Development of M-Stage Decision Rule for Scheduling N Jobs Through M Machines

Abstract

This paper describes an algorithm that will yield an optimum sequence for n jobs requiring processing through M machines when no passing is allowed. Theoretical development utilizing combinatorial analysis precedes the algorithm and an example problem.

Adaptive Production Scheduling and Control in One-Of-A-Kind Production

“…Dudek and Teuton extend Johnson's combinatorial approach to n-job m-machine flow shop problems to min(C max ) (Dudek & Teuton, 1964), comparing the same two sequences as in Johnson's proof, and then develop their dominance conditions. Dudek and Teuton began the analytical framework for the development of dominance conditions for flow shop scheduling, although their initial method is shown to be incorrect later (Karush, 1965).…”

Scheduling flexible flow lines with sequence-dependent setup times

“…The basic idea is that alternatives are compared and one chosen based on the results of these simple comparisons. Dudek and Teuton (1964) developed a multistep algorithm for M machines that uses comparisons to select jobs and the satisfaction of certain conditions to determine the placement of those jobs. Gupta (1972) described three of these types of algorithms, building on Smith and Dudek's work and Johnson's Rule for two machines.…”

A heuristic algorithm for the flowshop scheduling problem

“…Then, following the physical constraints of the problem (non-simultaneous processing of a job on two or more machines and non-simultaneous processing of two or more jobs by the same machine) and the assumptions outlined by Dudek and Teuton [6], the recursive relation for the completion time of the partial séquence a a of length (A:+l) at machine m, T(o a, m), is as foliows [4,8,9]:…”

“…Subséquent developments in scheduling theory have been extensions of Johnson's formulation, in that the number of machines is increased to the gênerai case M (M ^ 3). Recently, there has been considérable interest in finding suitable mathematical techniques to solve the flowshop scheduling problem and substantial progress has been made in the development of efficient algorithms for obtaining optimal or near-optimal solutions to the flowshop scheduling problems ( [1][2][3][4][5][6], [8][9][10][11][12][13][14][15][16][17][18][19][20][21]). In all the algorithms, several restrictive assumptions are made, the complete statement of these assumptions is provided by Ashour [1] and Dudek and Teuton [6] and hence is not repeated here.…”