Library / Operations Management Principles Framework
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OPS.9:5.2 - A narrow capacity treatment with a feasible witness

A different constructed service must finish five ready jobs within twelve hours. All upstream inputs are complete. Each job requires two hours of final verification and then ten minutes of certification; the certificate service has reserved slots after each possible verification completion. Acceptance requires both results, with no failures or rework in this stated scenario.

The verifier is available for eight hours. Verification completions occur at hours 2, 4, 6 and 8, so no more than four jobs can be accepted. Extra upstream processing capacity cannot change that bound: the five inputs are already ready.

The resource owner can supply two additional verifier-hours within the same twelve-hour horizon. With that change, the fifth verification completes at hour 10 and certification at hour 10 plus ten minutes. The comparison therefore returns a feasible five-job treatment candidate under the stated conditions. Its selection still uses the supplied resource cost, permission and protected consequences.

If certification availability later falls to two reserved slots, the old verifier treatment no longer supports five accepted jobs. The same result definition now exposes another limiting relation. Adding further verifier time cannot repair that missing certification capacity.