Showing papers on "Job shop scheduling published in 1981"

A Review of Production Scheduling

Abstract: Production scheduling can be defined as the allocation of available production resources over time to best satisfy some set of criteria. Typically, the scheduling problem involves a set of tasks to be performed, and the criteria may involve both tradeoffs between early and late completion of a task, and between holding inventory for the task and frequent production changeovers. The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling. This paper will highlight problem areas for which there is both a significant discrepancy between practice and theory, and for which the practice corresponds closely to the theory.

Loading and control policies for a flexible manufacturing system

Abstract: An experimental investigation of operating strategies for a computer-controlled flexible manufacturing system is reported. The system is a real one, consisting of nine machines, an inspection station and a centralized queueing area—all interconnected by an automatic material-handling mechanism. The operating strategies considered involve policies for loading (allocating operations and tooling to machines) and real-time flow control. A detailed simulation was employed to test alternatives. The results are different from those of classical job shop scheduling studies, showing the dependence of system performance on the loading and control strategies chosen to operate this flexible manufacturing system. Loading and control methods are defined that significantly improve the system's production rate when compared to methods which were previously applied to the system. Finally, some conclusions are presented concerning the control of these automated systems.

Minimizing the average deviation of job completion times about a common due date

Abstract: This paper considers a single-machine scheduling problem in which penalities occur when a job is completed early or late. The objective is to minimize the total penalty subject to restrictive assumptions on the due dates and penalty functions for jobs. A procedure is presented for finding an optimal schedule.

An algorithm for the computer control of production in a flexible manufacturing system

Abstract: The problem of management of production for an automated manufacturing system is described. The system consists of machines which can perform a variety of operations on a family of parts. The machines are unreliable, and the chief difficulty the control system faces is to meet production requirements while the machines fail and become repaired at random times. A three-level hierarchical control algorithm is proposed which involves stochastic optimal control, network optimization, and scheduling. An example is presented.

Due Date Assignment for Production Systems

Abstract: This paper is concerned with the study of the constant due-date assignment policy in a dynamic job shop. Assuming that production times are randomly distributed, each job has a penalty cost that is some non-linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time the job arrives to the shop. This constant time allowed in the shop is the lead time that a customer might expect between time of placing the order and time of delivery. The objective is to minimize the expected aggregate cost per job subject to restrictive assumptions on the priority discipline and the penalty functions. This aggregate cost includes 1 a cost that increases with increasing lead times, 2 a cost for jobs that are delivered after the due dates: the cost is proportional to tardiness and 3 a cost proportional to earliness for jobs that are completed prior to the due dates. We present an algorithm for solving this problem and show that the optimal lead time is a unique minimum point of strictly convex functions. The algorithm utilizes analytical procedures; computations can be made manually. No specific distributions are assumed; the distribution of total time a job is in the shop is utilized by the algorithm. This distribution can be theoretical or empirical. An example of a production system is presented.

Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan

Abstract: The problems of minimizing the expected makespan and minimizing the expected tic for a finite set of independent tasks with exponential service-time distributions on m ~ 2 it processors are considered. It is shown that a scheduling policy minimizes the expected flow timq only if it is shortest expected processing time tint, and that a policy minimizes the expected make and only if it is longest expected processing time fast. rE,,' WORDS ArCD PHRASES: scheduling, flow time, makespan, sequencing, policy C R C A T E G O R I E S : 5.39, 5.42

Analytical Evaluation of Hierarchical Planning Systems

Abstract: Hierarchical planning systems have become popular for multilevel decision problems. After reviewing the concept of hierarchical planning and citing some examples, we describe a method for analytic evaluation of a hierarchical planning system. We show that multilevel decision problems can be nicely modeled as multistage stochastic programs. Then any hierarchical planning system can be measured against the yardstick of optimality in this stochastic program. We demonstrate this approach on a hierarchical system that can be shown to be asymptotically optimal for a job shop design/scheduling problem.

An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice

Abstract: A scheduling problem associated with teaching practices at colleges of education is formulated as a 3-dimensional assignment problem. An efficient algorithm for its solution, based on Lagrangean relaxation, is described.

Preemptive Scheduling of Independent Jobs with Release and Due Times on Open, Flow and Job Shops

Abstract: We study the problem of obtaining feasible preemptive schedules for independent jobs. It is assumed that each job has associated with it a release and due time. No job can begin before its release time. All jobs must be completed by their respective due times. It is shown that determining the existence of feasible preemptive schedules for two processor flow and job shops is NP-hard in the strong sense even when all jobs have the same due time. A linear programming formulation for the open shop problem is obtained. Also, a fast polynomial time algorithm is obtained for a restricted class of open shop problems.

