Showing papers on "Flow shop scheduling published in 1978"

A General Bounding Scheme for the Permutation Flow-Shop Problem

Abstract: Branch-and-bound methods are commonly used to find a permutation schedule that minimizes maximum completion time in an m-machine flow-shop. In this paper we describe a classification scheme for lower bounds that generates most previously known bounds and leads to a number of promising new ones as well. After a discussion of dominance relations within this scheme and of the implementation of each bound, we report on computational experience that indicates the superiority of one of the new bounds.

Performance Guarantees for Scheduling Algorithms

Abstract: One approach to coping with the apparent difficulty of many schedule-optimization problems, such as occur in machine shops and computer processing, is to devise efficient algorithms that find schedules guaranteed to be "near-optimal." This paper presents an introduction to this approach by describing its application to a well-known multiprocessor scheduling model and illustrating the variety of algorithms and results that are possible. The paper concludes with a brief survey of what has been accomplished to date in the area of scheduling using this approach.

Four simple heuristics for scheduling a flow-shop

Abstract: This paper concerns the minimization of a complex cost function in a flow-shop. Four heuristic methods for obtaining a good solution to the sum of weighted tardiness and weighted flow-time problem are proposed. Computational results are provided and a, recommendation is made with respect to other objective functions.

Group production scheduling for minimum total tardiness Part(I)

Abstract: This paper considers the problem of group scheduling on a single stage to minimize total tardiness. It is assumed that jobs are classified into several groups on the basis of group technology. Optimal decision as to scheduling sequences will be made as to product group and specific job. This paper proves basic theorems that establish the relative order in which pairs of groups are processed in an optimal schedule. In general, scheduling problems of moderate size may be at least partially ordered so that very few schedules remain to be searched. Two practical algorithms for determining the optimal group schedule and the near optimal group schedule are proposed. Numerical examples are presented in detail.

Combinatorial Problems: Reductibility and Approximation

Abstract: Recent research in the theory of algorithms has determined that many classical operations research problems are computationally related; i.e., an efficient algorithm for one implies the existence of efficient algorithms for everyone or a proof that one is inherently difficult implies they are all so. This paper presents a tutorial of this concept. In contrast to other surveys it does so by selecting a few problems knapsack, traveling salesperson, multiprocessor scheduling, and flow shop and carefully shows how they are related. References to most other problems of interest to operations researchers are given. The second part of this paper is a survey on the relatively recent progress in the study of approximation algorithms. These algorithms hold great promise for they work fast and in many cases are guaranteed to work well. Again the techniques for devising and analyzing these algorithms are explained through the continued use of these examples.

Permutation flow‐shop theory revisited

Abstract: The paper provides a new theoretical framework for generating dominance conditions and lower bounds and for solving special cases. All existing and new results have been derived in a routine and simple manner.

A Combinatorial Approach to Dynamic Scheduling Problems

Abstract: We introduce a combinatorial approach for studying multiple-processor scheduling problems that involve the preemptive scheduling of independent jobs. Unlike most combinatorial models used for studying scheduling problems, ours assumes that jobs arrive over time but that scheduling decisions must be made without knowledge of what jobs will arrive in the future. We seek dynamic algorithms that make scheduling decisions based on changing information. An algorithm is considered to be "optimal" only if it consistently produces schedules no worse than those produced by any omniscient algorithm that has exact knowledge of attributes of all jobs in advance. Measures of performance examined include the maxima and means of completion time, flow time, and lateness. "Optimal" algorithms are established in a few cases, while it is determined in other cases that such "optimal" algorithms require more information than the model provides.

The Presentation of Information to the Job-Shop Scheduler

Abstract: Three graphic methods of presenting scheduling information were compared with each other and with a conventional, numerical presentation. The graphic methods were based on the Gantt chart, and all three proved more effective than the numerical presentation in helping the subjects produce efficient schedules. One method in particular which used a machines-by-time organization and identified machines by color code proved superior to the others. This is explained in terms of the perceptual nature of problem solution using these methods. It is suggested that this organization of information be adopted when the primary criterion for schedule evaluation is machine utilization and there are limitations on the display space and color-coding available.

