Showing papers on "Job shop scheduling published in 1977"

Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors

Abstract: The finishing time properties of several heuristic algorithms for scheduling n independent tasks on m nonidentical processors are studied. In particular, for m = 2 an n log n time-bounded algorithm is given which generates a schedule having a finishing time of at most (√5 + 1)/2 of the optimal finishing time. A simplified scheduling problem involving identical processors and restricted task sets is shown to be P-complete. However, the LPT algorithm applied to this problem yields schedules which are near optimal for large n.

Deterministic Processor Scheduling

Abstract: This paper surveys the deterministic scheduling of jobs m uniprocessor, multiprocessor, and job-shop environments. The survey begins with a brief introduction to the representation of task or job sets, followed by a discussion of classification categories. These categories include number of processors, task interruptlbility, job periodicity, deadlines, and number of resources. Results are given for single-processor schedules in job-shop and multIprogramming environments, flow-shop schedules, and multiprocessor schedules. They are stated in terms of optimal constructive algorithms and suboptimal heuristics. In most cases the latter are stated in terms of performance bounds related to optimal results. Annotations for most of the references are provided in the form of a table classifying the referenced studies m terms of various parameters.

Job-Shop Scheduling by Implicit Enumeration

Abstract: The classical combinatorial optimization problem of minimizing maximum completion time in a general job-shop has been the subject of extensive research. In this paper we review and extend this work. A general bounding approach is developed which includes all previously presented lower bounds as special cases. The strongest bound obtainable in this way is combined with two enumeration schemes, the relative merits of which are discussed. The results of some computational experiments and a large bibliography are included as well.

Scheduling Equal-Length Tasks Under Treelike Precedence Constraints to Minimize Maximum Lateness

Abstract: A basic problem of deterministic scheduling theory is that of scheduling n equal length tasks on m identical processors subject to precedence constraints. Although the general problem of finding a schedule which minimizes makespan is NP-complete, the important special case with “treelike” precedence constraints can be solved by a well-known algorithm of T. C. Hu. We consider an extension of this special case model to include the possibility of individual task deadlines, in which case the goal is to minimize maximum lateness. Our results show that it makes a considerable difference whether the precedence is of “in-tree” or “out-tree” form. In the former case the problem can be solved in lime On log n; in the latter it is NP-complete. We also discuss applications of our results to related scheduling problems.

Analysis of a switch matrix for an SS/TDMA system

Abstract: Time slot scheduling problem for a satellite switched/time-division multiple access (SS/TDMA) system is discussed and an algorithm called "Greedy Algorithm" is presented. This algorithm guarantees a most efficient utilization of a frame period with n2- n (n is the number of beams) number of switchings at most. Another problem discussed in this paper is the choice of the type of microwave switch matrix to be put on board the satellite. A switch-matrix structure called rearrangeable multistage matrix is shown to have high reliability and low-insertion-loss characteristics. Also brief discussions are made on the experimental results of an engineering model SS/TDMA system.

Centralized Scheduling and Priority Implementation Heuristics for a Dynamic Job Shop Model

Abstract: The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. A multi-pass heuristic program, which has proven effective in earlier research, is applied to the up-dated static scheduling problem at each review time. A procedure is proposed for implementing priorities on the shop floor between review times. The procedure is expressly designed to integrate the scheduling of newly arriving jobs to modify the schedule. In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination. Comparison with another procedure that gives the centralized schedule precedence over new arrivals indicates the importance of the implementation procedure when periodic centralized scheduling is used in a dynamic situation.

Dynamic course scheduling for college faculty via zero-one programming*

Abstract: This paper formulates a multi-period course scheduling problem as a zero-one programming model. Under various constraints, and for a planning horizon of several terms, the model seeks to maximize: (1) the faculty course preferences in assigning faculty members to courses, and (2) the faculty time preferences in allocating courses to time blocks, via a two-stage optimization procedure. The multi-period structure of the model, strengthened by the explicit inclusion of a wide-range of constraints designed to represent various special requirements has enabled the model to capture the many dynamic features of the course scheduling problem at the college level. As such, it can be used not only for long-range or short-range departmental planning, but also as a suitable framework toward the development of a larger, and all-inclusive course scheduling decision system. The paper begins with a brief review of several related studies and then presents a multi-period scheduling model and its extensions. Some numerical examples are used to test the model, and the authors' experience, resulting from such tests with several computer codes, is reported. The possible directions for future research are also suggested.

