Showing papers on "Job shop scheduling published in 1971"

A Functional Heuristic Algorithm for the Flowshop Scheduling Problem

Abstract: By exploiting the relationship between scheduling and sorting, this paper describes a functional heuristic algorithm for seeking a quick and approximate solution to the n-job, M-machine flo...

An Algorithm for Optimal Project Scheduling under Multiple Resource Constraints

Abstract: An algorithm is described which permits the computation of optimal (minimum-duration) solutions for the resource-constrained project network scheduling problem under conditions of multiple resource requirements per job (activity). The approach is a form of bounded enumeration and employs techniques originally developed for the solution of the assembly line balancing problem. Initial computational results are given, along with an example of the type problems solved. Among the advantages of the procedure are that resource requirements can vary over job duration, and various assumptions concerning job continuity are allowable, with no extra computational effort.

Integer Programming Methods for a Vessel Scheduling Problem

Abstract: In a previous paper, Appelgren (Appelgren, L. 1969. A column generation algorithm for a ship scheduling problem. Trans. Sci. 3 53–68.), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and-bound algorithm, where the branching is performed on one of the “essential” fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the Dantzig-Wolfe decomposition, since the constraints g...

A Multivehicle Tanker Scheduling Problem

Abstract: The Dantzig and Fulkerson Tanker Scheduling Problem is concerned with the determination of the minimum size and optimal routing of a fleet of homogeneous tankers needed to meet a prescribed schedule of deliveries. This problem has been formulated as a network flow problem. Later formulations consider an existing nonhomogeneous tanker fleet and relax the fixed shipping schedule. These problems are treated as multicommodity minimal cost flow problems. This paper further extends the problem to consider differing carrying capabilities of the vehicles and formulates a mixed integer linear program that permits partially loaded tankers. A branch-and-bound enumerative scheme in conjunction with a decomposed linear program with network sub-problems is presented.

Optimality Criteria for Flowshop Schedules

Abstract: This article considers the problem of scheduling n jobs on M machines in a flowshop and examines the present formulation of the problem. To understand the true nature of the problem, this article provides economic interpretations of various optimality criteria which are being used for solving the scheduling problem. A general optimization criterion, called minimization of opportunity cost, is proposed for flow-shop scheduling problems and the results of the sensitivity analysis of various optimality criteria are reported which indicate the need to reformulate the scheduling problem.

M-stage scheduling problem—a critical appraisal

Abstract: The deterministic M-stage scheduling problem is reviewed and critically appraised from the points of view of variety, contents, assumptions, recent solution procedures and criteria of optimality. The complications of practical problems are discussed to explore the true nature of the problem formulation. Several implications of the present formulation of scheduling problem are discussed and directions for future research in scheduling theory are suggested.

Technical Note—An Improved Combinatorial Algorithm for the Flowshop-Scheduling Problem

Abstract: This paper examines the combinatorial approach to the solution of the n-job, M-machine flowshop scheduling problem under the assumptions outlined by Dudek and Teuton [Opns. Res. 12, 471–497 (1964)] and proposes an improved combinatorial algorithm that, according to our computational experience, is more efficient than the Smith-Dudek algorithm [Opns. Res. 15, 71–82 (1967), and 17, 756 (1969)].

A Precedence Graph Algorithm for the Shop Scheduling Problem

Abstract: This paper is concerned with the development of a precedence graph algorithm for solving certain combinatorial problems. This algorithm is applied mainly to job-shop scheduling problems; however, the extension of its applicability can be demonstrated by considering project scheduling, travelling salesman and explosion problems. The algorithm employs linear graphs to construct the quantified precedence matrix, a powerful criterion to resolve the conflict between the tied operations, and the use of a quasi-Boolean procedure to evaluate the obtained sequence.

Optimal flowshop scheduling with due dates and penalty costs

Abstract: The classical n-job, M-machine flowshop scheduling problem is considered where jobs are to be delivered by certain pre-assigned due dates, failing which there is some penalty cost associated with the time by which a job is delivered late. Based on the concepts of lexicographic search, an algorithm is presented for the solution of the problem under the assumption that the same ordering of jobs is followed on all machines and the penalty cost for any job is a non-negative and non-decreasing function of time by which the job is late.

Integrated circuit shop simulation for capacity planning and scheduling

Abstract: A large flow shop with cycling has been modeled with GASP II in an effort to study the effects of scheduling rules and capacity constraints. Consisting of multiple codes requiring 150-175 operations on 55 facilities, the shop, an integrated circuit line, was previously simulated in Fortran IV for the express purpose of determining the frequency of input messages to a shop information system. However, the Fortran IV model did not possess enough flexibility or efficiency for doing further analysis. By utilizing GASP II and its list processing techniques, shorter running times and implementations of scheduling algorithms could be achieved in a compact manner. The GASP II model is also capable of handling rework loops, yield distributions for each facility, priority assignments, and multiple channels per facility. Ultimately the model will have application for production scheduling in an on-line, real-time shop information system.

A New Approach to Job Shop Scheduling with Due Dates

Abstract: : The classical formulation of the static job shop scheduling problem with job due dates implies that the question of interest to the manager is: What is the best that can be done to meet due dates with fixed resources. In this paper, two alternative formulations of the problem are proposed; one because of its practical appeal, the other because of its methodological appeal. The latter is used to develop a multi-pass heuristic scheduling procedure aimed at providing a practical tool for attacking any of the three formulations of the problem. The procedure was programmed and applied to a set of nineteen test problems for which solutions satisfying all job due dates are known to exist. The problems range in size up to 10 jobs, 9 machines and 14 jobs, 7 machines. Solutions were attained for each of the test problems. The average and maximum IBM 360-91 computing times were 1.23 and 3.28 seconds, respectively. (Author)