Stochastic sequencing with job families, set-up times, and due dates

We consider the problem of allocating a single server to families of jobs with random service times and due dates. Furthermore, a set-up is required when the server switches from one job family to another. We address the problems of minimizing expected weighted flow time, expected maximum lateness, and total weighted tardiness with emphasis on problems for which it is assumed that each family can be set up only once (the Group Technology assumption). We derive conditions under which simple sequencing rules are optimal for each of these problems with group technology.