Showing papers on "Flow shop scheduling published in 1973"
Posted Content•
TL;DR: The paper describes the development of a hierarchical planning and scheduling system for a multiple plant, multiple product, seasonal demand situation where optimal decisions at an aggregate level provide constraints for detailed decision making.
Abstract: : The paper describes the development of a hierarchical planning and scheduling system for a multiple plant, multiple product, seasonal demand situation. In this hierarchical structure, optimal decisions at an aggregate level (planning) provide constraints for detailed decision making (scheduling). (Modified author abstract)
578 citations
01 Jan 1973
TL;DR: Types of industrial scheduling problems were investigated by personal visits to plants and by questionnaires mailed to scheduling departments and results indicate that most of the present procedures in theoretical research cannot handle average industrial problems.
Abstract: Types of industrial scheduling problems were investigated by personal visits to plants and by questionnaires mailed to scheduling departments. Information on problem sizes, job flow, optimization criteria and job similarity was obtained. Results indicate that most of the present procedures in theoretical research cannot handle average industrial problems. Also most commonly used objective criteria differ from industrial goals. There is a definite need for better communication between sequencing researchers and scheduling practioners.
155 citations
TL;DR: In this paper, the relative advantage of short processing time and minimum slack dispatching rules for job shop dispatching has been evaluated in terms of the amount of work-in-process inventory and the tightness of the promises.
Abstract: This paper attempts to provide an economic framework in which various job shop dispatching rules can be evaluated. It shows the relative advantage of shortest processing time rules in gaining increased utilization of the shop facilities and the relative advantage of minimum slack rules in meeting promise commitments. The paper graphs each of four kinds of costs costs of long promises, costs of missed promises, costs of idle resources, and costs of carrying inventory against two independent variables, the amount of work-in-process inventory and the tightness of the promises. It demonstrates the kind of cost structure which causes a minimum slack rule to be superior to a shortest processing time rule.
112 citations
01 Jan 1973
TL;DR: This paper considers the most general type of “network” flow shop in which jobs pass through several stages, each of which is composed on one or more identical processors.
Abstract: This paper considers the most general type of “network” flow shop in which jobs pass through several stages, each of which is composed on one or more identical processors. Jobs are processed on any one of the processors at each stage in ascending order of stage numbers and the objective is minimization of makespan. The class of shops considered is characterized by prohibited in-process inventory and slightly restricted job ordering per processor. Originally designed for the scheduling of nylon polymerization, the algorithms developed in the paper have numerous applications, especially in the chemical processes and petrochemical production areas.
109 citations
01 Jan 1973
TL;DR: It is shown that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases, tantamount to showing that the scheduling problems mentioned are intractable.
Abstract: We show that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases.(1) All jobs require one time unit.(2) All jobs require one or two time units, and there are only two processors.As a consequence, the general preemptive scheduling problem is also polynomial complete.These results are tantamount to showing that the scheduling problems mentioned are intractable.
103 citations
TL;DR: This paper proves an optimal ordering rule, previously conjectured by Talwar, which is derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs.
Abstract: This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.
66 citations
Book•
01 Jan 1973
TL;DR: This chapter discusses Scheduling Problems by Applying Cost Operators to Assignment Models and some Extensions of Akers-Friedman Production Scheduling Problem.