On the computational efficiency of branch-and-bound algorithms

Abstract: The behavior of the number of partial problems T(A) which are decomposed in a branch­ and-bound algorithm A (T(A) may be taken as a measure for the computational efficiency of A) is investigated in a fairly general setting. The first result is that the mean number f(n) of T(A) when A is applied to problems of size n grows at least as fast as exponentially with n, under relatively mild conditions, if A uses only the lower bound test as most of the conventional branch-and-bound algorithms do. Then it is pointed out that a possible way to avoid this exponential growth is to use the dominance test together with the lower bound test. The dominance test is also interesting from the view point of unifying a wide variety of algorithms as branch-and-bound. These points are exemplified by the well known Dijkstra algorithm for the shortest path problem and the Johnson algorithm for the two-machine flow-shop scheduling problem, for which f(n) :s: n-1 holds by virtue of the dominance test.

Note---A Note on Single Machine Sequencing with Random Processing Times

Abstract: It is shown that Lawler's efficient order n2 algorithm for the n-job, one-machine scheduling problem where the objective is to minimize the maximum deferral cost subject to arbitrary precedence relationships also applies when the processing times are random variables and the objective is to minimize the maximum expected deferral cost. Several special cases are explored.

An approximate solution of machine scheduling problems by decomposition method

Abstract: SUMMARY To obtain an approximate solution for a large-scale job-shop scheduling problem the decomposition method was investigated. This means that an original problem is decomposed into subproblems, which are solved separately, and then the solution of the original problem is composed from the subproblems' solutions. Different methods to decompose the problem were tested by computational experiments and evaluated from the viewpoint of the goodness of schedule and computation time.

Heuristic Strategy for Scheduling Farm Operations.

Abstract: A farmer has to plan what to produce and how to produce it. To assist his decision-making a number of techniques are employed. A work study shows in detail how the production is or can be done. On the other hand linear programming is a tool for selecting crops. Work management (machinery selection and scheduling of operations) is somewhere in between these two approaches. The machinery selection problem and the selection of crops depend on each other and so both require constraints for man and workable time of machine operations. These constraints are insufficient to represent correctly the scheduling of operations. The scheduling of farm operations depends on the available men and machinery, on the available materials (products, cattle) and on the weather and properties of materials (moisture content). Scheduling has been studied for one material (corn) or one operation (harvesting), but seldom for several materials and operations competing for the use of men and machinery. This scheduling problem is a dynamic programming problem where each stage of the system coincides with a decision date. Three subsystems can be distinguished. The biological subsystem consists of materials waiting for operations which are performed by gangs from the man/machine subsystem. The climate subsystem influences the properties of the materials and the application of gangs. In Fig. 1 terms and relations for the grain harvest are given. The aim of the present study is to develop a simulation method to solve the scheduling problem that correctly represents the use of men and machinery and the resulting flow of materials and uses hourly data on weather and properties of materials. To decide at each decision date which operations are to be executed, a heuristic strategy is developed to evaluate the current state of the system. This detailed model of the scheduling problem is simplified by omitting, for example, the setup and service of machines and by aggregating the weather information within days or weeks. So a range of problems is formulated that are solved by the simulation model. The most simple problem can easily be tailored for a linear programming model. With a range of problems we can evaluate to what extent scheduling problems might be relaxed (using less constraints). The heuristic strategy uses the concept of urgency of processing a material. This idea is based on the existence of a timeliness function of each material with a maximum return at a given date (moment of time for example 1 August 20h00). After that optimum date the return diminishes with time. These timeliness losses are partly unavoidable because the capacity of men and machinery to process materials is limited. With the given men and machinery the decision maker only can decide to process a material or not, where not processing means an avoidable timeliness loss (the urgency). The urgency of a material is calculated for each material separately on the basis of the available quantity. For the grain harvest a state of the system is given in Fig.2. The quantity of materials (wheat, straw etc.) is represented by a queue of so-called 'fields'. Fields differ in some property of a material, for instance ripening date or moisture content and may also refer to geographical position. The operation period for the available quantity of a material is derived from the expected workable time, the estimated fraction of the time men and machinery are available for processing the material and the capacity of processing the material. Not starting the processing of some acreage of a material at the current decision date is equivalent to a delay until the end of the operation period. So the value of the timeliness function at the decision date minus the value at the end of the period is the avoidable loss, and an element of the urgency of a material. The fraction of the time men and machine are available for processing the material is derived from a linear programming model with weekly periods and is input for the simulation models. The capacity of processing the material is derived from the combinations (sets of gangs) and the capacity of the gangs (men and machinery performing an operation on a material according to a method). The farmer can only decide to use one combination or another or none at all. Therefore it is necessary to assign the urgency of materials to the gangs and to the combinations by distributing the urgency of materials among the gangs processing that material relative to their capacities. Such an urgency of a gang (in $ per hour) is corrected by subtracting the variable costs of, for example, overtime. The urgency of a combination is the sum of the urgency of those gangs which have a positive corrected urgency and can operate in the combination. Whether a gang is applied depends on equipment, weather, material properties (moisture content), available material for processing and available storage for the materials delivered. After selecting the preferred combination (with maximum urgency), the next decision date is found as the minimum from a number of potential decision dates determined by end of operation, filling the storage, start of overtime or pause or no- work time, change of weather expectation or properties of materials, machine failure or by finish of repair or service. Executing operations performed by the gangs in the preferred combination results in processing and delivering materials. Thus transformation of the quantity of materials is necessary to learn the state of the system on the next decision date. This state again is evaluated by the strategy resulting in urgencies of processing materials and a preferred combination; this cycle is repeated until the job is completed. The transformation also results in recording the timeliness loss of materials, the use of men, machinery and variable costs for overtime or drying. The delivery of materials introduces new fields. The grain harvest in the Netherlands is used to learn about the behaviour of the simulation model. The wheat is harvested with a combine harvester and the wet grain (19-23% moisture content) is dried; the straw is baled, loaded and stored in the barn and the stubble is ploughed. Eight years with hourly weather and material data from 1 August-15 September are used. Some general results from the experiments are that the simulation model is suitable for deriving relations between acreage, yield and machinery (Section 3.5.5) and that relaxed problems (simplified problems; Section 3.5.6) result in lower estimated costs or are more optimistic about the scheduling of operations than the strategy in the detailed scheduling problem. So if the detailed problem is acceptable for scheduling operations with a satisfactory use of equipment and variable costs and a correct representation of the flow of materials, then the simplified problems and the linear programming model result in too low estimated costs. The validation of the heuristic strategy is impossible because there are no data available. The results of the experiments, however, contribute to our knowledge of the scheduling problem and so the model is useful. Comparing different experiments shows the danger of using relaxed problems. Experiments with the simulation model for the scheduling problem show the sensitivity of different machinery systems, which is of use in training farmers to improve their management ability. Further research is necessary to find better urgencies simultaneously for all materials, gangs and combinations and to optimize the schedule for a number of decision dates instead of only one.

