Showing papers on "Job shop scheduling published in 1978"

On a Real-Time Scheduling Problem

Abstract: We study the problem of scheduling periodic-time-critical tasks on multiprocessor computing systems. A periodic-time-critical task consists of an infinite number of requests, each of which has a prescribed deadline. The scheduling problem is to specify an order in which the requests of a set of tasks are to be executed and the processor to be used, with the goal of meeting all the deadlines with a minimum number of processors. Since the problem of determining the minimum number of processors is difficult, we consider two heuristic algorithms. These are easy to implement and yield a number of processors that is reasonably close to the minimum number. We also analyze the worst-case behavior of these heuristics.

Complexity of Scheduling under Precedence Constraints

Abstract: Precedence constraints between jobs that have to be respected in every feasible schedule generally increase the computational complexity of a scheduling problem. Occasionally, their introduction may turn a problem that is solvable within polynomial time into an NP-complete one, for which a good algorithm is highly unlikely to exist. We illustrate the use of these concepts by extending some typical NP-completeness results and simplifying their correctness proofs for scheduling problems involving precedence constraints.

The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling

Abstract: The time-dependent traveling salesman problem may be stated as a scheduling problem in which n jobs have to be processed at minimum cost on a single machine. The set-up cost associated with each job depends not only on the job that precedes it, but also on its position time in the sequence. The optimization method described here combines finding shortest paths in an associated multipartite network with subgradient optimization and some branch-and-bound enumeration. Minimizing the tardiness costs in one-machine scheduling in which the cost is a non-decreasing function of the completion time of each job is then attacked by this method. A branch-and-bound algorithm is designed for this problem. It uses a related time-dependent traveling salesman problem to compute the required lower bounds. We give computational results for the weighted tardiness problem.

On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming

Abstract: It IS shown that certain problems of optimal preemptive scheduling of unrelated parallel processors can be formulated and solved as hnear programming problems As a by-product of the linear programming formulaUons of these problems, upper bounds are obtained on the number of preempuons required for optimal schedules In particular it is shown that no more than O(m 2) preemptions are necessary, m order to schedule n jobs on m unrelated processors so as to minimize makespan

An Efficient Integer Programming Algorithm with Network Cuts for Solving Resource-Constrained Scheduling Problems

Abstract: In this paper we describe an integer programming algorithm for allocating limited resources to competing activities jobs, tasks, etc. of a project such that the completion time of the project is minimal among all possible completion times. Typical of such problems is the minimization of the completion time of projects of the PERT/CPM variety where limits on resource availability force the postponement of selected activities during project performance. Also included in this class of problems for which our procedure is applicable is the assignment of jobs to machines such that the elapsed time for completing all jobs makespan is a minimum over all possible job-machine assignments. The procedure developed consists of a systematic evaluation enumeration of all possible job finish times for each task in the project. To limit the number of task assignments which have to be explicitly evaluated, an artifice called a network cut is developed which removes from consideration the evaluation of job finish times which cannot lead to a reduced project completion time. Results reported demonstrate that the procedure developed is a reliable optimization technique for projects consisting of up to 30--50 jobs and three different resource types. The procedure is particularly applicable in those instances in which computer primary storage is limited. Many of the mini-computers available today are capable of implementing our approach without extensive programming being required for writing to auxiliary storage, making the technique available to the project manager in those environments in which extensive computer resources for scheduling are not readily available.

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Minimal Resources for Fixed and Variable Job Schedules

Abstract: We treat the following problem: There are n jobs with given processing times and an interval for each job's starting time. Each job must be processed, without interruption, on any one of an unlimited set of identical machines. A machine may process any job, but no more than one job at any point in time. We want to find the starting time of each job such that the number of machines required to process all jobs is minimal. In addition, the assignment of jobs to each machine must be found. If every job has a fixed starting time the interval is a point, the problem is well-known as a special case of Dilworth's problem. We term it the fixed job schedule problem FSP. When the job starting times are variable, the problem is referred to as the variable job schedule problem VSP, for which no known exact solution procedure exists. We introduce the problems by reviewing previous solution methods to Dilworth's problem. We offer an approximate solution procedure for solving VSP based on the entropy principle of informational smoothing. We then formulate VSP as a pure integer programming problem and provide an exact algorithm. This algorithm examines a sequence of feasibility capacitated transportation problems with job splitting elimination side constraints. Our computational experience demonstrates the utility of the entropy approach.

