Single facility scheduling with major and minor setups

This article considers the problem of scheduling a given set of jobs at a single facility, where jobs can be grouped into different classes and these classes can be further grouped into different families. A major setup and a minor setup are required when jobs are switched from one family to another while only a minor setup is required when jobs are switched from one class to another within the same family. The minimum mean flow time schedule of this problem can be solved optimally by dynamic programming (DP), but the exponential behaviour of the DP solution precludes its use to solve problems with a large number of classes. An efficient heuristic is thus developed in which a sequence of two-class problems is solved. Computational results show that the heuristic produces solutions that deviate 0.118% on average from the optimum.