Showing papers on "Job shop scheduling published in 1986"
TL;DR: This work describes the relationship between the general employee scheduling problem and related problems, and reports computational results for a procedure that solves these more complex problems within 98–99% optimality and runs on a microcomputer.
298 citations
27 Oct 1986
TL;DR: A novel scheduling problem is defined; it is solved by repeated, rapid, approximate reschedulings, which leads to a first optimal PRAM algorithm for list ranking, which runs in logarithmic time.
Abstract: We study two parallel scheduling problems and their use in designing parallel algorithms. First, we define a novel scheduling problem; it is solved by repeated, rapid, approximate reschedulings. This leads to a first optimal PRAM algorithm for list ranking, which runs in logarithmic time. Our second scheduling result is for computing prefix sums of logn bit numbers. We give an optimal parallel algorithm for the problem which runs in sublogarithmic time. These two scheduling results together lead to logarithmic time PRAM algorithms for the connectivity, biconnectivity and minimum spanning tree problems. The connectivity and biconnectivity algorithms are optimal unless m = o(nlog*n), in graphs of n vertices and m edges.
196 citations
TL;DR: This paper focuses on an environment for seeking, studying, and evaluating approaches for yielding good sequences in an assembly line designed to produce various cars, and relies on the automated reasoning program ITP.
Abstract: The ‘job-shop scheduling problem’ is known to be NP-complete. The version of interest in this paper concerns an assembly line designed to produce various cars, each of which requires a (possibly different) set of options. The combinatorics of the problem preclude seeking a maximal solution. Nevertheless, because of the underlying economic considerations, an approach that yields a ‘good’ sequence of cars, given the specific required options for each, would be most valuable. In this paper, we focus on an environment for seeking, studying, and evaluating approaches for yielding good sequences. The environment we discuss relies on the automated reasoning program ITP. Automated reasoning programs of this type offer a wide variety of ways to reason, strategies for controlling the reasoning, and auxiliary procedures that contribute to the effective study of problems of this kind. We view the study presented in this paper as a prototype of what can be accomplished with the assistance of an automated reasoning program.
156 citations
TL;DR: In this paper, the static two-machine flow shop scheduling problem is considered and it is shown that the problem is NP-complete and that permutation schedules for this problem do not always minimize makespan.
118 citations
TL;DR: The effect of fire on forest yields has been well documented in stand-level analyses; however, forest-level effects are less widely known.
Abstract: The effect of fire on forest yields has been well documented in stand-level analyses; however, forest-level effects are less widely known. A set of dynamic equations can be constructed that describe the evolution of a forest under the impact of harvesting and random fire. When fire is treated in a deterministic fashion, these equations can be used to formulate an optimal harvest scheduling problem that can be solved using linear programming. Examples using white spruce data for the Fort Nelson Timber Supply Area of British Columbia show that even modest rates of fire can have a dramatic impact and that present harvest scheduling models may be considerably overestimating projected forest harvest levels. Results also show that the deterministic approach appears to be a reasonable approximation of the true stochastic fire problem.
111 citations
TL;DR: Analysis of approximation methods for the vehicle routing and scheduling problem with time window constraints shows that their worst-case behavior on n customer problems is at least order of n for minimizing the number of vehicles used, the total distance traveled, and the total schedule time.
Abstract: We consider the vehicle routing and scheduling problem with time window constraints. Analytical results concerning the behavior of approximation methods for this problem class are derived through worst-case analysis. For a variety of heuristics, it is shown that their worst-case behavior on n customer problems is at least order of n for minimizing the number of vehicles used, the total distance traveled, and the total schedule time.
103 citations
TL;DR: An exact algorithm is described which exploits the structure of the single-vehicle routing and scheduling problem with time windows, partial loads, and dwell times, and a route improvement heuristic is constructed based on the master problem.
Abstract: SYNOPTIC ABSTRACTWe apply Benders' decomposition procedure to the single-vehicle routing and scheduling problem with time windows, partial loads, and dwell times. We provide a formulation and demonstrate that the scheduling subproblem is the dual of a network flow problem. We describe an exact algorithm which exploits its structure, and construct a route improvement heuristic based on the master problem. A heuristic for building an initial route is also presented.
101 citations
TL;DR: In this paper, the scheduling of n jobs around a common due date, so as to minimize the average total earliness plus total lateness of the jobs, is studied. And the model is extended to allow for the availability of multiple parallel processors and an efficient algorithm is developed for that problem.
Abstract: This article concerns the scheduling of n jobs around a common due date, so as to minimize the average total earliness plus total lateness of the jobs. Optimality conditions for the problem are developed, based on its equivalence to an easy scheduling problem. It seems that this problem inherently has a huge number of optimal solutions and an algorithm is developed to find many of them. The model is extended to allow for the availability of multiple parallel processors and an efficient algorithm is developed for that problem. In this more general case also, the algorithm permits great flexibility in finding an optimal schedule.
