Showing papers on "Flow shop scheduling published in 1991"

A Computational Study of the Job-Shop Scheduling Problem

Abstract: The job-shop scheduling problem is a notoriously difficult problem in combinatorial optimization. Although even modest sized instances remain computationally intractable, a number of important algorithmic advances have been made in recent years by J. Adams, E. Balas and D. Zawack; J. Carlier and E. Pinson; B. J. Lageweg, J. K. Lenstra and A. H. G. Rinnooy Kan; and others. Making use of a number of these advances, we have designed and implemented a new heuristic procedure for finding schedules, a cutting-plane method for obtaining lower bounds, and a combinatorial branch and bound algorithm. Our optimization procedure, combining the heuristic method and the combinatorial branch and bound algorithm, solved the well-known 10×10 problem of J. F. Muth and G. L. Thomson in under 7 minutes of computation time on a Sun Sparcstation 1. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Algorithms for scheduling imprecise computations

Abstract: The imprecise computation technique, which prevents timing faults and achieves graceful degradation by giving the user an approximate result of acceptable quality whenever the system cannot produce the exact result in time, is considered. Different approaches for scheduling imprecise computations in hard real-time environments are discussed. Workload models that quantify the tradeoff between result quality and computation time are reviewed. Scheduling algorithms that exploit this tradeoff are described. These include algorithms for scheduling to minimize total error, scheduling periodic jobs, and scheduling parallelizable tasks. A queuing-theoretical formulation of the imprecise scheduling problem is presented. >

A formal approach to the scheduling problem in high level synthesis

Abstract: An integer linear programming (ILP) model for the scheduling problem in high-level synthesis is presented. In addition to time-constrained scheduling and resource-constrained scheduling, a scheduling problem called feasible scheduling, which provides a paradigm for exploring the solution space, is constructed. Extensive consideration is given to the following applications: scheduling with chaining, multicycle operations by nonpipelined function units, and multicycle operations by pipelined function units; functional pipelining; loop folding; mutually exclusive operations; scheduling under bus constraint; and minimizing lifetimes of variables. The complexity of the number of variables in the formulation is O(s*n) where s and n are the number of control steps and operations, respectively. Since the as soon as possible (ASAP), as late as possible (ALAP), and list scheduling techniques are used to reduce the solution space, the formulation becomes very efficient. A solution to a practical problem, such as the fifth-order filter, can be found optimally in a few seconds. >

A genetic algorithm for job shop

Abstract: Genetic algorithms (GAs) constitute a technique that has been applied with advantage to a variety of combinatorial problems. This work shows how the GAs can be used to optimize the job shop problem with many tasks, many machines, and precedence constraints. The authors introduce the technique of GAs and then show what makes the treatment of the job shop scheduling difficult. They then present an encoding of the problem that overcomes these difficulties. The performance of the algorithm is demonstrated with examples of real-world size. >

The impact of operating system scheduling policies and synchronization methods of performance of parallel applications

Abstract: Shared-memory multiprocessors are frequently used as compute servers with multiple parallel applications executing at the same time. In such environments, the efficiency of a parallel application can be significantly affected by the operating system scheduling policy. In this paper, we use detailed simulation studies to evaluate the performance of several different scheduling strategies, These include regular priority scheduling, coscheduling or gang scheduling, process control with processor partitioning, handoff scheduling, and affinity-based scheduling. We also explore tradeoffs between the use of busy-waiting and blocking synchronization primitives and their interactions with the scheduling strategies. Since effective use of caches is essential to achieving high performance, a key focus is on the impact of the scheduling strategies on the caching behavior of the applications.Our results show that in situations where the number of processes exceeds the number of processors, regular priority-based scheduling in conjunction with busy-waiting synchronization primitives results in extremely poor processor utilization. In such situations, use of blocking synchronization primitives can significantly improve performance. Process control and gang scheduling strategies are shown to offer the highest performance, and their performance is relatively independent of the synchronization method used. However, for applications that have sizable working sets that fit into the cache, process control performs better than gang scheduling. For the applications considered, the performance gains due to handoff scheduling and processor affinity are shown to be small.

Improved approximation algorithms for shop scheduling problems

Abstract: In the job shop scheduling problem, there are $m$ machines and $n$ jobs. A job consists of a sequence of operations, each of which must be processed on a specified machine, and the aim is to complete all jobs as quickly as possible. This problem is strongly ${\cal NP}$-hard even for very restrictive special cases. The authors give the first randomized and deterministic polynomial-time algorithms that yield polylogarithmic approximations to the optimal length schedule. These algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order. Comparable bounds can also be obtained when there are $m'$ types of machines, a specified number of machines of each type, and each operation must be processed on one of the machines of a specified type, as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints.

