Showing papers on "Job shop scheduling published in 1976"

Due dates in job shop scheduling

Abstract: Much of job-shop scheduling research is based on the assumption that due dates are outside the control of the scheduler. The paper examines several procedures for specifying due dates, largely dependent on the expected processing time for jobs and on the level of congestion in the shop. The effect of these procedures is examined in the case of three loading rules (FIFO, St and SI∗) On waiting times, on missing due dates and on notional cost functions. The study is based on numerous simulations of a given shop operating at various levels of load ratio and the case of a fluctuating load is briefly examined.

An Integer Programming Approach to the Vehicle Scheduling Problem

Abstract: This paper describes an integer programming formulation of the vehicle scheduling problem and illustrates how such a formulation can be extended to incorporate restrictions on work load, coverage and service that occur in real world vehicle scheduling problems. The integer programme is solved using the Revised Simplex method, additional constraints being introduced to retain integrality during convergence. The feasible region of this integer programme is initially restricted so that only routes constructed through sets of radially contiguous locations are considered. The effect of relaxing these over-constraints is explored. The method is demonstrated on fifteen problems ranging in size from 21 to 100 locations and the results generally show an improvement on previously published results. This is particularly true of the larger problems. This method compares favourably with other methods in computational efficiency.

An Experimental Method of Determination of Optimal Maintenance Schedules in Power Systems Using the Branch-and-Bound Technique

Abstract: An experimental method of scheduling the necessary maintenance activities on generator units in a power system is developed. The problem is identified as an integer programming problem, and a method based on the branch-and-bound technique is developed. The maintenance scheduling problem is characterized by a large number of complex constraints. The method presented is capable of taking into account all these constraints and hence, results in a practically implementable solution, if a feasible solution exists. Other features of the method are employment of a number of different objective functions and discovery of a feasible solution if one exists. Furthermore, unlike most present methods, it actually finds the optimal solution. The operation of the method is exemplified by application to a realistic system.

The Engine Scheduling Problem In A Railway Network

Abstract: We present the mathematical version of a scheduling problem faced by a railway company that employs several engine types to provide power for its trains. Each train has motive power requirements that are determined by the weight and length of the train, and the route it travels. The operating constraint is to provide a train with sufficient engines to meet its motive power requirements. We give a mathematical formulation of selecting the mix of engine types that gives the lowest capital investment and operating cost and explore a method of solution based on the decomposition method of Benders. The computational results we obtained are satisfactory for medium size problems and unsatisfactory for large size problems. We also discuss the relevance of the model and comment on its utility in practice.

Note---A Note on the Single-Machine Multi-Product Lot Scheduling Problem

Abstract: This note develops a procedure for automatically generating feasible solutions for the single-machine multi-product lot scheduling problem.

Technical Note-Finding Some Essential Characteristics of the Feasible Solutions for a Scheduling Problem

Abstract: This note is concerned with some essential characteristics of the feasible solutions for a job-shop scheduling problem in which the jobs are constrained by fixed starting times and due dates. These characteristics are related to the scheduling order of operations on each machine and to the fixed starting and completion times for each operation. We present the basic principles enabling one to define these characteristics and propose a procedure for finding them.

Optimal flowshop schedules with no intermediate storage space

Abstract: In this paper the problem of finding an optimal schedule for the n-job, M-machine flowshop scheduling problem is considered when there is no intermediate space to hold partially completed jobs and the objective function is to minimize the weighted sum of idle times on all machines. By assuming that jobs are processed as early as possible, the problem is modeled as a traveling salesman problem and solved by known solution techniques for the traveling salesman problem. A sample problem is solved and a special case, one involving only two machines, is discussed.

Flowshop sequencing problem with ordered processing time matrices: A general case

Abstract: The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.

A Vehicle Scheduling Procedure Based Upon Savings and a Solution Perturbation Scheme

Abstract: This paper is concerned with the classical vehicle scheduling problem where a set of vehicles with known capacities are to service a known set of points with deterministic demands at least cost. An extension of previous work is developed and an algorithm is presented. Suitable computational experience with the procedure is provided for both the symmetric and the non-symmetric problems.

The production capacity of job shops with limited storage space

Abstract: Suppose the number of jobs which can be stored in front of the machines in a job shop is limited. As a result, arriving jobs for which there is no space in the shop will form a shop queue. The production capacity or maximum departure rate of jobs from the shop will depend on the way in which jobs are selected from the shop queue for release to the machine queues. For a job shop with two identical machines and random routing of jobs a number of release rules are compared. It is shown that the production capacity is increased when the number of jobs in the shop is kept less than the available storage space. Among release rules independent'of job processing times and number of operations the optimum release rule is shown, using dynamic programming, to be the idle machine rule, i.e. only release a job to the shop when a machine would otherwise be idle.