Two-machine scheduling under arbitrary precedence constraints

Abstract: Suppose jobs, in the Johnson's two-machine n-job flow-shop scheduling problem, are grouped into disjoint subsets within which a job order that may not be preempted is specified. Furthermore, suppose that a precedence relation between these subsets is given such that the processing of a subset must be completed, on each machine, before the processing of another subset begins on the machine. This paper considers a problem to fmd a sequence in which jobs are to be processed on the machines in order to minimize the total elapsed time, under such general precedence constraints, from the start of the first job on machine I until the end of the last job on machine 11. An efficient algorithm to obtain an optimal sequence is given and a simpl(, example is shown.

A convex property of an ordered flow shop sequencing problem

Abstract: A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.

Computer Scheduling of Beer Tanker Deliveries

Abstract: Recently Foster and Ryan developed a new method for the vehicle scheduling problem (VSP). This article applies their method to a practical VSP involving the delivery of pressurised fluids, and demonstrates its effectiveness.

The 'hub' and 'wheel' scheduling problems. part 1. the 'hub' scheduling problem: the myopic case

Abstract: The problem is that of scheduling truck movement (loaded and empty) between a central depot (the hub) and a number of outlying cities. Current demand is known deterministically, but future demand is uncertain. The myopic case treats two periods only: the current period and one future period. The objective is to minimize the expected total operating penalty, consisting of the costs of moving empties and the costs of delaying shipments. In two special cases the procedures of solution reduce to simple marginal analysis that has been previously solved by Minas and Mitten. In the general case, a network flow model is proposed that is easily solved.

A Practical Optimisation Technique for a Queueing System

Abstract: A scheduling problem in an outpatient clinic is considered. First the system is represented by means of a simple queueing model. The problem of minimising the patients' total queueing time is then formulated as a non-linear program and solved by applying the Kuhn-Tucker conditions. The results obtained enable the person who manages the appointment system to allocate appointment dates to patients who have different priorities.

