Showing papers on "Job shop scheduling published in 1973"
TL;DR: An algorithm for solving resource-constrained network scheduling problems, a general class of problems that includes the classical job-shop-scheduling problem, that uses Lagrange multipliers to dualize the resource constraints, forming a Lagrangian problem.
Abstract: This paper presents an algorithm for solving resource-constrained network scheduling problems, a general class of problems that includes the classical job-shop-scheduling problem. It uses Lagrange multipliers to dualize the resource constraints, forming a Lagrangian problem in which the network constraints appear explicitly, while the resource constraints appear only in the Lagrangian function. Because the network constraints do not interact among jobs, the problem of minimizing the Lagrangian decomposes into a subproblem for each job. Algorithms are presented for solving these subproblems. Minimizing the Lagrangian with fixed multiplier values yields a lower bound on the cost of an optimal solution to the scheduling problem. The paper gives procedures for adjusting the multipliers iteratively to obtain strong bounds, and it develops a branch-and-bound algorithm that uses these bounds in the solution of the scheduling problem. Computational experience with this algorithm is discussed.
257 citations
TL;DR: In this article, an iterative procedure for determining near optimal frequencies of production for the products and the associated fundamental cycle time is presented, which 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.
202 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
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
TL;DR: This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available.
Abstract: The applicability of critical path scheduling is limited by the inability of the algorithm to cope with conflicting resource demands. This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available. These heuristic rules are evaluated on their ability to solve a large multiproject scheduling problem.
98 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
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TL;DR: This note treats the optimization problem of minimizing the completion time of jobs in a job-shop with no wait in process with techniques presented for restricted cases of the problem.
Abstract: This note treats the optimization problem of minimizing the completion time of jobs in a job-shop with no wait in process. Techniques are presented for restricted cases of the problem.
49 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: 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.
33 citations
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 survey of the major developments in the area of sequencing with a single resource type can be found in this paper, where the authors focus on performance measures involving makespan, flowtime, and tardiness criteria.
Abstract: SUMMARY This paper surveys the major developments in the area of sequencing with a single resource type. The survey considers both independent and dependent tasks in single and multiple resource problems in order to review existing work and to provide a context for future research. The study focuses on performance measures involving makespan, flowtime, and tardiness criteria and indicates the kinds of job information around which sequencing procedures have been successfully devised.
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: In this paper, the optimal load flow solutions are obtained such that both maximum economy and reliability of the system are achieved, and the optimal solution found here is guaranteed to be the unique optimal solution.
Abstract: The hydrothermal scheduling problem is discussed. Optimal load flow solutions are obtained such that both maximum economy and reliability of the system are achieved. The scheduling problem is solved by use of functional analysis, and in this case the minimum norm formulation is employed. It is emphasized that the optimal solution found here is guaranteed to be the unique optimal solution.
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.
TL;DR: This paper demonstrates how the model can be used experimentally to obtain model parameters which, in the judgment of management, achieve a desirable balance between objectives.
Abstract: This paper describes a methodology to treat multiple objectives in a mathematical programming problem. A linear programming model is developed for the short-term manpower scheduling problem in a post office so as to get a desirable balance between mail transit times and resource expenditures. The scheduling problem is of particular interest because of 1) the multiplicity of objectives, 2) the existence of several mail classes, each having different arrival patterns, routings, and dispatch times, and 3) the complexity of the different scheduling options available. The paper demonstrates how the model can be used experimentally to obtain model parameters which, in the judgment of management, achieve a desirable balance between objectives. Once the parameters are determined, the model prescribes how to vary the overtime usage, reassign workers to the various work stations, and adjust the priorities of the mail classes. The model has indirect use in studying the effects of changing work capacities, dispatch schedules, and mail arrival patterns.
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.
Book•
01 Jan 1973
01 Jan 1973
TL;DR: An out-of-kilter algorithm to deal with the machine sequencing problem in which both job precedence and machine non-interference constraints are involved is developed, inspired by the graph theoretical representation of the problem.
Abstract: The primary objective of this paper is to develop an out-of-kilter algorithm to deal with the machine sequencing problem in which both job precedence and machine non-interference constraints are involved. This approach is inspired by the graph theoretical representation of the problem. In addition to the out-of-kilter concept, the algorithm employs a waiting feature and pertinent criteria for the selection of resolutions. The basic concepts of the approach are presented and the entire algorithm is then summarized and condensed to five basic steps. A sample problem is presented and manually solved to illustrate the technique to job-shop problems. Computational experiences as well as comparative evaluations of other existing techniques are included. Finally, a diagnostic view of the scheduling problem is reported with reference to specific characteristics which comprise a major share of the difficulty surrounding the problem.
01 Jan 1973
TL;DR: Using a generalized random walk model, this article analyzed the problem of processing a fixed number of jobs on each of two machines, where the order of processing is unconstrained, and the processing times are exponential random variables.
Abstract: Using a generalized random walk model, we analyze the problem of processing a fixed number of jobs on each of two machines. The order of processing is unconstrained, and the processing times are exponential random variables. Rather simple formulas are obtained for the machine idle time distribution and the mean makespan.
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...
10 Aug 1973
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 Jan 1973
TL;DR: In this article, a branch-and-bound algorithm is proposed for searching an optimal schedule, in which the order of selection of resource orders is carefully controled, and the sequence of this selection constructs a search tree.
Abstract: NUMBER 2 For solving general scheduling problem (including job-shop prob lem), order-assignment model is proposed. In this model the schedul ing problem results in the selection of resource orders which are assigned for the purpose of resolving resource constraints, and the sequence of this selection constructs a search tree. The proposed algorithm for searching an optimal schedule is based on a branch-and bound method, in which the order of selection of resource orders is carefully controled.
01 Jan 1973
TL;DR: In this paper, a multi-facility, multi-product production-inventory scheduling problem with backordering is considered over a finite planning horizon, where product demands are assumed to be constant over a period but not necessarily the same in all periods.
Abstract: : A multi-facility, multi-product production-inventory scheduling problem with backordering is considered over a finite planning horizon. The horizon consists of discrete production periods during which at most one product can be assigned to each facility. Product demands are assumed to be constant over a period but not necessarily the same in all periods. The problem objective is to determine an assignment of products to facilities which meets all product demands on a first-come, first-serve basis and minimizes the sum of production, inventory and backordering charges over the horizon. In a straightforward manner this problem is formulated as a linear, mixed integer program which can be given a network flow interpretation. However, the problem can be solved as a minimal-cost flow problem only for a very special case. It is then shown that the general problem can be reformulated as an all integer program which can be solved using any of the very efficient algorithms for finding minimal-cost flows in single commodity networks. (Author)
01 Jan 1973
TL;DR: A measure of effectiveness is developed which allows both absolute and relative evaluation of different scheduling techniques and the conditions for profit maximization under a customer service constraint are presented.
Abstract: The problem of predicting the effectiveness of simulation results as applied to job shop production is discussed. A measure of effectiveness is developed which allows both absolute and relative evaluation of different scheduling techniques and the conditions for profit maximization under a customer service constraint are presented. The development is based upon a model of the shop process which assumes random scheduling behavior and which serves as the reference point for evaluating schedules.