Showing papers on "Single-machine scheduling published in 1994"

Scheduling: Theory, Algorithms, and Systems

Abstract: This book on scheduling covers theoretical models as well as scheduling problems in the real world. Author Michael Pinedo also includes a CD that contains slide-shows from industry and movies dealing with implementations of scheduling systems. The book consists of three parts. The first part focuses on deterministic scheduling with the associated combinatorial problems. The second part covers probabilistic scheduling models. In this part it is assumed that processing times and other problem data are not known in advance. The third part deals with scheduling in practice. It covers heuristics that are popular with practitioners and discusses system design and development issues. Each chapter contains a series of computational and theoretical exercises. This book is of interest to theoreticians and practitioners alike. Graduate students in operations management, operations research, industrial engineering and computer science will find the book to be an accessible and invaluable resource. Scheduling will serve as an essential reference for professionals working on scheduling problems in manufacturing and computing environments. Michael Pinedo is the Julius Schlesinger Professor of Operations Management at New York University.

Distributed scheduling of flexible manufacturing systems: stability and performance

Abstract: We consider a manufacturing system producing several part-types on several machines. Raw parts are input to the system. Each unit of a given part-type requires a predetermined processing time at each of several machines, in a given order. A setup time is required whenever a machine switches from processing one part-type to another. For a single machine system with constant demand rates, we present a class of generalized round-robin scheduling policies for which the buffer level trajectory of each part-type converges to a steady state level. Furthermore, for all small initial conditions, we show that these policies can be Pareto-efficient with respect to the buffer sizes required. Allowing the input streams to have some burstiness, we derive upper bounds on the buffer levels for small initial conditions. For non-acyclic systems, we consider a class of policies which are stable for all inputs with bounded burstiness. We show how to employ system elements, called regulators, to stabilize systems. Using the bounds for the single machine case, we analyze the performance of regulated systems implementing generalized round-robin scheduling policies. >

Minimizing mean tardiness and earliness in single machine scheduling problems with unequal due-dates

Abstract: We consider a single-machine scheduling problem with the objective of minimizing the mean (or equivalently, total) tardiness and earliness when due dates may differ among jobs. Some properties of the optimal solution are discussed, and these properties are used to develop both optimal and heuristic algorithms. Results of computational tests indicate that optimal solutions can be found for problems with up to 20 jobs, and that two of the heuristic procedures provide optimal or very near optimal solutions in many instances. © 1994 John Wiley & Sons, Inc.

Resource optimal control in some single-machine scheduling problems

Abstract: We consider a problem to schedule a set of jobs on a single machine under the constraint that the maximum job completion time does not exceed a given limit. Before a job is released for processing, it must undergo some preprocessing treatment which consumes resources. It is assumed that the release time of a job is a positive strictly decreasing continuous function of the amount of resources consumed. The objective is to minimize the total resource consumption. We show that ordering jobs in nonincreasing processing times yields an optimal solution. We then consider a bicriterion approach to the problem in which the maximum job completion time and the resource consumption are simultaneously minimized and present a polynomial time solution algorithm. Finally, we consider a related problem in which the job release times are given but the processing times are functions of the amount of resource consumed. We show that ordering jobs in nondecreasing release times gives an optimal solution and that the problem to minimize both the maximum completion time and resource consumption is polynomially solvable. >

LP-based solution methods for single-machine scheduling problems

Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Multi-item, single-machine scheduling problem with stochastic demands: a comparison of heuristics

Abstract: This paper discusses the results of simulation tests for multi-item, single-machine production systems facing stochastic, time-varying demands. Six different heuristics are compared with the objective of minimizing the sum of changeover and inventory costs. Tests are performed to evaluate the effect of the stationarity of the demand process and of the level of forecast errors on the performance of the heuristics tested.

Single machine scheduling with deadlines to minimize the weighted number of tardy jobs

Abstract: This paper considers as single machine scheduling problem in which jobs have due dates and deadlines. A job may be completed after its due date, but not after its deadline, in which case it is tardy. A branch and bound algorithm is proposed to find a schedule which minimizes the weighted number of tardy jobs. It uses lower bounds which are derived using the dynamic programming state-space relaxation method. Computational experience with test problems having up to 300 jobs indicates that the lower bounds are extremely effective in restricting the size of the branch and bound search tree.

