C.29.BB:5.2 - Moving and reworking a job preserve one count but change its distribution

Count accepted jobs that have not yet been completed. Each job occupies one of two stages, including any processing position in that stage. Initially A contains 6 jobs and B contains 4.

During an interval, 12 new jobs arrive at A, 9 move from A to B, and 7 are completed at B. With no other arrivals, completions or membership changes,

A at end = 6 + 12 - 9 = 9
B at end = 4 + 9 - 7 = 6
unfinished total at end = 10 + 12 - 7 = 15.

A limit of 12 unfinished jobs is therefore exceeded at the endpoint. Determining whether the limit was exceeded earlier requires the event history or a bound on its prefixes.

If 2 of B’s remaining jobs return to A for rework before the endpoint, the stage totals become 11 and 4; the unfinished total remains 15. The extra work is consequential, but moving the same jobs changes their distribution rather than their count.

If the question instead counts separately created work orders, specify that new population and its creation rule. A parent job and two newly opened orders cannot be mixed into the earlier job count without changing its meaning. The next operations-management question may need workload or completion-time modeling in addition to this balance.