This paper considers a reentrant job shop with one hub machine which a
job enters K limes. Between any two consecutive entries into the hub:
the job is processed on other machines. The objective is to minimize
the total Bow time. Under two key assumptions, the bottleneck assumpti
on and the hereditary order (HO) assumption on the processing times of
the entries, it is proved that there is an optimal schedule with the
shortest processing time (SPT) job order and a dynamic programming alg
orithm is derived to find such a schedule. An approximation algorithm
based on the shortest path algorithm and the SPT job order is also pro
posed ro solve the problem. The approximation algorithm finds an optim
al clustered schedule. In clustered schedules, jobs are scheduled in d
isjoint clusters; they resemble hatch processing and seem to be of pra
ctical importance. Worst-case bounds for clustered schedules are prove
d with the HO assumption relaxed. Two special cases with the restricti
on that there are only two entries to the hub machine are further anal
yzed to offer more insight into the structure of optimal solutions.