The transition-point method to meet due-dates and minimize the make-span in the general job-shop sequencing problem∗

Abstract It is illustrated that no solution exists at any make-span below the minimum, but that a solution exists at all make-spans at and above the minimum, so that to find the minimum make-span, it is merely necessary to find the transition-point. The method uses a job-proeess-time matrix, which is not unlike a Gantt chart, to determine whether a solution exists at a particular make-span. Various make-spans are tested in a procedure that rapidly converges on the minimum. Due-dates are one kind of constraint applicable to the job-process-time matrix. The procedure can be used to solve problems with due-dates, repeated processes, passing, labour shortages, machine maintenance, limited floor space, initial work in progress, suspended processing and so on.