Showing papers on "Job 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. >

Job-shop scheduling with multi-purpose machines

Abstract: Consider the following generalization of the classical job-shop scheduling problem in which a set of machines is associated with each operation of a job. The operation can be processed on any of the machines in this set. For each assignment μ of operations to machines letP(μ) be the corresponding job-shop problem andf(μ) be the minimum makespan ofP(μ). How to find an assignment which minimizesf(μ)? For problems with two jobs a polynomial algorithm is derived.

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. >

A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem

Abstract: We give a new formulation to the multiple-depot vehicle scheduling problem as a set partitioning problem with side constraints, whose continuous relaxation is amenable to be solved by column generation. We show that the continuous relaxation of the set partitioning formulation provides a much tighter lower bound than the additive bound procedure previously applied to this problem. We also establish that the additive bound technique cannot provide tighter bounds than those obtained by Lagrangian decomposition, in the framework in which it has been used so far. Computational results that illustrate the robustness of the combined set partitioning-column generation approach are reported for problems four to five times larger than the largest problems that have been exactly solved in the literature. Finally, we show that the gap associated with the additive bound based on the assignment and shortest path relaxations can be arbitrarily bad in the general case, and as bad as 50% in the symmetric case.

Matchup Scheduling with Multiple Resources, Release Dates and Disruptions

Abstract: This paper considers the rescheduling of operations with release dates and multiple resources when disruptions prevent the use of a preplanned schedule. The overall strategy is to follow the preschedule until a disruption occurs. After a disruption, part of the schedule is reconstructed to match up with the preschedule at some future time. Conditions are given for the optimality of this approach. A practical implementation is compared with the alternatives of preplanned static scheduling and myopic dynamic scheduling. A set of practical test problems demonstrates the advantages of the matchup approach. We also explore the solution of the matchup scheduling problem and show the advantages of an integer programming approach for allocating resources to jobs.

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.

Gain Scheduling: Potential Hazards and Possible Remedies

Abstract: A common gain scheduling rule-of-thumb is to "schedule on a slow variable." In this paper, it is shown how current gain scheduling practice is necessarily limited to slow variations in the scheduling variable. These limitations are revealed to be consequences of fundamental control concepts. Furthermore, it is shown how a reformulation of the gain scheduling procedure can lead towards ultimately removing these restrictions.

Maintenance scheduling by using simulated annealing method (for power plants)

Abstract: The thermal power plant generator maintenance scheduling problem is addressed. The problem is formulated as a mixed-integer programming problem, and it is solved by using an optimization method known as simulated annealing. Since the simulated annealing method assumes an analogy between a physical multiparticle system and a combinatorial optimization problem, a global minimum can be found with high probability through a careful annealing process. Numerical results on a real-scale test system are given, and the effectiveness of the proposed method is demonstrated. >

Composing real-time systems

Abstract: We present a method to construct real-time systems using as components anytime algorithms whose quality of results degrades gracefully as computation time decreases. Introducing computation time as a degree of freedom defines a scheduling problem involving the activation and interruption of the anytime components. This scheduling problem is especially complicated when trying to construct interruptible algorithms, whose total run-time is unknown in advance. We introduce a framework to measure the performance of anytime algorithms and solve the problem of constructing interruptible algorithms by a mathematical reduction to the problem of constructing contract algorithms, which require the determination of the total run-time when activated. We show how the composition of anytime algorithms can be mechanized as part of a compiler for a LISP-like programming language for real-time systems. The result is a new approach to the construction of complex real-time systems that separates the arrangement of the performance components from the optimization of their scheduling, and automates the latter task.

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.

On the competitiveness of on-line real-time task scheduling

Abstract: The authors study the performance of online algorithms in environments where no value is obtained for the partial execution of a request. They prove that no online scheduling algorithm can have a competitive factor greater than 0.25 times the optimal. They further refine this bound by considering the effect of the loading factor. Other models of task systems (for example, tasks systems consisting of many types of task requests), are considered. Similar upper bounds on the competitive factor that can be made by online scheduling algorithms in these environments are proved. It is shown that the performance bound of 0.25 is tight by means of a simple online uniprocessor scheduling algorithm has a competitive factor of 1/4. The authors extend the discussion to systems with dual processors. They show that the upper bound for the dual-processor online scheduling problem is 1/2 if all tasks have the same value density. This bound is tight if the tasks all also have zero laxity. >