Overtime usage in a job shop environment

Abstract: Problems are encountered in a job shop which has a fixed capacity if the total work content of the jobs passing through the shop increases sufficiently. Even the use of effective priority dispatching rules and/or expediting does not adequately shorten the queues which develop if the total work content continually exceeds shop capacity. To avoid losing job orders because the orders are unduly delayed, the job shop might resort to overtime usage. This study examines the efficient and economic use of overtime to relieve the backlog problem and uses overtime as the basic criterion for evaluation of overtime usage. The study employs GPSS V programming language to simulate a hypothetical job shop. The shop is loaded to various proportions of its normal capacity and various levels of overtime are tested. Findings show that overtime should not be assigned indiscriminately but rather should be based on a shop's unique conditions of overtime cost, the priority rule being employed, and the level of capacity utilization. Marginal benefit-cost ratio curves are developed to determine whether overtime usage is economically reasonable. These curves may also be used to determine the maximum or limiting amount of overtime to use under specific shop conditions.

Network Models for Production Scheduling Problems with Convex Cost and Batch Processing

Abstract: This paper considers a class of production scheduling problems which can be modeled as network flow problems. The problems are addressed under the assumption that production occurs in batches. We also require that the cost function be convex and separable. The model applies for a number of well known production scheduling problems and will handle multiple products and multiple facilities.

Solving large scheduling problems by minimizing conflict

Abstract: The scheduling of tasks (such as jobs through a com puter, different pulses through a radar system, or machining efforts through a production line) is a problem that is encountered quite frequently in practice. Traditionally, analysts have endeavored to develop schedules that minimize make-span (the time that elapses between the start of the first task in a sequence until the finish of the last task in a sequence). However, there are often many other appropriate measures of scheduling effectiveness. In this paper we address the problem of maximizing the number of jobs completed in an environment where each job is in competition with other jobs for certain scarce resources. Further, we shall assume that the number of jobs and possible start times is so large as to eliminate the possibility of the use of any exact technqiue.

Job scheduling in multiprogrammed computer systems

Abstract: The job-scheduling function in a multiprogramming computer system plays a key role in the achievement of the performance goals for the system. It is possible and convenient to partition this scheduling function into a priority assignment function and resource assignment function. Implementation of a general purpose resource assignment module permits a large family of scheduling strategies to be implemented via different priority calculation schemes. The implications of this partitioning of the scheduling function are studied by use of a simulation model. A system embodying this approach to job scheduling is discussed as an application of the approach to other types of systems.

Production scheduling decision rules in changing and non-linear environments

Abstract: Holt at al. (1960) modollod the production scheduling problem with quadratic costs and derived an optimal set of scheduling rules. Our experiment found those rules may not be effective if costs are non-quadratic. This may explain the relative lack of use of these rules in industry.

An investigation of multiproduct, multimachine production scheduling and inventory control of a flow-shop system

Abstract: Unlike most of the previous studies of the multiproduct, multimachine systems, hero an attempt is made to consider the man-machine overtime and idleness costs together with the usual inventory-related costs (the set-up costs, carrying costs, and back-logging costs). The major assumptions of the model include: (a) demand for each product is captive and constant; (b) single or multiple facility work centres may be employed: (c) the total manufacturing operations of any single product must be completed before another product can be started; (d) all the manufacturing facilities are set up simultaneously for each of the products and its production can be started only after all the machines are ready. The annual total variable cost function is found to be very complex. Therefore, a recursive algorithm is required to solve this function for the values of optimal produetion-cycle-thnes of the individual products, Tj *,s . As the facilities are assumed to produce only one product at a time, these cycle time values...

Seqential approach in job shop scheduling

Abstract: This study investigats a new approach‐the sequential approach‐ in job shop scheduling. The objective is to minimize the total of lateness cost and set‐up cost in job shops. Whenever a scheduling decision has to be made as to which job should receive the next processing, this approach considers each cost sequentially. One of the two costs is considered first, and every time all waiting jobs must be examined in terms of this cost, and only those jobs qualified would the second cost apply to and from which a job would be selected for processing. This investigation was carried out by using GASP IV simulation under a variety of job shop situations. The effectiveness of this approach and job selection mechanism constitute the main theme of this study.

