A General Algorithm for Solution of the n-Job, M-Machine Sequencing Problem of the Flow Shop

Abstract

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

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

“…Smith and Dudek correct Dudek and Teuton's combinatorial approach, by introducing partial enumeration into dominance conditions (Smith & Dudek 1967). They propos two checks of dominance conditions.…”

Flowshop scheduling research after five decades

“…The first paper of this decade is difficult to identify as there are several papers that appeared around the same time. The combinatorial approach started by Dudek and Teuton (1964) was corrected and improved by Smith and Dudek (1967), McMahon (1969), Gupta (1971), and Szwarc (1971Szwarc ( , 1973. The branch and bound solution approaches were also developed during this time by Lomnicki (1965), Brown and Lomnicki (1966), McMahon and Burton (1967), Gupta (1969bGupta ( , 1970, and others.…”

A Research Methodology for Studying Complex Service Systems

“…The earliest work centered upon abstractions of certain job shop type production sequencing problems as static and deterministic combinatorial ~roblems. Extensive research3 has been devoted to these combinatorial problems leading to extremely limited exact results (8) for small-scale systems and a number of algorithms for feasibly generating approximate solutions for large-scale systems (4), (12), (14). Dissatisfaction with the static and deterministic This work was principally supported by the Office of Naval Research under Task 047-003, and partially by the Western Management Science Institute under a grant from the Ford Foundation.…”