98 citations
TL;DR: In this article, the authors present a procedure for solving the short-term generation scheduling problem for a large hydrothermal system that includes transmission limitations, where the integrated system is divided into a hydro and a thermal subsystem.
Abstract: This paper presents a procedure for solving the short term generation scheduling problem for a large hydrothermal system that includes transmission limitations. The integrated system is divided into a hydro and a thermal subsystem. A reduced gradient algorithm is employed for the solution of the hydro subproblem. This algorithm is specialized to efficiently solve nonlinear network flow problems with additional constraints of non-netwrk type. The thermal subsystem is solved using a fast unit commitment and dispatch algorithm. A case study with the Swedish system is discussed.
93 citations
TL;DR: In this article, a mixed integer linear program (MILP) is formulated with considerably reduced number of integer binary variables, than if the same problem were formulated with integer variables defined as X ij=1 if job i is sequenced immediately before job j, and 0 otherwise.
Abstract: SUMMARY The problem of an n-job, M-stage flowshop with sequence dependent set-up times is discussed. A mixed integer linear program (MILP) is formulated with considerably reduced number of integer binary variables, than if the same problem were formulated with integer variables defined as X ij=1 if job i is sequenced immediately before job j, and 0 otherwise. The inclusion of set-up times, sequence dependency and M stages makes this formulation different from most other flowshop formulations in the literature, since such problems have not been given due consideration. This paper contributes a unique formulation to handle flowshop problems in the process industry where the set-up times have a definite dependence on the sequence in which jobs are processed. Computational results have been compared for problems up to six jobs and stages where the objective has been to minimize the makespan. The MILP has been solved using the SCICONIC-V/M mixed integer solution package on the Prime-550 minicomputer.
93 citations
01 Oct 1986
TL;DR: A new medium-grained model based on column-oriented tasks is introduced, and it is shown to correspond structurally to the filled graph of the given sparse matrix and give an overall scheme for parallel sparse Cholesky factorization, appropriate for parallel machines with shared-memory architecture like the Denelcor HEP.
Abstract: In this paper, a systematic and unified treatment of computational task models for parallel sparse Cholesky factorization is presented. They are classified as fine-, medium-, and large-grained graph models. In particular, a new medium-grained model based on column-oriented tasks is introduced, and it is shown to correspond structurally to the filled graph of the given sparse matrix. The task scheduling problem for the various task graphs is also discussed. A practical algorithm to schedule the column tasks of the medium-grained model for multiple processors is described. It is based on a heuristic critical path scheduling method. This will give an overall scheme for parallel sparse Cholesky factorization, appropriate for parallel machines with shared-memory architecture like the Denelcor HEP.
TL;DR: Two test data sets for the vehicle routing and scheduling problem with time window constraints are studied and initial solutions are obtained using a variety of heuristics, then improved using branch exchange procedures modified to incorporate the timewindow constraints.
Abstract: SYNOPTIC ABSTRACTBranch exchange techniques, such as the well-known 2-opt and 3-opt procedures, are among the most powerful heuristics available for the solution of the classic vehicle routing problem. The imposition of time window constraints on customer delivery time within the vehicle routing problem, however, introduces several complexities that can reduce the power of these techniques. In this paper, two test data sets for the vehicle routing and scheduling problem with time window constraints are studied. Initial solutions are obtained using a variety of heuristics. These solutions are then improved using branch exchange procedures modified to incorporate the time window constraints.
TL;DR: This paper presents an extension of an earlier model developed by the authors, formulating the generalized N job, M machine standard flow-shop problem as a mixed-integer goal-programming model, which allows the incorporation of the makespan as well as the mean flow-time criteria, instead of optimization being based on a single objective.
Abstract: Until recently, the majority of models used to find an optimal sequence for the standard flow-shop problem were based on a single objective, typically makespan. In many applications, the practitioner may also want to consider other criteria simultaneously, such as mean flow-time or throughput time. As makespan and flow-time are equivalent criteria for optimizing machine idle-time and job idle-time, respectively, these additional criteria could be inherently considered as well. The effect of job idle-time, measuring in-process inventory, could be of particular importance.
TL;DR: A stochastic generalization of this problem in which job processing times are independent random variables implies that the makespan becomes stochastically smaller when two adjacent jobs in a given job sequence are interchanged.