An Improved Heuristic Procedure for a Nonlinear Cutting Stock Problem

Abstract: Many industries acquire stocks of material in large standard sizes which are then reduced to required widths or lengths according to demand. Scheduling the cutting operations is a particularly difficult problem when a few cutting patterns must be chosen from a vast number of feasible patterns such that the total cost of the reduction process is minimised. Physical constraints and economic considerations restrict the number and type of pattern which can be used. Haessler [Haessiler, R. W. An application of heuristic programming to a nonlinear cutting-stock problem occurring in the paper industry. Unpublished doctoral dissertation, The University of Michigan, Ann Arbor, 1968, available through University Microfilms, Ann Arbor, Dissertation No. 69--12, 119; Haessiler, R. W. 1971. A heuristic programming solution to a nonlinear cutting-stock problem. Management Sci.17 12, August 793--802.] has described a typical problem in the paper industry and a heuristic procedure for obtaining satisfactory schedules. An improved procedure is proposed in which the type of pattern generated and accepted into the schedule is constrained to improve the likelihood that the residual scheduling problem has a feasible and economic solution. Results obtained by the proposed procedure are compared with those obtained manually and by Haessler for a set of eleven actual problems.

Two-machine scheduling under required precedence among jobs

Abstract: In a general two-machine n-job scheduling problem, it is assumed that every possible sequence of jobs can be executed, so that whichever best served a given measure can be selected. This paper considers two more restricted cases in which certain orderings are prohibited, either by technological constraints or by externally imposed policy. In the first case, some of the decisions of a schedule have already been made and the schedule must be completed without altering what has been decided. In the second case, jobs are grouped into disjoint subsets within which a job order is specified, but which may be preempted between jobs. For each of these two cases, a rule is given for determining the sequence in which jobs are to be processed on the machines in order to minimize the total elapsed time.

The theory-practice gap in job-shop scheduling

Abstract: This job-shop scheduling problem is perhaps the most common form of industrial scheduling problem, it is also probably the most complex. This paper examines the nature of the problem and reviews the state of the art of scheduling theory and its relevance to the solution of practical problems.

Due-Dates and Instantaneous Load in the One-Machine Shop

Abstract: The due-date assignment problem occurs when due-dates are assigned within, rather than outside, a job shop. This study explores the importance of instantaneous and future shop loads in setting due-dates in shops operating under due-date dependent queue discipline. The assignment of due-dates to arriving jobs in an m-machine shop is formulated as a stochastic dynamic programming problem in the first part of this study. A computational experiment using dynamic programming is performed in the second part and due-dates are developed for specific instantaneous load conditions in a simulated one-machine shop. The importance of instantaneous and future shop loads for assigning due-dates in a one-machine shop, with constant interarrivals and exponential service times, is shown.

A decision-making process for the real time control of a production unit†

Abstract: The scheduling of jobs on machines in a job-shop is considered using a multilevel decision-making structure The levels are coordinated by considering as constraints on one level the decision made on the preceding level For job-shop scheduling a tool is proposed to enable one to find and to analyse the set of feasible schedules in the light of the decision taken on the previous level The information obtained as to the earliest starting and latest finishing times for performing the operations, as well as the logical sequence constraints acts as decision aids for the scheduling of the operations The decision is made by choosing, from amongst the actions which are possible in the light of the overall objective, an action which takes into account secondary elements and considerations particular to the job-shop

On the Computational Complexity of a Generalized Scheduling Problem

Abstract: The parallel scheduling of a partially ordered set of tasks has received great attention. The partially ordered tasks can be viewed as components of a straight-line program. In this note, we discuss some aspects of the nonpreemptive parallel scheduling of a program with more general control structures. We examine the existence of optimal k-processor schedules, and in line with recent interest in the complexity of computer computations and algorithms, we study the complexity of constructing optimal k-processor schedules. In particular we show that, for every k > 1, any algorithm that would yield an optimal k-processor schedule of a loop-free program, when such a schedule exists, will be of exponential-time complexity.

A heuristic algorithm for the flowshop scheduling problem

Abstract: — This paper describes a simple heuristic algorithm for seeking a quick and approximate solution to the n-job, M-machine flowshop scheduling problem under the assumptions that the process times o f the jobs are deterministic and the same order of jobs is followed on ail machines, The proposed algorithm is based on the f act that the flowshop scheduling problem may be considered as (M— 1) quasi equivalent sortingproblems and that an approximate solution to the flowshop scheduling problem, then, may be obtained by solving the corresponding sorting problems. The proposed heuristic algorithm can be executedby hand for reasonably large-sized problems and yields solutions that are comparative ly doser to optimal solutions than those obtained by Campbell-Dudek-Smith heuristic algorithm. These computational results are discussed and efficiency of the proposed heuristic is compared with that of Campbell-DudekSmith algorithm.