A new continuous model for job-shop scheduling

Abstract: In this paper arguments are presented for the use of a new continuous model for job-shop scheduling. In this model each job is regarded as infinitely divisible. Formulating the job-shop problem in this way leads to optimal control problems of a type which recent work has shown to be efficiently solvable. Solutions to these continuous problems can be used to generate heuristic loading rules. Some simulation results from small job-shops are presented. These demonstrate that loading rules based on the continuous model perform well in practice.

The Application of a Graph Coloring Method to an Examination Scheduling Problem

Abstract: This paper describes the application of a vertex coloring procedure to a real life examination scheduling problem. The accessories used in deriving and compressing the schedule and in rearranging the time frames to make the solution acceptable for the spring semester of 1980 are described.

Combined scheduling system for reducing job tardiness in a job shop

Abstract: Two formulae to give the mean and the standard deviation of job flow-times are derived from the machine number, the load ratio, the required number of operations, and the mean and the standard deviation of processing times, which specify the characteristics of a job shop. On the basis of the two formulae, a method of due-date assignment which contains a due-date adjustment factor is proposed. The assignment method is combined with the sequencing procedure to construct the total scheduling system for reducing job tardiness. Two new dispatching rules are presented as the second phase of the system. The experimental comparison shows that the efficiency of the proposed systems can be better than the conventional scheduling systems

Computer scheduling of public transport. urban passenger vehicle and crew scheduling. papers based on presentations at the international workshop held at the university of leeds, 16-18 july, 1980 (contd)

Abstract: (Continued from TRIS 349000.) Practical Aspects in Automatic Crew Scheduling (Piccione,C, Cherici,A, Bielli,M and La Bella,A); Crew Scheduling by Computer: A Test on the Possibility of Designing Duties for a Certain Bus Line (Borret,JMJ and Roes,AW); HASTUS 1: A Mathematical Programming Approach to the Bus Driver Scheduling Problem (Lessard,R, Rousseau,JM and Dupuis,D); An Integer Programming Approach to Scheduling (Ryan,DM and Foster,BA); A Computer Based Crew Scheduling System Using a Mathematical Programming Approach (Mitra,G and Welsh, APG); A Problem Decomposition Approach to Scheduling the Drivers and Crews of Mass Transit Systems (Ward,RE, Durant,PA and Hallman,AB); Experimentation with a Computerized System for Scheduling Mass Transit Vehicles and Crews (Ball,MO, Bodin,LD and Dial,R); Attendance and Rostering System (Jachnik,JK); Automating Extraboard Assignments and Coach Operator Timekeeping (Schmidt,JW and Fennessy,RJ); A Glossary of Terms in Bus and Crew Scheduling (Hartley,T). (TRRL)

An investigation of the advantages of using a man-computer interactive scheduling methodology for job shops

Abstract: Scheduling has been a difficult problem for job shops which manufacture discrete parts. The research described in this paper investigates the hypothesis that interactive man-computer scheduling methodology is more effective in this task than a batch scheduling methodology. This hypothesis is investigated under eight different problem configurations generated by varying three job description parameters. The results have been evaluated statistically and the effectiveness of an interactive schedule compared to the slack-per-remaining-operation heuristic is investigated. Influences of the level of variation in job description parameters on the quality of the interactive schedule have also been analysed in this study. Results show that scheduling interactively is significantly more effective in most problem situations, and that the level of variation of some of the parameters has a significant impact on the quality of the interactive schedule.

Scheduling Jobs with Exponential Processing and Arrival Times on Identical Processors so as to Minimize the Expected Makespan

Abstract: In this note we study a problem related to the scheduling of jobs on p identical processors p ≥ 2. Jobs arrive randomly, interarrival times being exponentially distributed. The processing times are also exponential with mean drawn upon arrival from an arbitrary distribution function. Preemptions are allowed. The objective is to minimize the expected time until this M/G/p queuing system is first empty. We prove that an optimal policy processes jobs currently in the system in decreasing order of expected processing time.

On J-maximal and J-minimal Flow-Shop Schedules

Abstract: Scheduling problems are considered for a common kind of flow shop where the execuuon Ume for certain tasks in each job is always longer or shorter than that for the other tasks NP-completeness ts shown for some cases, stmple opttmal algorithms are found for the others, and bounds are gtven for the worst cases.

Minimizing maximum lateness in a two-machine unit-time job shop

Abstract: AnO (nlogn)-algorithm is given for the two-machine, job-shop scheduling problem withn unit-time tasks in which maximum lateness is to be minimized. This algorithm generalizes recent results by Hefetz and Adiri for the corresponding makespan problem.