Scheduling a single machine to minimize two criteria: maximum tardiness and number of tardy jobs

Abstract: In this paper we consider a single machine scheduling problem with two criteria; minimizing both maximum tardiness and the number of tardy jobs. We present both heuristic and branch-and-bound algorithms to find the schedule which minimizes the number of tardy jobs among all schedules having minimal maximum tardiness. Computational results show that problems with up to 40 jobs can be solved in less than one minute of computer time, and solution difficulty tends to increase as the range of due dates increases relative to the total processing time. We extend our results to generate all nondominated schedules for the two criteria. Computational experiments indicate that all non-dominated solutions to problems with 40 jobs can be generated. However, solution difficulty for these problems is highly dependent on problem parameters.

Single Machine Earliness-Tardiness Scheduling Problems Using the Equal-Slack Rule

Abstract: The purpose of this paper is to analyse a special case of the non-pre-emptive single machine scheduling problem where the distinct due dates for each job are related to processing times according to the Equal–Slack rule. The scheduling objective is to minimize the sum of earliness and tardiness penalties. After determining some properties of the problem, the unrestricted case is shown to be equivalent to a polynomial time solvable problem, whereas the restricted case is shown to be NP-hard, and suggestions are made for further research.

Job Shop Scheduling under a Non-Renewable Resource Constraint

Abstract: In this paper we consider the job shop scheduling problem under a discrete non-renewable resource constraint. We assume that jobs have arbitrary processing times and resource requirements and there is a unit supply of the resource at each time period. We develop an approximation algorithm for this problem and empirically test its effectiveness in finding the minimum makespan schedules. Most of the research done in the area of scheduling deals with the allocation of a single scarce resource over time to perform a collection of tasks. In this study, the scheduling environment is extended to include an additional non-renewable resource. The term non-renewable implies that the resource is actually being consumed by the jobs competing for it. Financial constraints are typical examples of such constraints and for this reason non-renewable resource constraints are often called financial constraints1. Materials shared by different products can also be regarded as a non-renewable resource in manufacturing environments. Considering these constraints explicitly is likely to yield more realistic schedules. A limited amount of research has been done in the area of non-renewable resource constrained scheduling. There are some polynomially bounded solution algorithms for precedence constrained scheduling problems2 and for pre-emptive scheduling of independent jobs on parallel machines1. In the case of arbitrary resource requirements and availabilities, Slowinski' states that Carlier has shown that even the non-preemptive single machine scheduling problem is NP-complete if job processing times are different from unity. In Toker et al.3, it is shown that when the amount of resource available at each time period is constant, the single machine non-renewable resource constrained problem is equivalent to a resource- free, two-machine flowshop problem. Hence it is solvable in polynomial time. They also extended their results to the m-machine case and showed how to transform different types of resource constrained problems into equivalent, unconstrained problems. The scheduling environment we consider is a job shop. A single non-renewable resource becomes available over time in equal quantities (say unity) and there is a set of jobs to be processed. Each operation requires an arbitrary amount of the non-renewable resource which must be available at the start of that operation and which is consumed during its processing. We used makespan as the performance measure. Optimization algorithms for the general job shop scheduling problem are restricted to implicit enumeration techniques, such as branch-and-bound based procedures4-7. On the other hand, approximation algorithms usually use a dispatching rule to give priorities to operations to be scheduled8. The non-renewable resource constrained job shop scheduling problem is NP-complete as, when all resource requirements are zero, it reduces to the unconstrained job shop problem which is NP-complete9. This complexity result serves as a formal justification to use approximation algorithms for the constrained problem. We first describe the approximation algorithm developed and then introduce two lower bounds for the n-job, m-machine resource-constrained job shop scheduling problem. Next, we discuss the computational results. Finally, we present our conclusions.

Algorithms for single-machine scheduling with stochastic outtree precedence relations to minimize expected weighted flow time or maximum expected lateness

Abstract: Stochastic single-machine scheduling problems with special tree-like GERT precedence constraints and expected weighted flow time or maximum expected lateness as objective functions are considered. To obtain polynomial algorithms for these problems, Smith's ratio rule and Lawler's rule for the deterministic problems 1¦outtree¦Σw v C v and 1¦prec¦f max , respectively, are generalized.

A note on ‘Single-machine scheduling for minimizing total cost with identical, asymmetrical earliness and tardiness penalties’

Abstract: We point out a flaw present in a recent publication, and show how methodology can be modified to correct it.