Scheduling Rules for Parallel Processors

Abstract: This paper investigates various criteria under which simple scheduling rules generate optimum schedules for m machine scheduling problems. The problems are considered under a “job-splitting” assumption. Some of the rules which generate optimum schedules with job splitting for the multi-machine problems, do not split jobs for the single machine problems. The relationship between the job splitting and no job splitting problem in these cases, is analogous to the situation when an optimum solution to a linear program has all the variables integer and hence is optimum to the corresponding integer program.

Note---A Note on “Critical Ratio Scheduling: An Experimental Analysis”

Abstract: A recent journal article [Berry, W. L., Rao, V. 1975. Critical ratio scheduling: an experimental analysis. Management Sci.22 2, October 192--201.] by Berry and Rao on job shop scheduling reported some counterintuitive results concerning the use of dynamic operating information in making priority scheduling decisions. The results of the article, based on a simulation experiment, indicate that dynamic information on queue waiting time at individual machines and on the inventory status of individual items fails to improve the performance of the production system. In fact, the reported performance of the dynamic rule was inferior to the static rules in five out of six cases. The purpose of this note is to call attention to the possibility that it is Berry and Rao's construction and/or use of this information, and not the value of the information itself, which is in question.

Johnson's approximate method for the 3 × n job shop problem

Abstract: The effectiveness of Johnson's Approximate Method (JAM) for the 3 × n job shop scheduling problems was examined on 1,500 test cases with n ranging from 6 to 50 and with the processing times Ai, Bi, Ci (for item i on machines A, B, C) being uniformly and normally distributed. JAM proved to be quite effective for the case Bi ⩽ max (Ai, Ci) and optimal for Bi, ⩽ min (Ai, Ci).

The cyclic separation scheduling problem

Abstract: This paper deals with the problem of scheduling items (tasks, employees, equipment, etc.) over a finite time horizon so as to minimize total cost expenditures while maintaining a predefined separation between certain items. The problem is cyclic, because the same schedule will be repeated over several consecutive time periods of equal length. Thus, requirements are present to maintain the separation of items not only within the individual time periods considered, but also between items in adjoining periods. A special purpose branch-and-bound algorithm is developed to solve this scheduling problem by taking advantage of its cyclic nature. Computational results are given.

Methods and Techniques Used for Job Shop Scheduling

Abstract: .The job shop scheduling problem, in whicn we must determine the order or sequence for processing a set of jobs through several machines in an optimum manner, has received considerable attention. In this paper a number of the methods and techniques are reviewed and an attempt to categorize them according to their appropriateness for effective use in job shop scheduling has been made. Approaches are classified in two categories: a) analytical techniques and b) graphical methods. Also, it should be noticed that this report does not include all the attempts and trials, especially the heuristic approaches.

Note---A Note on Shwimer's Theorem A

Abstract: In 1972 Joel Shwimer published some interesting research “on the n-job, one-machine, sequence-independent scheduling problem with tardiness penalties... where the goal is to minimize the total penalty costs resulting from the tardiness of the jobs” Shwimer, J. 1972. On the n-job, one-machine, sequence-independent scheduling problem with tardiness penalties: a branch-bound solution. Management Sci.18 6 B-301--B313.. The proposed algorithm is essentially based on his Theorem A. Unfortunately the given proof of Theorem A contains an inconsistency. In this note we present a different proof of the mentioned theorem.

Optimal Selection and Scheduling of Investments in Urban Public Transport Systems

Abstract: The selection of an optimal urban public transport system is prepared by a feeding-back planning process based on systems analysis. The decision situations are presented graphically, they define a plausible area of value judgements and insert into the figure indifference lines for each pair of alternative systems. The scheduling problem is handled by applying utility profile theory and zero–one optimization technique. By means of a particular formulation of variables and constraints, horizontal and vertical interdependencies between investment alternatives can be integrated.

Optimal Performance of a Firm in a Dynamic Market

Abstract: The problem of optimal dynamic transition of a firm with market power from a predetermined initial condition to a known statically optimal equilibrium state is formulated. The model of the firm is linear, discrete time, and behavioristic in nature with production, demand, inventory, and order and sales sectors. Prices and changes in the production rate constitute the decision variables which are assumed to be bounded. The optimal control sequence subject to bounded control efforts is derived to minimize a quadratic performance index by invoking the maximum principle. It consists of maximum effort transitions followed by a series of singular steps which ultimately drive the system to the equilibrium state. Existence and optimality of the solution are proved. Two typical numerical examples are included.