Job shop scheduling—A case study

Abstract: A missile range is essentially a large-scale job-shop, involving prodigious amounts of test equipment and formidable problems of coordination. Because of its characteristics, a missile range can be considered a one-machine, N-job situation. For this problem the major scheduling methods were examined and tested, but all were discarded as unfeasible except one which used a Monte Carlo scheduling procedure adjoined with statistical stopping rules. An algorithm based on these ideas was constructed, and it has proven to be flexible and workable, providing predictably near optimum schedules for the missile range within a probabilistic and statistical framework. Even though there is not total implementation yet, considerable benefits to the missile range have already been experienced. For example, in order to automate the scheduling process, it was necessary to codify the goals of the range, something that had never been formalized before. This involved an unprecedented scrutiny and precision of definition of these goals, and from this study a reasonable numerical optimization criterion was constructed. Also, in order to use any automated scheduling algorithm, data files had to be stored on tape for ready access, which in turn has improved other operations on the missile range that were dependent on these data. Furthermore, the scheduling algorithm is providing conflict-free schedules in a few minutes of computer time.

Personnel scheduling in public systems: a survey

Abstract: In many public systems efficiencies may be realized by improved personnel scheduling. This paper surveys the literature on personnel scheduling in the public domain. Two general problems are considered: the daily scheduling problem where hourly employee work day patterns are determined and the weekly scheduling problem where day off and day on work week patterns are constructed. The daily problem is discussed in terms of scheduling with and without simultaneous work assignment; and the weekly problem is dichotomized into those schedules based on cyclical personnel requirements and those that are not.

A new approach for the optimum solution of the M by J production scheduling problem

Abstract: The purpose of this paper is to develop an algorithm which solves the M by J scheduling problem on the basis of interatively changing the data of the problem while maintaining an optimum solution along the path. The algorithm is applicable to a rather broad class of optimization problems of the classical O.R. (operations research) literature where objective functions are involved which have a certain monotony property with respect to the data variables of the problem. The algorithm is then applied to the M by J scheduling problem. The approach highlights the required research in the area of analysing the structure of the set of optimum solutions of a problem which could lead to much more efficient solutions to practical problems in manufacturing industry than the available methods of O.R.

A Series-Parallel Multiple-Criteria Model for a Scheduling Problem in the Dress-Making Industry

Abstract: In industrial scheduling problems, before finding suitable algorithms for solving mathematical programs, one often encounters difficulties in formulation and formalizing the problems themselves. This is especially the case when some optimal control is desired. There are several reasons for this: (a) It is difficult to arrive at a general agreement on defining what are precisely good (or optimal) operating conditions of the manufacturing process. (b) There are generally many criteria and constraints inter-related each to the other in a complex manner. (c) Data are not always available.

A Note on the Bounded Interval Generalized Assignment Problem.

Abstract: : The bounded interval generalized assignment problem is exemplified by the problem of assigning tasks to agents so that each task is assigned to exactly one agent and the time required to complete the set of tasks assigned to any one agent falls between prespecified lower and upper bounds. This note describes an efficient algorithm for solving this problem. (Author)

Aspects of job scheduling

Abstract: A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

Optimal linking of tasks and schedule development for military air transport

Abstract: This paper considers the scheduling problem faced by a military air transport division when required to assign a set of tasks lo a limited fleet of available aircraft. Each task is specified by a desired departure time and an allowable interval during which it can depart. We present a two phase method for combining tasks into single flights, when optimal to do so, and then programming the resulting “tasks"”(some of which are now combinations) on the aircraft. The linking/ scheduling algorithm determines a schedule which minimizes total flying time, while giving attention to priority, customer satisfaction, and maintenance efficiency.

Manpower Scheduling Models In Service Operations

Abstract: : This research arises to study and develop manpower scheduling algorithms which would efficiently schedule food service workers at military installations. The objective of this research is to provide a manager with an automated (computerized) program for scheduling manpower. At the present time, the scheduling of food service workers at a military installation is accomplished manually by each of the dining hall stewards. The number of workers to be scheduled at a given dining facility ranges from 12 to 125 depending upon the number of customers and hours of operation. Some of the benefits to be realized by implementation of an automated scheduling system are expected to include: saving of time spent by the manager to create a schedule, saving in labor cost due to a more efficient schedule, improved employee morale due to a fairer and more efficient schedule, and better customer service because employees are working in the right place at the right time.

On a Two Facility Scheduling Problem with Sequence Dependent Processing Time

Abstract: This paper is concerned with a problem involving two processing facilities where it is assumed that the two facilities are to process operations of a particular project or job. Some of the operations can only be performed by one of the facilities, some by the other, and the remaining operations, by either facility. Further, it is assumed that the processing times for all operations are sequence dependent as well as processor dependent. An algorithm is proposed which obtains minimum or near minimum completion time of all operations. Suitable computational experience is provided.

An Algorithm for Route Deviation Service

Abstract: In this investigation, a routing and scheduling algorithm is developed which can be applied to both conventional fixed route transportation systems and demand-activated transportation systems. The algorithm treats the routing and scheduling problem of route-deviation transportation systems with a cumulative approach and heuristic techniques. A simulation model was designed for investigating the performance of the algorithm and for studying the characteristics of route-deviation transportation systems. The algorithm is capable of solving the scheduling and routing problems of both fixed route and route-deviation transportation systems, or systems with combinational demands, complex lead time demands, and repetitive demands.