to model processor availability by columns of the constraint matrix, where 1's indicate processor availability for production and 0's indicate idle periods Efficiently solvable problems have generally been identified in terms of special patterns of 1's within the matrix Exploiting the fact that idle time is the complement of production time, we identify classes of problems that are efficiently solvable because of special patterns of 0's In particular, several interesting idle-time scheduling problems are shown to be solvable as finite and bounded series of network flow or matching problems
TL;DR: An abstract model of a scheduling system which formalizes the notion of priority is presented and a criterion for the implementation efficiency of an algorithm is developed and results in the definition of time-invariant algorithms, which include most of the commonly implemented ones.
Abstract: This paper presents a scheme for classifying scheduling algorithms based on an abstract model of a scheduling system which formalizes the notion of priority. Various classes of scheduling algorithms are defined and related to existing algorithms. A criterion for the implementation efficiency of an algorithm is developed and results in the definition of time-invariant algorithms, which include most of the commonly implemented ones. For time-invariant algorithms, the dependence of processing rates on priorities is derived. The abstract model provides a framework for implementing flexible schedulers in real operating systems. The policy-driven scheduler of Bernstein and Sharp is discussed as an example of
TL;DR: A quantitative comparison between three types of capacity planning or shop loading techniques is presented and the results were obtained from simulation experiments.
Abstract: A quantitative comparison between three types of capacity planning or shop loading techniques is presented. The results were obtained from simulation experiments.
TL;DR: This paper summarizes known analytical results and solution procedures for the 3 × n flow-shop problem and states that not every permutation that is an AB and BC optimum simultaneously is an optimal solution of the entire problem.
Abstract: Consider the 3 × n flow-shop problem with machines A, B, and C. By AB and BC optimum we mean optimal solutions produced by Johnson's method for the two-machine problems AB and BC, respectively. Although not every permutation that is an AB and BC optimum simultaneously is an optimal solution of the entire problem, the set P of such permutations does contain an ABC optimum whenever it is not empty. We summarize known analytical results and solution procedures for the 3 × n flow-shop problem.
TL;DR: To obtain an approximate solution for a large-scale job-shop scheduling problem the decomposition method was investigated, which means that an original problem is decomposed into subproblems, which are solved separately, and then the solution of the originalproblem is composed from the subpro problems' solutions.
Abstract: SUMMARY To obtain an approximate solution for a large-scale job-shop scheduling problem the decomposition method was investigated. This means that an original problem is decomposed into subproblems, which are solved separately, and then the solution of the original problem is composed from the subproblems' solutions. Different methods to decompose the problem were tested by computational experiments and evaluated from the viewpoint of the goodness of schedule and computation time.
TL;DR: In this paper, it is shown how Lawler's procedure for the one-machine case can be combined with Johnson's rule to produce a branch-and-bound algorithm for the two-machine version.
Abstract: It is shown how Lawler's procedure for the one-machine case can be combined with Johnson's rule to produce a branch-and-bound algorithm for the two-machine version.
TL;DR: In this article, a flow shop sequencing problem with ordered processing time matrices is considered and a convex property for the makespan sequences of such problems is discussed, and an efficient optimizing algorithm is presented.
Abstract: A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.
TL;DR: A production control plan is described which may be used in a shop whose product line consists of numerous items which vary extensively in their demand pattern, and which is capable of stabilizing production by allowing inventories to fluctuate with moderate demand fluctuations.
Abstract: SUMMARY This paper describes a production control plan which may be -used in a shop whose product line consists of numerous items which vary extensively in their demand pattern. The plan is capable of: (a) stabilizing production by allowing inventories to fluctuate with moderate demand fluctuations; (b) minimizing inventories of finished goods while providing protection against serious Btockout; (c) detecting significant changes in demand patterns and revising production schedules accordingly; and (d) scheduling production economically. Employing several well-known concepts, such as the control limits principle used in quality control, the plan considers simultaneously forecasted demand, forecast error, inventory position and shop capacity to arrive at production decisions. For this purpose, control limits are applied to both demand and inventory, and production is stabilized with a simple production smoothing procedure. Simulation results, based on data taken from a medium size production shop, demonstra...
TL;DR: The relationship between the job splitting and no job splitting problem in these cases, is analogous to the situation when an optimum solution to a linear program has all the variables integer and hence is optimum to the corresponding integer program.
Abstract: This paper investigates various criteria under which simple scheduling rules generate optimum schedules for m machine scheduling problems. The problems are considered under a “job-splitting” assumption. Some of the rules which generate optimum schedules with job splitting for the multi-machine problems, do not split jobs for the single machine problems. The relationship between the job splitting and no job splitting problem in these cases, is analogous to the situation when an optimum solution to a linear program has all the variables integer and hence is optimum to the corresponding integer program.
TL;DR: The results of the article indicate that dynamic information on queue waiting time at individual machines and on the inventory status of individual items fails to improve the performance of the production system.
Abstract: A recent journal article [Berry, W. L., Rao, V. 1975. Critical ratio scheduling: an experimental analysis. Management Sci.22 2, October 192--201.] by Berry and Rao on job shop scheduling reported some counterintuitive results concerning the use of dynamic operating information in making priority scheduling decisions. The results of the article, based on a simulation experiment, indicate that dynamic information on queue waiting time at individual machines and on the inventory status of individual items fails to improve the performance of the production system. In fact, the reported performance of the dynamic rule was inferior to the static rules in five out of six cases. The purpose of this note is to call attention to the possibility that it is Berry and Rao's construction and/or use of this information, and not the value of the information itself, which is in question.
TL;DR: In this paper, the general design and the basic characteristics of the individual components of a construction scheduling mechanism for electric utilities, which is currently being implemented at the City Public Service of San Antonio, Texas, are described.
Abstract: The general design and the basic characteristics of the individual components of a construction scheduling mechanism for electric utilities, which is currently being implemented at the City Public Service of San Antonio, Texas, are described. The operational-planning portion of this mechanism is comprised of four conventional quantitative-analysis models with the tasks of developing pertinent cost parameters, optimally assigning construction projects to service centers, and routing service crews to project sites. Also described is HAMPS, a developed heuristic program which schedules the projects and performs resource allocation. An example is given to illustrate the operation of HAMPS on which the focus of the discussion is placed. The other portion of the construction scheduling mechanism is a strategic-planning package for estimating, at low cost, future resource requirements as an aid in the daily resource-allocation process.