A practical use of Jackson's preemptive schedule for solving the job shop problem

Abstract: In this paper, we present a polynomial algorithm for optimally adjusting heads and tails in the job shop problem. This algorithm is based on Jackson's preemptive schedule for the one-machine problem. We next use this algorithm to construct a new branch and bound method. Computational results show the superiority of this method over the classical ones.

Schedules for a two-stage hybrid flowshop with parallel machines at the second stage

Abstract: Approximate solution algorithms are developed to find a minimum makespan schedule in a two-stage hybrid flowshop when the second stage consists of multiple identical machines. Computational experience comparing the ‘approximate’ makespans with their respective global lower bounds for large problems indicates that proposed polynomially bounded approximate algorithms are quite effective. It is shown that the proposed heuristic algorithms can be used to improve the efficiency of an existing branch and bound algorithm.

Scheduling approaches for random job shop flexible manufacturing systems

Abstract: This research examines the influences that scheduling schemes and the degree of routeing flexibility have on random, job shop flexible manufacturing systems within a static environment. The first factor in the experiment includes three scheduling schemes. Two of these schemes are off-line schemes which schedule many operations prior to actual production. The first of the off-line schemes establishes an overall optimal solution, and the second off-line scheme decomposes the problem into a loading subproblem and a resulting scheduling subproblem and finds optimal solutions to both subproblems. The third scheme uses control policies and dispatching rules to establish a schedule in a real-time mode. The number of alternative machine options (i.e., the degree of routeing flexibility) is a second factor in the experiment and includes eleven levels. In addition, the effects of interaction between scheduling and routeing flexibility on performance are explored.

A scheduling algorithm for conditional resource sharing

Abstract: A novel scheduling algorithm for dataflow graphs with nested conditional branches is presented. The algorithm employs a bottom-up approach to transform a dataflow graph with conditional branches into an 'equivalent' one that has no conditional branches. A schedule is then obtained for the latter, using a conventional scheduling algorithm, from which a schedule for the former is derived. Experimental results demonstrated that such an approach is quite effective. The proposed bottom-up hierarchical approach is computationally more effective than a global nonhierarchical one. >

Job Shop Scheduling with Tooling Constraints: a Tabu Search Approach

Abstract: Flexible manufacturing systems (FMSs) are automated factories in which many different part types are produced simultaneously. The tool-loading problem now adds further to the delicate task of finding an optimal schedule for such systems. In this paper, a tabu search approach is developed to solve the job shop scheduling problem with tooling constraints.

Scheduling parallel machines on-line

Abstract: The authors study the problem of scheduling jobs on parallel machines when the existence of a job is not known until an unknown release date and the processing requirement of a job is not known until the job is processed to completion. They demonstrate two general algorithmic techniques for converting existing polynomial-time algorithms that require complete knowledge about the input data into algorithms that need less advance knowledge. They prove information-theoretic lower bounds on the lengths of online schedules for several basic parallel machine models and then show that the algorithms construct schedules with lengths that either match or come within a constant factor of the lower bounds. >

Minimizing the sum of the job completion times in the two-machine flow shop by Lagrangian relaxation

Abstract: A branch-and-bound algorithm is presented for the two-machine flow shop problem with the objective of minimizing the sum of the job completion times. Lower bounds and precedence constraints result from a Lagrangian relaxation of this problem. The Lagrangian subproblem turns out to be a linear ordering problem that is polynomially solvable for appropriate choices of the Lagrangian multipliers. The best choice within this class yields a lower bound that dominates previous bounds. In fact, the existing bounds correspond to particular choices of the multipliers. Several dominance criteria are given to restrict the search tree. Computational experiments show that the proposed algorithm outperforms the previously best method.

Job and Family Scheduling of a Flow-Line Manufacturing Cell: A Simulation Study

Abstract: This paper compares four part family scheduling procedures, which seek to avoid setups by sequencing similar jobs consecutively, with four job scheduling procedures which are oblivious of part family affiliations. Of these eight scheduling procedures, four are applied intermittently to finite job sets in stochastic and dynamic environments while the other four rules are dispatching heuristics applied dynamically in the same environments. The shop configuration is a 5-stage pure flow-line manufacturing cell. Besides determining the ranking of the procedures in various operating environments, the impact on relative scheduling performance of the mean time between job arrivals, the number of part families processed, and the family setup-to-job processing time ratio is investigated. Significant interaction effects between all these factors were detected. It can be concluded that, for the scheduling procedures and conditions used in this study, family-based scheduling approaches can generate marked imp...

Automated Two-machine Flowshop Scheduling: A Solvable Case

Abstract: This paper considers new flowshop scheduling problems related to automated manufacturing systems in which n jobs are processed on two machines Ma and Mb in this order. The job transportation between two machines is done by a single automated guided vehicle (AGV), and is crucial because no machine has buffer storage for work-in-process (WIP) and hence a machine cannot release a finished job until the empty AGV becomes available at that machine, while the AGV cannot transfer an unfinished job to a machine until the machine is empty. O(n 3) algorithms are given in this paper to find optimal sequences of n jobs that minimize their maximum completion time (i.e., makespan). Some numerical results are also given to evaluate the effect of computing optimal sequences.