A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs

Abstract: The scheduling problem 1|pmtn, r j|Σw jU j calls forn jobs with arbitrary release dates and due dates to be preemptively scheduled for processing by a single machine, with the objective of minimizing the sum of the weights of the late jobs. A dynamic programming algorithm for this problem is described. Time and space bounds for the algorithm are, respectively,O(nk 2W 2) andO(k 2W), wherek is the number of distinct release dates andW is the sum of the integer job weights. Thus, for the problem 1|pmtn, r j|ΣU j, in which the objective is simply to minimize the number of late jobs, the pseudopolynomial time bound becomes polynomial, i.e.O(n 3k 2).

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.

Batch sizing and job sequencing on a single machine

Abstract: We study a single-machine scheduling problem in which the items to be processed have to be batched as well as sequenced. Since processed items become available in batches, flow times are defined to be the same for all items in the same batch. A constant set-up delay is incurred between consecutive batches. For any fixed, but arbitrary item sequence, we present an algorithm that finds a sequence of batches such that the total flow time of the items is minimized; we prove that for a set ofn items, the algorithm runs inO(n) time. We show that, among all sequences, the one leading to the minimum flow time has the items in non-decreasing order of running times. Thus, the optimal algorithm for the combined problem, called thebatch-sizing problem, runs inO(n logn) time. We also prove that this algorithm yields an improved solution to a scheduling problem recently studied by Baker [1].

A Comparative Evaluation of Labor Tour Scheduling Methods

Abstract: This paper presents an initial study of relative performance for a number of the labor tour scheduling heuristic methods proposed in the literature. These heuristic methods were classified as either linear programming (LP) based or construction. Each of the methods was applied to a tour scheduling problem, subject to a variety of labor demand requirements distributions, with the singular objective being the minimization of total labor hours scheduled. Statistical analysis revealed that effective tour schedule solutions were generated by both LP-based and construction methods. Since the performances of the Keith [13], Morris and Showalter [18], and Bechtold and Showalter [5] methods were superior, their solutions were also compared across a number of secondary criteria. An overall analysis of the performances of these three methods resulted in the identification of a number of important managerial and decision-making issues. We conclude that service operations management should consider integrating these heuristic methods into a decision support system. Finally, suggestions for future research are provided.

Some extensions of the discrete lotsizing and scheduling problem

Abstract: In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) is considered. DLSP relates to capacitated lotsizing as well as to job scheduling problems and is concerned with determining a feasible production schedule with minimal total costs in a single-stage manufacturing process. This involves the sequencing and sizing of production lots for a number of different items over a discrete and finite planning horizon. Feasibility of production schedules is subject to production quantities being within bounds set by capacity. A problem classification for DLSP is introduced and results on computational complexity are derived for a number of single and parallel machine problems. Furthermore, efficient algorithms are discussed for solving special single and parallel machine variants of DLSP.

Scheduling chain-structured tasks to minimize makespan and mean flow time

Abstract: We consider the problem of scheduling a set of chains onm > 1 identical processors with the objectives of minimizing the makespan and the mean flow time. We show that finding a nonpreemptive schedule with the minimum makespan is strongly NP-hard for each fixedm > 1, answering the open question of whether this problem is strongly NP-hard for trees. We also show that finding a nonpreemptive schedule with the minimum mean flow time is strongly NP-hard for each fixedm > 1, improving the known strong NP-hardness results for in-trees and out-trees. Finally, we generalize the result of McNaughton, showing that preemption cannot reduce the mean weighted flow time for a set of chains. The last two results together imply that finding a preemptive schedule with the minimum mean flow time is also strongly NP-hard for each fixedm > 1, answering another open question on the complexity of this problem for trees.

Dynamic setup scheduling and flow control in manufacturing systems

Abstract: We propose a method for flow control of parts in a manufacturing system with machines that require setups. The setup scheduling problem is investigated in the context of a multilevel hierarchy of discrete events with distinct frequencies. The higher level of the hierarchy calculates a target trajectory in the surplus/backlog space of the part types which must be tracked at the level of setups. We consider a feedback setup scheduling policy which usescorridors in the surplus/backlog space of the part types to determine the timing of the set-up changes in order to guide the trajectory in the desired direction. An interesting case in which the trajectory leads to a target point (e.g., a hedging point) is investigated in detail. It is shown that in this case the surplus/backlog trajectory at the setup level can lead to a limit cycle. Conditions for linear corridors which result in a stable limit cycle are determined.