A Computer-Assisted System for the Routing and Scheduling of Street Sweepers

Abstract: This paper discusses a computer-assisted method for routing and scheduling street sweepers in a municipality. We present the basic structure of this vehicle routing and scheduling problem, formulate the street-sweeper routing problem, and explain the algorithm. The computer implementation based on this algorithm is then described. Computational experience with the system in New York City and Washington, D.C., is presented and the obstacles to and successes with implementation are discussed.

An adjacent pairwise approach to the mean flow-time scheduling problem.

Abstract: In this paper, sufficient conditions to decide the precedence relation between neighboring two jobs are presented by means of an adjacent pairwise interchage method for minimizing mean flow·time in flow-shop scheduling. On the bases of the sufficient conditions, a computational algorithm is proposed for an optimal or near optimal solution. The mean flow-time by this algorithm puts 90% of the optimal value as an average of over one hundred problems. The algorithm can be executed even by manual calculations within the time proportional to nxm2 , where n and m are the number of jobs and machines respectively. Ever so muc h research [I 'V 9] has been devoted to f low-shop scheduling, yet relatively few results exist for performance measures other than maximal flow-time. For instance, Nabeshima [5] presented an algorithm based on the sufficient conditions to minimize maximal flow-time in flow-shop scheduling where no passing is allowed. The same approach, however, has not been applied to the mean flow-time problem, which is as significant a performance measure as the maximal flow-time. In this paper, the sufficient conditions are given to decide the preced­ ence relation between neighboring two jobs to minimize the mean flow-time in flow-shop scheduling problem. An algorithm based on the sufficient conditions is also presented for an optimal or near optimal solution. The computational experience shows that the approximation ratio between obtained solutions and the optimal ones indicates 90 % as an average of over one hundred problems. Moreover, it shows that the algorithm can be executed even by manual calculations within the time proportional to (the number of jobs) x (the number of machines) 2 .

Technical Note—Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties

Abstract: We consider a single-machine scheduling problem where penalties occur for jobs that either commence before their target start date or are completed after their due date. The objective is to minimize the maximum penalty subject to certain assumptions on the target start times, due dates, and penalty functions. A more efficient algorithm than the existing one is presented for this problem. The number of computations in the proposed algorithm is of the order of n log n, while in the existing algorithm it is of the order of n2.

An Investigation of Visual Interactive Simulation Methods Using the Job-Shop Scheduling Problem

Abstract: This paper describes the use of the job-shop scheduling problem in order to investigate the potential of visual interactive simulation methods. Batch simulation methods are compared with visual interactive simulation methods for the job-shop problem. The paper shows that improved solutions can be obtained by having a visual, dynamic representation of a job-shop problem.

An Industrial application of the traveling salesman's subtour problem

Abstract: Practical applications of the classical traveling salesman problem are rare because in most real world situations there are constraints upon the tour. To increase the range of useful applications, the classical structure must be modified to realistically deal with these constraints. In this application an industrial scheduling problem, called the traveling salesman's subtour problem, is formulated and defined. A time constraint restricts the salesman to a small subset of his total customers per planning period. Hence, the solution requires the simultaneous selection of the proper subset and the identification of the calling order. The problem is formulated to maximize expected sales subject to the time constraint. Lagrangean relaxation is used and by taking advantage of the underlying transportation structure of the problem the “gaps” are taken into account, thus providing a tight upper bound for the optimizing branch and bound routine in the algorithm.

A problem of aggregate scheduling An application of goal programming

Abstract: The paper introduces mi overall scheduling problem. One crucial aspect is identified; this is the production of an aggregate schedule which is to be fed into the detailed scheduling package currently employed. The problem is seen to be that of achieving a balance between a smooth work-load on the factory floor and matching production with promised delivery dates. A goal programming model for this coordination is developed and discussed. Numerical examples illustrating the approach are presented, and computational experience is discussed.