Abstract: I Survey Papers- "A Critique of Project Planning with Constrained Resources"- "Sequencing Research and the Industrial Scheduling Problem"- II Applications- "The Engine Scheduling Problem in a Railway Network" - Abstract- "Detail Scheduling Models and Systems"- "A Naval Air Rework Facility Scheduling Problem"- "Some Scheduling Applications in Chemical Industry"- "A Solution to a Special Class of Flow Shop Scheduling Problem"- "Two Recent Developments in Scheduling Applications"- "Toward a Man-Machine Interactive System for Project Scheduling"- III Theory- "Efficient Solution Procedures for Certain Scheduling and Sequencing Problems"- "On the Set Representation and the Set Covering Problem"- Discussion of Murty's paper- "Selected Comments Concerning Optimization Techniques for Functions of Permutations"- Discussion of Rau's paper- IV Models of Processes- "An Out-of-Kilter Approach for Machine Sequencing Problems"- "Trading Rules for a Decentralized Exchange Economy"- "Scheduling with Early Start and Due Date Constraints" - Abstract- "The Scheduling of a Multi-Product Facility"- "The Two-Machine Job Shop with Exponential Processing Times"- "Optimal Solutions of Scheduling Problems Using Lagrange Multipliers, Part II"- Discussion of Fisher's paper- "On Project Cost-Duration Analysis Problem with Quadratic and Convex Cost Functions"- "A Problem in Single Facility Scheduling with Sequence Independent Change-Over Costs"- "Random Patrol Scheduling Under Operational Constraints"- "Interaction Between Aggregate and Detailed Scheduling in a Job Shop" - Abstract- "An Extension of Moore's Due Date Algorithm"- "Solving Scheduling Problems by Applying Cost Operators to Assignment Models"- "Some Extensions of Akers-Friedman Production Scheduling Problem"- "On a Feasibility Approach to Optimal Schedules"
64 citations
TL;DR: This paper shows that the elimination method of Szwarc removes at least as many solutions as any other method, and is therefore optimal, and how to construct a general counterexample to any procedure that removes more sequences than this optimal method.
Abstract: For solving the flow-shop scheduling problem, this paper examines elimination techniques that reduce the set of solutions to a subset that must contain the optimal solution being sought. The paper shows 1 that the elimination method of Szwarc [Naval Res. Log. Quart. 18, 295-305 1971] removes at least as many solutions as any other method, and is therefore optimal, and 2 how to construct a general counterexample to any procedure that removes more sequences than this optimal method.
54 citations
TL;DR: The n job, one-machine scheduling problem is considered where set-up and processing times are random and the objective is to minimize the number of late jobs.
Abstract: The n job, one-machine scheduling problem is considered where set-up and processing times are random and the objective is to minimize the number of late jobs. In the deterministic case, Moore's algorithm is known to produce an optimal schedule. A chance-constrained formulation of the nondeterministic problem is derived in which a job is processed if the probability that it will be completed prior to its due date is greater than a specified level. A deterministic equivalent problem is achieved to which application of a modification of Moore's algorithm is proven to produce an optimal schedule.
45 citations
TL;DR: Simulation results showed that the shortcomings of simple dispatching rules are remedied by using the SPT-T scheduling rule.
Abstract: This paper discusses the development of a scheduling rule and summarizes the results of the evaluation of its performance with respect to some tardiness related criteria. Studies done on job shop scheduling indicated that the simple dispatching rules which mostly perform well with respect to a criterion of performance may have undesirable results with respect to other criteria. In this paper, a scheduling rule with truncation process called SPT-T is introduced and studied. Simulation results showed that the shortcomings of simple dispatching rules are remedied by using the SPT-T scheduling rule.
39 citations
TL;DR: The basic structure of the scheduling procedure, the machine coding of a specific version of the procedure, and computational experience with a set of test problems ranging in size up to fourteen jobs and seven machines are described.
Abstract: The classical formulation of the static job shop scheduling problem with job due dates implies that the question of interest to the manager is: What is the best that can be done to meet due dates with fixed resources? Here, two alternative formulations of the problem are proposed; one because of its practical appeal, the other because of its methodological appeal. The latter is used to develop a multi-pass heuristic scheduling procedure aimed at providing a practical tool for attacking any of the three formulations of the problem. This paper describes the basic structure of the scheduling procedure, the machine coding of a specific version of the procedure, and computational experience with a set of test problems ranging in size up to fourteen jobs and seven machines.
TL;DR: A branch-and-bound algorithm, using a powerful bounding procedure, has been developed for obtaining an optimal solution and it is shown that it is practical in problems of moderate size.
Abstract: SUMMARY The shop scheduling problem with which this paper is concerned is to determine a sequence of J jobs on each of the M machines such that the schedule time is minimized. The machine ordering of each job is pre-specified but independent of those of other jobs. A branch-and-bound algorithm, using a powerful bounding procedure, has been developed for obtaining an optimal solution. An illustrative example is solved. Computational experience with this algorithm shows that it is practical in problems of moderate size. However, for larger problems, the algorithm can be applied without backtracking in which an optimal or near-optimal solution may be obtained. The quality of solutions obtained by the branch-and-bound algorithm without backtracking has been investigated. The optimal-producing algorithm is compared favourably with other published methods The number of nodes explored and the computational time are considered as bases for evaluation.