Approximation results in parallel machines stochastic scheduling

Abstract: We consider scheduling a batch of jobs with stochastic processing times on parallel machines. We derive various new formulae for the expected flowtime and weighted flowtime under general scheduling rules. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time provides a natural heuristic for this problem. We obtain a bound on the worst case difference between the expected weighted flow time under Smith's Rule and under an optimal policy. For a wide class of processing time distributions, this bound is of oderO(1) and does not increase with the number of jobs.

A preliminary investigation of multi-attribute based sequencing rules for assembly shops

Abstract: This paper updates the current literature on assembly shop scheduling to include multi-attribute based sequencing rules that have recently been introduced and measures of shop performance that more accurately reflect management's view toward tardiness and inventory. In addition, a new set of sequencing rules, called importance ratio (IR), is proposed. The operation of a hypothetical assembly shop is simulated to test the performance of eight sequencing rules on three distinct sets of product structures. Four measures of system inventory and four measures of job tardiness are used to evaluate sequencing rule performance. The study shows that sequencing rules which incorporate attributes of both job shop and assembly shop scheduling do not necessarily produce the best performance. Moreover, multiple measures of inventory and tardiness performance do provide important insight into the operation and particular benefits of different sequencing rules. Finally, the importance ratio rules introduced are viable ca...

Solvable Cases of the No-Wait Flow-Shop Scheduling Problem

Abstract: The no-wait flow-shop scheduling problem (NWFSSP) with a makespan objective function is considered. As is well known, this problem is 𝒩𝒫-hard for three or more machines. Therefore, it is interesting to consider special cases, i.e. special structured processing time matrices, that allow polynomial time solution algorithms. Furthermore, it is well known that the NWFSSP with a makespan objective function can be formulated as a travelling salesman problem (TSP). It is observed that special structured processing time matrices for the NWFSSP lead to special structured distance matrices for which the TSP is polynomially solvable. Using this observation, it is shown that some NWFSSPs with fixed processing times on all except two machines are well solvable while the others are conjectured to be 𝒩𝒫-hard. Also, it is shown that NWFSSPs with a mean completion time objective function restricted to semi-ordered processing time matrices are easily solvable.

An algorithm for component selection in performance optimized scheduling

Abstract: The authors describe a novel algorithm that combines the hardware scheduling and component selection phases for high level synthesis. The algorithm improves on previous work in scheduling, by being able to simultaneously select components from a given library. This enlarges the design space, resulting in better optimized designs. Experimental results on the elliptic filter benchmark demonstrate that exploiting all available components in the library results in designs with smaller area compared to designs produced by scheduling with a single implementation for each component type. >

A crane scheduling problem in a computer-integrated manufacturing environment

Abstract: This paper addresses a crane scheduling and machine layout problem in a Computer Integrated Manufacturing (CIM) Environment. A single crame is used to move all the Work-in-Process (WIP) in the system. The overall system objective is to maximize the yield rate subject to the flow time limit of the WIP. We formalize the problem, and analytically and empirically show that cyclic scheduling provides a near optimal solution, which is superior to dispatching rules. First, we illustrate the optimality and benefits of cyclic scheduling in a simple environment. Then, for multiple-product problems, we show that for a given sequence, finding the minimum cycle time becomes the maximum cost circular network flow problem in a graph. Based on the insights developed, a heuristic for sequencing product types in a cycle is derived that approximately minimizes the cycle time over all sequences. Finally, computational experiments are reported and various assertions made in the paper are empirically verified.

Scheduling of a Two-machine Flowshop with Travel Time Between Machines

Abstract: We consider the classical two-machine flowshop sequencing problem with the following additional constraint. When a job is completed on the first machine it must be transported to the second machine; a single transporter is available. A completed job on the first machine will block the machine if the transporter is in transit. A constructive algorithm to minimize makespan is presented in the paper.

A Simulation Study of Sequencing Rules in a Kanban‐Controlled Flow Shop*

Abstract: This paper addresses the problem of sequencing in decentralized kanban-controlled flow shops. The kanban production control system considered uses two card types and a constant withdrawal period. The flow shops are decentralized in the sense that sequencing decisions are made at the local workstation level rather than by a centralized scheduling system. Further, there are no material requirements planning (MRP)-generated due dates available to drive dispatching rules such as earliest due date, slack, and critical ratio. Local sequencing rules suitable for the decentralized kanban production-control environment are proposed and tested in a simulation experiment. These rules are designed so that they can be implemented with only the information available at the workstation level. Example sequencing problems are used to show why the shortest processing time rule minimizes neither average work-in-process inventory nor average finished-goods withdrawal kanban waiting time. Further, it is shown how work station supervisors can use the withdrawal period, in addition to the number of kanbans, to manage work-in-process inventories.