A Routing and Scheduling Problem for a Rail System: A Case Study

Abstract: Railways are extensively used in the Australian sugar industry to transport cane from farms to the factories. Development of efficient schedules manually is difficult, given a weak set of constraints and the need to consider operating and capital costs and the deterioration of cane in the period between harvesting and processing. The Cane Railway Scheduling Problem deals with the design of a regular schedule. The algorithm devised is based on a serial decomposition (with routing and scheduling considered separately) to generate a trial solution, modification of the trial solution to provide a first feasible solution and iterative refinement to provide the final solution. Comparison of solutions produced by the algorithm and those generated manually suggests potential savings ranging from 20% to 30% in annual operating costs with accompanying reductions in rolling stock requirements. Use of the model in the industry is noted.

The vehicle scheduling problem: a survey

Abstract: SUMMARY The vehicle scheduling problem is concerned, with routing a fleet of vehicles each with a capacity constraint and which are based at a central depot, to visit a set of delivery points. The optimality criterion is most frequently taken as the total distance travelled which is to be minimized. This paper discusses this problem, surveys the literature on it and presents some new ideas on heuristic solution procedures.

Well structured parallel programs are not easier to schedule

Abstract: The scheduling problem for unit time task systems with arbitrary precedence constrainls is known to be NP-complete. We show that the same is true even if the precedence constraints are restricted to certain subclasses which make the corresponding parallel programs more structured. Among these classes are those derived from hierarchic cobegin-coend programming constructs, level graph forests, and the parallel or serial composition of an out-tree and an in-tree. In each case, the completeness proof depends heavily on the number of processors being part of the problem instances.

EHV Operating Problems Associated with Reactive Control

Abstract: This paper is one of a series prepared for use in Current Operations Problems (CoPs) forums with the goal of focusing the attention of the industry on high priority problems faced by those who are involved in the actual operation of power systems.

Hastus i: a mathematical programming approach to the bus driver scheduling problem. from the book computer scheduling of public transport

Abstract: This paper presents a mathematical programming formulation of the bus driver scheduling problem in a transit company. A relaxation of the problem and a solution strategy are described. The implementation and results obtained in Quebec City are briefly overviewed.

A Probabilistic Production Costing Methodology for Systems with Storage

Abstract: Using the concept of an Expected Incremental Generation Cost Curve (EIGC), a new probabilistic production cost methodology is presented. This method, somewhat related to the Baleriaux-Booth equivalent load concept, is useful for production costing in both traditional systems and those involving storage. In fact, the probabilistic storage-thermal scheduling problem is shown to reduce to a deterministic scheduling problem easily solved using a linear programming approach.

Counterexamples to optimal permutation schedules for certain flow shop problems

Abstract: It is well known that a minimal makespan permutation sequence exists for the n × 3 flow shop problem and for the n × m flow shop problem with no inprocess waiting when processing times for both types of problems are positive. It is shown in this paper that when the assumption of positive processing times is relaxed to include nonnegative processing times, optimality of permutation schedules cannot be guaranteed.

Scheduling on profiles of constant breadth

Abstract: n unit-executive-time tasks subject to precedence constraints are to be scheduled on a system of identical processors. The precedence constraints are represented as a directed acyclic graph (dag). A sequence of natural numbers, called a profile, specifies how many processors are available in each time-slot. We seek an optimal schedule for a given dag and profile. The complexity of this scheduling problem depends strongly on the breadth of the profile, which is the maximum number of processors that are available in any time-slot. For the case where the breadth of the profile is two efficient algorithms has been published. If the breadth of the profile is unbounded, then the corresponding decision problem is NP-complete. We give polynomial algorithms for special cases of the remaining open problem: finding an optimal schedule in the case where the profile has constant breadth m (GREATERTHEQ) 3. Our main method is the following: Finding an optimal schedule for a dag of at least m components and a profile of breadth m reduces to finding an optimal schedule for the subdag consisting of all components that are higher than one plus the height of an m-th highest component. That is, given an optimal schedule for this subdag, then an optimal schedule for the whole dag can be found in time O(n + e), where e is the number of edges in the dag. Using the above result combined with dynamic programming we achieve the following time bounds: O(n('m-1)) if the dag is a level order or an inforest, O(n('m-1)log n) for outforest, O(n('4m-4)log n) for opposing forest, and O(n('h(m-1)+1)) for dags of height h. In all the above polynomial cases, the corresponding decision problem becomes NP-complete if the breadth of the profile is unbounded. In the Appendix we discuss known and new NP-completeness results. In particular, we show that deciding whether there exists a schedule for a dag of height one and a profile of the following form is NP-complete: an unbounded number of processors in exactly one slot and one processor in all other slots.

Interaction between constraints and decision making in scheduling problems

Abstract: The main objectives of a scheduling problem result from a decision taken at an upper level. In the presented approach, these objectives are taken into account through constraints in order to ensure a rigorous coordination between two successive decision levels. This paper looks at some questions which result from this problem definition : the characterization of feasible schedules, the comparison of schedules according to feasibility.