A Method of Solution for General Machine-Scheduling Problems

This paper proposes a general method of solution for problems, involving the allocation of jobs to machines and the sequencing of jobs on machines, in which a number of jobs, each consisting of a number of operations that may be performed on a given set of machines, is to be completed in some optimal fashion. Considering constraints on machine availability, job completion dates, and zoning, the paper demonstrates the underlying relation of a wide variety of machine-job problems with reference to their graphical representation, states a branch-and-bound method of solution, solves an illustrative example, and gives the mode of application to specific problems (for several of these the method reduces to methods published elsewhere). The algorithm represents not only a general framework of theoretical interest, but also a practical approach to certain specific problems.