Establishment of Linear Sequences

Abstract

This paper deals with the sequencing problem as an initial step to the study of production system. Sequence may be classified roughly into linear sequence and compound sequence. This paper descrives the systematical method of establishing linear sequences and the problem of minimum transition value as an example of determining an optimum linear sequence. The points to analyze the former are as follows : (1) The representative method of precedence relations. (2) The systematical method of establishing linear sequences. (3) The total number of feasible linear sequences. For these purposes, the fundamental matrix which makes precedence diagram into the form available to theoretical analysis, sequential product as the operational method by which precedence relations can be handled rationally, and then the linear product by which all of the feasible sequences can be established without overlapping have been introduced. Sequences are established easily, systematically and very mechanically by linear product. The technique to pick out the suitable sequences from tremendous feasible sequences is substantial to solve the latter. For this purpose, the concept of Lower Bound has been introduced. The algorithm can assure optimality. It can cope with the case of limitation in calculation time, and gives a suitable approximate solution.