TL;DR: A composite cost-oriented priority scheduling rule is compared to three other well-known rules, that are basically time-oriented, that suggest that SPT and cost rides are preferred in most of the criteria.
Abstract: SUMMARY In this paper, a composite cost-oriented priority scheduling rule is compared to three other well-known rules, that are basically time-oriented. The criteria used for comparison include : total cost per job, number of late jobs, machine utilization, in-process inventory and the number of late jobs in-process. Repeated measures analysis of variance is used and followed by mean comparisons. Results suggest that SPT and cost rides are preferred in most of the criteria.
TL;DR: The proposed algorithm is compared to the existing decomposition approach and is found to be superior to Ashour's decomposition algorithm, both in increased solution quality and decreased computational time required to solve the problem.
Abstract: SUMMARY This paper investigates the classical n-job, M-machine flow-shop scheduling problem under the assumption that jobs are processed on all machines in the same order. Baaed on the heuristic job-pairing technique and the decomposition strategy, a heuristic decomposition algorithm is developed which will generate at least a near-optimal schedule for the flow-shop scheduling problem. The proposed algorithm is compared to the existing decomposition approach and is found to be superior to Ashour's decomposition algorithm, both in increased solution quality and decreased computational time required to solve the problem.
01 Jan 1973
TL;DR: The talk is an abstract of a Ph.D. dissertation submitted to the Alfred P. Sloan School of Management on May 4, 1972 in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Abstract: The talk is an abstract of a Ph.D. dissertation submitted to the Alfred P. Sloan School of Management on May 4, 1972 in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
01 Jan 1973
TL;DR: An iterative procedure for directly determining near optimal frequencies of production for the products and the associated fundamental cycle time which, in many cases, can be used directly for constructing production schedules.
Abstract: Most of the procedures that have been developed to find solutions to the single-machine, multi-product lot scheduling problem depend on judgment to define the desirable frequencies of production for the products. In this paper we describe an iterative procedure for directly determining near optimal frequencies of production for the products and the associated fundamental cycle time which, in many cases, can be used directly for constructing production schedules. In cases where feasible schedules cannot be constructed using the values from the iterative procedure, the procedure provides a basis for changing the production frequencies and the fundamental cycle time to obtain feasible schedules.
01 Jan 1973
TL;DR: The paper gives a reduction of the scheduling problem to a transportation problem and thereby extend the class of known non enumerative scheduling algorithms to include identical processors and gives a scheduling algorithm having desirable properties with respect to both maximum finishing- time and mean finishing-time.
Abstract: In this paper we study the problem of scheduling a set of independent tasks on m ≥ 1 processors to minimize the mean finishing-time (mean time in system). The importance of the mean finishing-time criterion is that its minimization tends to reduce the mean number of unfinished tasks in the system. In the paper we give a reduction of our scheduling problem to a transportation problem and thereby extend the class of known non enumerative scheduling algorithms [1]. Next we show that the inclusion of weights (weighted mean finishing-time) complicates the problem and speculate that there may be no non enumerative algorithm for this case. For the special case of identical processors we study the maximum finishing-time properties of schedules which are optimal with respect to mean finishing-time. Finally we give a scheduling algorithm having desirable properties with respect to both maximum finishing-time and mean finishing-time.
01 May 1973
TL;DR: An interactive model which builds on a multi-pass heuristic scheduling procedure for the due-date problem is presented, which allows a human scheduler to interact to improve schedules and modify problem descriptions in an attempt to arrive at a satisfactory solution.
Abstract: : Interactive scheduling procedures for job shop problems are appealing because current scheduling techniques cannot deal with the problem in its full complexity. The report presents an interactive model which builds on a multi-pass heuristic scheduling procedure for the due-date problem. The program allows a human scheduler to interact to improve schedules and modify problem descriptions in an attempt to arrive at a satisfactory solution. A discussion of the model's capabilities and detailed operating procedures are contained in the report. (Author)
TL;DR: A branch-and-bound algorithm is proposed for implicitly producing an optimal schedule such that the schedule time is minimized, utilizing a set of heuristic rules, in addition to a powerful bounding procedure, to guide the search.
