This paper describes a simple algorithm for the solution of very large sequence problems without the use of a computer. It produces approximate solutions to the n job, m machine sequencing problem where no passing is considered and the criterion is minimum total elapsed time. Up to m − 1 sequences may be found.

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A flowshop sequencing problem having an ordered processing time matrix is defined. Job and machine characteristics resulting in processing time relationships that have logical and practical bases are discussed. An optimizing solution procedure for a special class of ordered matrix problem is presented along with proof of optimality.

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.