Abstract: A set of n jobs is to be processed by two machines in series that are separated by an infinite waiting room; each job requires a known fixed amount of processing from each machine. In a classic paper, Johnson gave a simple rule for ordering of the set of jobs to minimize the time until the system becomes empty, i.e., the makespan. This paper studies a stochastic generalization of this problem in which job processing times are independent random variables. Our main result is a sufficient condition on the processing time distributions that implies that the makespan becomes stochastically smaller when two adjacent jobs in a given job sequence are interchanged. We also give an extension of the main result to job shops.
TL;DR: In this paper, a traveling salesman problem formulation is proposed for the case where jobs are processed continuously through the shop and the results are used to describe an approximate algorithm for a case where limited or infinite intermediate storage space is available to hold partially completed jobs.
Abstract: The flowshop scheduling problem with sequence dependent setup times is considered and shown to be NP-complete A traveling salesman problem formulation is proposed for the case where jobs are processed continuously through the shop These results are used to describe an approximate algorithm for the case where limited or infinite intermediate storage space is available to hold partially completed jobs The effectiveness of the proposed approximate approach is discussed and some empirical results are reported
01 Apr 1986
TL;DR: A software implementation in PROLOG of a constraint-based analysis module is presented which may be used either in a static way in order to generate a plan over a certain horizon or in a dynamic way inorder to help in making real time decisions.
Abstract: This paper deals with operation scheduling on machines in a job shop. The jobs which consist of a set of related operations are supposed to be constrained by limit times (earliest starting times and due dates). The approach aims at generating restrictions on local scheduling decisions by only considering limit times and resource availability constraints (constraint based analysis). This is achieved through an inference process which is defined from generic knowledge arising in scheduling problems : limit times associated with each operation, logical sequencing conditions between operations, inference rules relating to limit times and sequencing conditions. A software implementation in PROLOG of a constraint-based analysis module is presented. Such a module may be used either in a static way in order to generate a plan over a certain horizon or in a dynamic way in order to help in making real time decisions. In this last case it can be held to act the part of a flexible planning function.
TL;DR: This paper contains a brief discussion of why loading of multiple flexible manufacturing cells is important, and a discussion of the number of variables and constraints necessary to solve the program for a real world sized system.
TL;DR: A heuristic approach is presented which identifies the basic components of the problem and solves each of them either exactly or heuristically and is particularly suitable for cases where heavy constraints on meal breaks are present.
TL;DR: In this paper, the Smith-heuristic is used for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a predefined maximum allowable tardiness.
Abstract: This paper analyzes the Smith-heuristic for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith-heuristic is guaranteed to lead to optimal solutions. We also provide a worst-case analysis of the Smith-heuristic; the analysis shows that the fractional increase in the objective function value for the Smith-heuristic from the optimal solution is unbounded in the worst case.
01 Nov 1986
TL;DR: Performance of the flow shop performance closely follows the job shop performance under the same dis patching rule at all work centers, and results indicate that shop congestion and process ing time variation affect the performance of theflow shop as well.
Abstract: Control of jobs being processed in a flow shop is important to management. Shop performance is affected by shop congestion, processing time variation, and the dispatching rule used to load the jobs. Most previous research has concentrated on the effects of varying these parameters in a job shop setting. A SLAM II net work model and simulation analysis of these parameter varia tions was applied in a two-work center flow shop. Performance of the flow shop was tested using combinations of 5 dispatching rules, 3 shop load levels, and 2 levels of processing time varia tion. Based on a series of performance measures, the shop using the shortest processing time dispatching rule in one work center and the due data based rule in the other compares favorably with the shop that used the shortest processing time rule in both work centers. Results indicate that shop congestion and process ing time variation affect the performance of the flow shop as well. Performances between the flow shop and job shop are com pared, ...
01 Apr 1986
TL;DR: The first part of this paper is devoted to the presentation of a software system for jobshop scheduling of batches under due date constraints and time-table constraints on work-stations based on a heuristic technique for sequencing the jobs.
Abstract: The first part of this paper is devoted to the presentation of a software system for jobshop scheduling of batches under due date constraints and time-table constraints on work-stations. It is based on a heuristic technique for sequencing the jobs. It is actually run in a real workshop. The second part of the parper deals with an expert system methodology currently under development for the same kind of problems. The idea is to be able to integrate two kinds of knowledge about the production process : theoretical knowledge (issued from scheduling theory) which achieves the management of time, and practical knowledge (provided by the shop-floor manager) about specific technological constraints which must be satisfied by the actual production process. These constraints are usually not taken into account at the theoretical level. The knowledge representation and processing techniques of Artificial Intelligence enable realistic schedules to be obtained by simultaneous use of both sources of information.
18 Dec 1986
TL;DR: A family of polynomial-time algorithms is given such that A∈ delivers a solution that is within a relative error of e of the optimum of the minimum makespan problem on uniform parallel processors.