Abstract: This paper considers the shop scheduling problem which involves both job precedence and machine interference constraints. Based on the graph-theoretical representation of the problem, a branch-and-bound algorithm is proposed for implicitly producing an optimal schedule such that the schedule time is minimized. The algorithm utilizes a set of heuristic rules, in addition to a powerful bounding procedure, to guide the search. An upper bound is also employed to recognize an optimal solution in earlier stages. The procedure is illustrated by a sample problem and its rapid convergence is demonstrated by a set of published problems. The proposed algorithm is compared favorably with existing procedures.
Journal Article•
Book•
01 Jan 1973
TL;DR: This article describes a heuristic algorithm which will yield an optimal or near optimal minimal makespan solution to a specific type of sequencing/scheduling problem defined as the dependent sequencing problem which includes the pure job-shop and flow-shop sequencing problems.
Abstract: This article describes a heuristic algorithm which will yield an optimal or near optimal minimal makespan solution to a specific type of sequencing/scheduling problem defined as the dependent sequencing problem which includes the pure job-shop and flow-shop sequencing problems. The name ‘ dependent sequencing ’ was selected for this model since it reflects the possibility of interdependence between activities of the technological processing order graph (GTPO) not present in ‘ pure ’ job -shop or f low-shop sequencing models. There are some approaches to this class of problem which provide optimal solutions, but their time to solutions and/or theoretical approaches make them difficult to understand and apply. Recent articles in the literature have recommended that research in the sequencing/ scheduling area be directed toward developing practical approaches which can be easily understood and applied. The dependent shop algorithm utilizes extensions of PERT/CPM techniques which are widely known and therefor...
01 Jan 1973
TL;DR: In this paper, the authors present the mathematical version of a scheduling problem that is faced by any railway company that employs several engine types to provide power for its trains and present a scheduling method that assigns available engines to trains on a short time horizon (e.g. a week ahead).
Abstract: In this paper we present the mathematical version of a scheduling problem that is faced by any railway company that employs several engine types to provide power for its trains. Usually, a railway employs engines of several types that differ in their tractive effort capability and horsepower rating. There are two distinct but related aims in reducing the engine costs to the railway. One is to select the mix of engine types that gives the lowest capital investment and operating cost for the trains operated by the railway. The other is to provide a scheduling method that assigns available engines to trains on a short time horizon (e.g. a week ahead). We describe the practical context of the former problem below.
TL;DR: In this paper, the problem of two-machine job shop sequencing is studied, where some jobs are processed first on machine 1 and then on machine 2, while the remaining jobs were processed in the reverse order.
Abstract: The problem studied is that of two-machine job shop sequencing where some jobs are processed first on machine 1 and then on machine 2, while the remaining jobs are processed in the reverse order. The objective is to determine an ordered sequence which minimizes the total processing time, subject to some specified lag time constraints. A rule is given for determining two different sequences for the two machines which represent an optimal solution.
TL;DR: In this paper, the framework of statistical decision theory is applied to selecting schedules by a heuristic procedure for the general J × M job shop problem, and sequential Bayesian strategies and explicit forms of stopping rules are obtained for the search procedure, together with bounds on required sample size.
Abstract: Following a brief account of its principal components, the framework of statistical decision theory is shown to be applicable to selecting schedules by a heuristic procedure for the general J × M job shop problem. Sequential Bayesian strategies and explicit forms of stopping rules are obtained for the search procedure, together with bounds on required sample size.
01 Feb 1973
TL;DR: The production scheduling problem is formulated as an optimal control problem and amended to ak-stage discrete control problem as well as Extensions to multi-products, production scheduling on one machine and uncertain demand are then considered.
Abstract: A production scheduling program with significant changeover costs is considered. This entails the determination of a step production function where the production levels and decision time are unknown. The production scheduling problem is formulated as an optimal control problem and amended to ak-stage discrete control problem. Extensions to multi-products, production scheduling on one machine and uncertain demand are then considered.