An Algorithm for Solving Job Sequencing Problems

The technique described in this paper was devised for sequencing jobs on individual machines having characteristics of: (1) high job changeover costs; (2) small backlogs (10-20 jobs); (3) occasional “rush” orders.

The algorithm starts with four-job sequences and from these constructs five-job sequences; from the five-job sequences, six-job sequences are constructed, and so on. At each stage, a large fraction of sequences are eliminated from further consideration. This elimination process makes the computation feasible because the number of all possible sequences becomes unmanageably large, even for small problems.

The technique always provides a minimum cost sequence. It also permits determination of optimum sequences of backlog sub-sets; thus, rush orders can be accommodated and anticipated changes in the job backlog can be recognized.