Sections 9-11: Prove that unweighted mean completion time becomes
adversarial under priority classification (Theorems 8-10), propose
PWCT/WSJF as alternatives with a worked IT service desk example,
and present honest counterarguments establishing the narrow conditions
under which the unweighted metric remains defensible.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Sections 7-8: Prove that optimizing unweighted mean completion time
maximizes slowdown inequality (Theorem 4), maximizes satisfaction
variance across clients (Theorem 5), provides zero throughput gain
(Theorem 6), and therefore simultaneously degrades client experience
while failing to improve productivity (Theorem 7).
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Mathematical proof that unweighted average task completion time
is gameable by scheduling policy (SPT), while work-weighted
completion time is schedule-invariant. Demonstrates that SPT's
apparent advantage is an artifact of the metric, not genuine
throughput improvement.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Mortdecai