A mathematical programming system for preference and compatibility maximized menu planning and scheduling

Abstract: In this paper, the analytical representation of food preference is used in a separable non-linear program to yield the serving frequencies of menu items for a finite time horizon. The frequencies obtained in this way insure cost and nutritional control. Subsequently, the scheduling problem dealing with item assignments to meals and days is formulated as an integer program consisting of several transportation problems linked by weekly nutritional constraints. This problem is solved using a branch and bound algorithm which employs Lagrangian relaxation to obtain bounds and to decide on branching strategy.

Technical Note-Three-Stage Flow-Shops with Recessive Second Stage

Abstract: Several papers have described special structural properties for which the minimum makespan flow-shop problem can be efficiently solved. We describe a new special case of the 3 × n problem with small second-stage processing times relative to the first and third stages for which Johnson's algorithm gives an optimal schedule.

Technical Note-Improved Dominance Conditions for the Three-Machine Flowshop Scheduling Problem

Abstract: Existing combinatorial or elimination approaches for solving the three-machine flowshop scheduling problem are not applicable for the situation where the jobs have their least processing time on the second machine. We present improved dominance conditions that extend the applicability of combinatorial approaches to this situation. To derive these conditions we use Johnson's two-machine results as well as the nature of unscheduled jobs.

Transportation network analysis and decomposition methods

Abstract: The report outlines research in transportation network analysis using decomposition techniques as a basis for problem solutions. Two transportation network problems were considered in detail: a freight network flow problem and a scheduling problem for a transportation system with multiple vehicle fleets. Several different approaches for decomposing the overall problems into smaller subproblems were examined. A third problem, dealing with the routing of vehicles over a series of demand points, was also examined using a different solution approach. The report presents detailed mathematical formulations of the different problems, discusses the solution approaches examined and presents computational results of the research.

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.

An Algorithm for the Space-Shuttle Scheduling Problem

Abstract: The mission scheduling problem of the NASA space-shuttle program requires a selection of mission launch times that minimize the number of missions flown late and that satisfy early start time and resource constraints. We present an algorithm for this problem that is easy to program, requires little computation and, under certain restrictive assumptions, provides an optimal solution. Computational experience with a test case is discussed.

Note---On “Production Runs for Multiple Products: The Two-Product Heuristic”

Abstract: The recent paper [Saipe, A. L. 1977. Production runs for multiple products: the two-product heuristic. Management Sci.23 12, August 1321--1327.] by Saipe considers the single-machine multi-product lot scheduling problem, this problem is concened with the determination of run sizes for a set of products which are produced on the same machine. In the paper [Saipe, A. L. 1977. Production runs for multiple products: the two-product heuristic. Management Sci.23 12, August 1321--1327.], a heuristic solution procedure, based on a solution procedure for the two-product lot scheduling problem, is proposed for the multi-product problem. The intent of this note is to raise three issues concerning the proposed heuristic procedure: a the optimality of the procedure for the two-product problem, b the performance of the procedure at full capacity for more than two products, and c the effectiveness of the procedure relative to alternative solution procedures.

An interactive procedure for minimizing makespan on parallel processors

Abstract: Consider scheduling n independent, single operation jobs, all available at time zero, on m identical processors. Further, assume that each job must be processed by exactly one of these processors, and it is desired to minimize makespan. This paper reports a computationally efficient procedure for treating this problem, which utilizes human ingenuity to improve on a traditional solution procedure. Computational experience with the procedure indicates that good solutions to large problems are easily obtained; in fact out of 240 test problems, the optimal solution was found in every case. The entire procedure is simple enough for a shop foreman to be able to solve large problems by hand.

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.

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.

A Target Selection Model.

Abstract: : A target selection model is discussed in which the decision maker must select from a set of targets the subset having maximum total value. The targets are presented in a fixed order known in advance to the decision maker, but the choices are related so that not all selections are possible. Optimal decision of a target set among several decision makers is considered and formulated as a dynamic programming problem. The problem with two decision makers is used to illustrate a formulation which leads to a more efficient computational scheme. An example is included. (Author)