On scheduling multi-processor systems with algebraic objectives

Abstract: One of the well-studied models of combinatorial optimization is the scheduling problem dealing with a finite set of tasks, which have to be executed on a fixed number of machines so that a given objective is minimized. Each task requires a set of characteristic data like operating time, due date, penalty cost and technological requirements. An algebraic approach to the objective leads to a general problem which includes all classical cases of sum and bottleneck objectives known in literature. By solving an algebraic transportation problem a lower bound for the objective value can be determined. To obtain an optimal solution we employ a branch and bound procedure. Furthermore we consider the general job shop scheduling problem with algebraic objective function.

An adaptive branching rule for the permutation flow-shop problem : (preprint)

Abstract: Abstract A branch-and-bound algorithm is presented for the permutation flow-shop problem in which the objective is to minimise the maximum completion time. A branching procedure is used in which jobs both at the beginning and at the end of the schedule have been fixed. Dominance rules are included in the algorithm. Also, during the initial stages of the algorithm, upper bounds are computed at certain nodes of the search tree. Computational results indicate that the proposed algorithm is superior to previously published algorithms.

Scheduling method synchronizing two lines of activities and minimizing waiting and pass-time

Abstract: In this paper, methods are suggested for solving a common class of job-shop scheduling problem. The type of job-shops considered consists of two parallel production lines ended by a group work station. The methods use a domination principle at first, of one line over the other, defining a master—slave hierarchy in the workshops. The solutions obtained from the optimal scheduling of the master line form the constraint domain of the slave line, the optimal schedules of which are worked out in turn. Parametrization of economical functions permits the dynamic modification of the optimization criteria of the slave line.

On A Restrictive Scheduling Scheme

Abstract: A restrictive scheduling scheme is defined and investigated, and some of its properties are developed and compared to those of a more conventional scheduling scheme, in an attempt to show its potential usefulness in the scheduling of multiprocessor systems. The major conclusion is that most of the schedules obtained using the restrictive scheduling scheme are comparable in length to those obtained using a more conventional scheduling scheme.

An Efficient Job scheduling Algorftbm for Mixed T unwound and Deadlhe Applications

Abstract: Computer job scheduling is often performed with little understanding of the formal properties of the jobs being scheduled. One reason for this is that optimal solutions for job scheduling on computers are difficult to obtain if the job stream has mixed objectives, i.e., it consists of some jobs whose turnaround time has to be minimized and others whose deadlines must be met. A practical algorithm for scheduling mixed job streams on monoprogrammed computers, with potential application to a multiprogramming environment is presented. The algorithm takes into account variable cost rates for each job. Experimental results illustrate the efficiency of the algorithm in terms of both its proximity to optimal solutions and its low computational complexity.

Resource constrained scheduling methods

Abstract: This chapter reviews resource constrained scheduling methods. The problem of scheduling activities under limited resources and precedence constraints is a relatively common one that has received considerable attention in the literature. This problem belongs to a class of problems for which currently optimal solution can be found only for unrealistically small problems of marginal practical value. For larger problems, a number of heuristic algorithms are available. There is considerable conflicting evidence regarding the relative merit of the heuristics used in these algorithms, and there are few, if any, guidelines available regarding the choice of a heuristic algorithm. The chapter presents a general flowchart of a scheduling algorithm utilizing dispatching rules or urgency factors. The basic premise of this algorithm is the requirement that all activities are to start as early as possible. When several activities are competing for a limited amount of resources, activities are selected one by one to start in accordance with some priority or urgency scheme. There are two approaches to the calculation of these urgency factors: (1) they may either be calculated prior to the scheduling process—static scheduling—or (2) they may be recalculated throughout the scheduling process as delays of activities cause a change in actual slack and finish times—dynamic scheduling.

Implementation of a computer job scheduling algorithm: A case history

Abstract: Multiprogramming systems require that a fair, equitable algorithm be used for the scheduling of jobs. This paper discusses some of the problems associated with this and proposes an automatic job scheduling algorithm. The major parts of the algorithm have been implemented and have been in use for over one year. The user interface is simplified and the operational complexities are minimized. The parameters used for the algorithm are the estimates of the central processor time and the memory required by the job. All types of jobs including those requiring operator attention during execution are covered under the scheme. Operational data and the reactions from the users indicate that the results have been as expected.