A new heuristic solution method in resource‐constrained project scheduling

Abstract: A new heuristic method is presented for the resolution of multiresource constrained conflicts in project scheduling. In attempting to find a minimal makespan solution, the algorithm employs a simple procedure to generate a feasible solution with no backtracking. A postanalysis phase then applies a hill-climbing search. The solution method is different from existing heuristic methods in that it repairs resource conflicts rather than constructs detailed schedules by dispatching activities. Resource-violating sets of activities are identified which must be prevented from concurrent execution because this would violate resource constraints. Repairs are made by imposing an arc to sequence two activities in such a resource violating set. Computational results are compared with those of existing heuristics for the minimal makespan problem.

Scheduling tasks and vehicles in a flexible manufacturing system

Abstract: Due to their increasing applicability in modern industry, flexible manufacturing systems (FMSs), their design, and their control have been studied extensively in the recent literature. One of the most important issues that has arisen in this context is the FMS scheduling problem. This article is concerned with a new model of an FMS system, motivated by the practical application that takes into account both machine and vehicle scheduling. For the case of a given machine schedule, a simple polynomial-time algorithm is presented that checks the feasibility of a vehicle schedule and constructs it whenever one exists. Then a dynamic programming approach to construct optimal machine and vehicle schedules is proposed. This technique results in a pseudopolynomialtime algorithm for a fixed number of machines.

Strongly Polynomial Algorithms for the High Multiplicity Scheduling Problem

Abstract: A high multiplicity scheduling problem consists of many jobs which can be partitioned into relatively few groups, where all the jobs within each group are identical. Polynomial, and even strongly polynomial, algorithms for the standard scheduling problem, in which all jobs are assumed to be distinct, become exponential for the corresponding high multiplicity problem. In this paper, we study various high multiplicity problems of scheduling unit-time jobs on a single machine. We provide strongly polynomial algorithms for constructing optimal schedules with respect to several measures of efficiency (completion time, lateness, tardiness, the number of tardy jobs and their weighted counterparts). The algorithms require a number of operations that are polynomial in the number of groups rather than in the total number of jobs. As a by-product, we identify a new family of nxn transportation problems which are solvable in O(n log n) time by a simple greedy algorithm.

Generation of schedules using a genetic procedure

Abstract: In the scheduling method disclosed herein, a genetic algorithm is employed to improve a population of possible schedules represented by respective chromosomes, where the chromosomes upon which the genetic algorithm operates are not a direct encoding of a possible schedules. Rather, the details of the scheduling problem and the real life constraints typically associated with such problems are hidden from the genetic algorithm by the use of a deterministic schedule builder which operates on lists of the desired tasks and which generates legal schedules, i.e. schedules which do not violate hard constraints. The legal schedules so generated are evaluated or scored and the scores are provided to the genetic algorithm as feedback for influencing subsequent operation of the genetic algorithm.

A neural network approach to job-shop scheduling

Abstract: A novel analog computational network is presented for solving NP-complete constraint satisfaction problems, i.e. job-shop scheduling. In contrast to most neural approaches to combinatorial optimization based on quadratic energy cost function, the authors propose to use linear cost functions. As a result, the network complexity (number of neurons and the number of resistive interconnections) grows only linearly with problem size, and large-scale implementations become possible. The proposed approach is related to the linear programming network described by D.W. Tank and J.J. Hopfield (1985), which also uses a linear cost function for a simple optimization problem. It is shown how to map a difficult constraint-satisfaction problem onto a simple neural net in which the number of neural processors equals the number of subjobs (operations) and the number of interconnections grows linearly with the total number of operations. Simulations show that the authors' approach produces better solutions than existing neural approaches to job-shop scheduling, i.e. the traveling salesman problem-type Hopfield approach and integer linear programming approach of J.P.S. Foo and Y. Takefuji (1988), in terms of the quality of the solution and the network complexity. >