《2016 Scheduling jobshops with some identical or similar jobs》.pdf

JOURNAL OF SCHEDULING J. Sched. 2001; 4:177–199 (DOI: 10.1002/jos.072) Scheduling jobshops wit hsome identical or similar jobs† Tami Boudouk 1, Michal Penn1;‡ and Gideon Weiss2;∗ ;§ 1Faculty of Industrial Engineering and Management; Technion; Haifa 32000; Israel 2Department of Statistics; The University of Haifa; Mount Carmel 31905; Israel SUMMARY We consider the following job-shop scheduling problem: N jobs move throug I machines, along R routes, wit hgiven processing times, and one seeks a schedule to minimize the latest job completion time. This problem is NP-hard. We are interested in the case where the number of routes and the number of machines are xed, while the number of jobs varies and is large. We distinguis htwo cases: If jobs on the same route are identical we provide an approximation algorithm whic his within constant of the optimum, no matter how many jobs there are. If jobs on the same route have dierent processing times, the job-shop scheduling problem can be crudely approximated by a continuous deterministic uid scheduling problem, wit hbuers of uid representing the jobs waiting for eac hoperation. The uid makespan problem is easily solved using constant ow rates out of eac hbuer for the entire schedule, and the optimal uid makespan is a lower bound on the discrete optimal makespan. We describe two heuristics whic himitate the uid solution. We present some preliminary numerical results. Copyright ? 2001 John Wiley Sons, Ltd. 1. INTRODUCTION The scheduling of computer and manufact