Sequencing Jobs Through a Multi-Stage Process in the Minimum Total Time—A Quick Method of Obtaining a Near Optimum

In the situation where a number of items must pass through a number of processes in the same order, it is suggested that the optimum (minimum total time) scheduling may be approximated by giving priority to items according to the extent to which process time increases with process number in order; this criterion is put in arithmetical form. This is confirmed by (a) a simple geometrical argument; (b) comparison with the known optimum schedules of a number of published three-process cases; (c) experiments on larger cases; it is not practical here to find the exact optimum. Methods are given for obtaining lower bounds which all scheduling times must equal or exceed; besides placing limits on the amount of effort to be expended, these bounds support the suggested approximate method.