It is shown how Lawler's procedure for the one-machine case can be combined with Johnson's rule to produce a branch-and-bound algorithm for the two-machine version.

N jobs are to be sequenced on a single machine, each job carrying a penalty cost which is a quadratic function of its completion time. The objective is to find a sequence which minimizes the total penalty. Criteria are developed for ordering a pair of adjacent jobs in a sequence and these are...

Each of n jobs is to be sequenced on m machines, with each job having a due date, and we wish to minimise the maximum tardiness of any job. The problem has been solved by Smith [Smith, W. E. 1956. Various optimizers for single-state production. Naval Research Logistics Quarterly 3 59-66] for the...