Abstract: In this paper we present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors. More specifically, the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible. We give a family of polynomial-time algorithms {A∈} such that A∈ delivers a solution that is within a relative error of e of the optimum. The technique employed is the dual approximation approach, where infeasible but superoptimal solutions for a related (dual) problem are converted to the desired feasible but possibly suboptimal solution.
TL;DR: In this article, a two level heuristic for the resource constrained scheduling problem is presented, which is based on a combination of priority rules where utilization of resources by the operations, the critical path of operations in a job, and the due dates of the jobs are taken into account.
Abstract: A two level heuristic for the resource constrained scheduling problem is presented. This heuristic is based on a combination of priority rules where utilization of resources by the operations, the critical path of operations in a job, and the due dates of the jobs are taken into account. The schedules that this heuristic generates have been compared with small problems for which optimal solutions are available and it is shown that these solutions are generally within 15% of the optimal. Also the polynomial time and space complexity of the heuristic is demonstrated.
TL;DR: Two heuristic algorithms are presented for solving the scheduling problem in a statically loaded Flexible Manufacturing System (FMS) and appear to out perform the other published techniques used in obtaining the schedules associated with minimum makespan, minimum average lead time and minimum cost of tardiness.
Abstract: Two heuristic algorithms are presented for solving the scheduling problem in a statically loaded Flexible Manufacturing System (FMS). The heuristics goal is to minimise the total cost resulting from the tardiness of jobs. Using the same heuristics, an iterative method is proposed to find an optimal makespan and the average lead time. Modifications required to handle the case of a dynamically loaded FMS are then presented. Simulation results show that the developed heuristics appear to out perform the other published techniques used in obtaining the schedules associated with minimum makespan, minimum average lead time and minimum cost of tardiness. Finally, the simulation of the dynamic case shows that the algorithms could be implemented locally on each station for the scheduling calculation.
TL;DR: In this paper, a counterexample is given for Carlier's contention that if a schedule obtained by Schrage's algorithm is optimal, then there exists a set of jobs J such that the makespan of the Schrage schedule is equal to min i e J a i + Σ ieJ d i + min; iϵJ q i where a i, d i and q i is the release date, processing time and the tail of job i, respectively.
TL;DR: In this article, several heuristics designed for the general flow shop problem are applied to the no idle time allowed constraint and results show that one application yields good solutions for problems with up to ten jobs.
01 Apr 1986
TL;DR: This paper focuses on developing a job scheduling model that considers the tool requirement of each job in an explicit fashion and avoids unnecessary set-up operations in order to effectively utilize the michines.
Abstract: The problems addressed in this paper arise in industry when flexible, automated machines are used to manufacture parts (jobs). These machines include numerically controlled (N/C) tools, robots,...etc. The goal is to avoid unnecessary set-up operations in order to effectively utilize the michines. In this paper we focus on developing a job scheduling model that considers the tool requirement of each job in an explicit fashion.
TL;DR: A simple necessary and sufficient condition for scheduling one machine when the production times of all jobs are identical is derived, any one of which ensures that if a feasible schedule on M machines exists, then a schedule also exists in which each part always executes on the same machine.
Abstract: This paper considers problems that arise in scheduling cyclic production of different parts on several identical machines where the cycle times are of the form kiw, with i varying only with each part. First we derive a simple necessary and sufficient condition for scheduling one machine when the production times of all jobs are identical. Then we describe three conditions, any one of which ensures that if a feasible schedule on M machines exists, then a schedule also exists in which each part always executes on the same machine. These conditions can be used to motivate heuristics to address the scheduling problem.
TL;DR: In this paper, a scheduling problem of a job shop type FMS with machine breakdown, taking into account alternative machine tools for each machining process of parts, is solved by a discrete event simulation using SLAM II simulation language.
TL;DR: In this article, the authors studied the effect of the variability of distribution Fj on the expected waiting costs of the n jobs and on the job sequencing which minimizes this total expected waiting cost.
Abstract: Consider an m-machine flow shop with n jobs. The processing time of job j, j = 1,…, n, on each one of the m machines is equal to the random variable Xj and is distributed according to Fj. We show that, under certain conditions, more homogeneous distributions F1,…, Fn result in a smaller expected makespan. We also study the effect of the variability of distribution Fj on the expected waiting costs of the n jobs and on the job sequencing which minimizes this total expected waiting cost. We show that the smallest (largest) variance first rule minimizes the total expected waiting cost on a single machine when the waiting cost function is increasing convex (concave). We also show that the smallest variance first rule minimizes, under given conditions, the total expected waiting cost in an m machine flow shop when the waiting cost function is increasing convex. Similar results are also obtained for the two-machine job shop. Similar results cannot be obtained when the processing times of job j on the various machines are i.i.d. and distributed according to Fj.