Minimum total coefficient based on adjacency matrix of the single machine scheduling

This paper addressed a single machine scheduling problem that minimum total coefficient based on adjacency matrix, the adjacency matrix is represented the affection coefficient that one job is processed before another job in the scheduling sequence. Modeling the problem of the mathematics, two theorems of optimal solutions are described for special condition of the problem. An enumeration algorithm by using property 2 is addressed. Four heuristic algorithms and an Interchange rule are described. A numerical example is described to demonstrate the problem at last.