Single-machine scheduling with release dates, due dates and family setup times

Abstract: We address the NP-hard problem of scheduling n independent jobs with release dates, due dates, and family setup times on a single machine to minimize the maximum lateness. This problem arises from the constant tug-of-war going on in manufacturing between efficient production and delivery performance, between maximizing machine utilization by batching similar jobs and maximizing customers' satisfaction by completing jobs before their due dates. We develop a branch-and-bound algorithm, and our computational results show that it solves almost all instances with up to about 40 jobs to optimality. The main algorithmic contribution is our lower bounding strategy to deal with family setup times. The key idea is to see a setup time as a setup job with a specific processing time, release date, due date, and precedence relations. We develop several sufficient conditions to derive setup jobs. We specify their parameters and precedence relations such that the optimal solution value of the modified problem obtained by ignoring the setup times, not the setup jobs, is no larger than the optimal solution value of the original problem. One lower bound for the modified problem proceeds by allowing preemption. Due to the agreeable precedence structure, the preemptive problem is solvable in On log n time.

Comparison of Heuristic Search Algorithms for Single Machine Scheduling Problems.

Abstract: This paper compares the performance of four heuristic search algorithms for single machine scheduling problems: local search, simulated annealing, tabu search and genetic algorithms. To investigate their potential, the algorithms are applied to a single machine scheduling problem to minimise tardiness of all jobs with arbitrary ready times, processing times and due times. This problem is known to be NP complete. The purpose of the comparison is to find a good approximation algorithm ie. the algorithm is not designed to search for an optimal solution to the problem.

Sequencing with chain structured precedence constraints and minimal and maximal separation times

Abstract: Considers a single machine scheduling problem which has been solved for a medical laboratory. In this problem, there are not only chain structured precedence constraints, but also minimal and maximal times separating successive jobs in a same chain. The criterion to be minimized is the makespan. This problem arises particularly in systems where chemical processes are involved. In these systems, jobs are transportation operations and chemical processes can be modeled as chains. Therefore the problem studied in this paper is of practical importance. The authors first state that the problem is NP-complete. As a consequence, the authors propose heuristics for large size problems and a branch and bound algorithm for small size problems. Computational results are reported. >

Minimization of Total Absolute Flow Time Deviation in Single and Multiple Machine Scheduling

Abstract: In this note, single machine scheduling and minimizing absolute flow time deviation (TAFD) are considered. The relationship between this problem and the mean absolute deviation of job completion times about a common due date (MAD) is discussed. Based on the MAD problem optimal solutions of the TAFD problem are given. Furthermore, the generalization of the problem to the multiple machine case is discussed and an efficient algorithm for generating many optimal solutions of the problem, in the multi-machine case, is given.

Single Processor Scheduling

Abstract: Single machine scheduling (SMS) problems seem to have received substantial attention because of several reasons. These type of problems are important both because of their own intrinsic value, as well as their role as building blocks for more generalized and complex problems. In a multi-processor environment single processor schedules may be used in bottlenecks, or to organize task assignment to an expensive processor; sometimes an entire production line may be treated as a single processor for scheduling purposes. Also, compared to multiple processor scheduling, SMS problems are mathematically more tractable. Hence more problem classes can be solved in polynomial time, and a larger variety of model parameters, such as various types of cost functions, or an introduction of change-over cost, can be analyzed. Single processor problems are thus of rather fundamental character and allow for some insight and development of ideas when treating more general scheduling problems.

Single Machine Stochastic Scheduling: Minimizing the Number of Tardy Jobs

Abstract: SYNOPTIC ABSTRACTThis paper deals with a single machine scheduling problem of determining a sequence so as to minimize the number of tardy jobs in a stochastic sense. In this model the processing times of jobs are assumed to be random variables with known distributions. When the processing time is a known constant, the problem of minimizing the number of tardy jobs on a single machine can be solved optimally by a well-known procedure due to Moore, but in a form suggested by Hodgson. In this paper, we show that if job processing times can be stochastically ordered, an approach which is similar to the Moore and Hodgson algorithm will yield an optimal solution.

A bicriteria scheduling problem with earliness and tardiness penalties

Abstract: In this paper, we study the problem of scheduling n jobs on a single machine to minimize the total earliness penalties subject to a maximum tardiness penalty of each job. From the viewpoint of multicriteria scheduling, the problem is different from the E/T scheduling problems mostly studied in the literature. A heuristic algorithm and a branch and bound algorithm are proposed, computational results are reported. >