Appendix: illustrative operating models

The frozen studies are distinct authored comparisons and boundary cases. Each retains its input, full output, scalar bindings, purpose, changed conditions, held-constant conditions and limitations. They are not actual project observations. Their role is to demonstrate how the canonical method responds and where its result requires a separate operating decision. A reader can open the exact bundle in the companion app and compare a recomputed result with the manuscript.

The operating-reference case establishes the common capability slate. The weak-ownership and weak-data studies each change one readiness judgment. The operations-ready study changes only the operations readiness judgment. The effort-constrained and budget-constrained studies each change one resource envelope. These controlled changes make the interpretation sharper than a collection of unrelated attractive examples. The author can identify which declared assumption caused the difference while retaining the rest of the slate.

The remaining cases use independent authored structures for particular boundaries. Zero-envelope retains the reference capabilities but removes the cost and effort envelopes. Zero-benefit-enabler tests a prerequisite with no direct annual benefit. Greedy-trap and feasible-alternative expose a better feasible additive combination missed by the original menu's first greedy choice. These cases challenge the method itself and its presentation, rather than merely confirm that sensible-looking inputs produce a plausible-looking recommendation.

The selection table presents totals with explicit units. Cost is USD thousands, effort is person-months and adjusted assumed annual benefit is USD thousands per year. Selected capability names are exact readings of the frozen outputs. The complete initial rankings and marginal step records remain in the JSON bundles. The table is a reading aid, not a substitute for those records or their limits.

A comparison should retain its scope when used in a briefing. The weak-ownership result does not show that weak authority is acceptable. The operations-ready result does not show that readiness improved. The effort-constrained result does not identify an actual staffing plan. The counterexample does show a feasible higher-benefit additive combination under its authored assumptions, because both option costs and the shared envelope are retained. These distinctions make the cases useful evidence about a method rather than fabricated evidence about an enterprise.

Weak-ownership lowers only the ownership readiness judgment. It retains the same final data, ownership, exception and planning selection, while adjusted assumed annual benefit becomes 231.70 USD thousands. The reference value is 251.65 USD thousands. The unchanged selection is central to the interpretation: a multiplier reduces a quantity but cannot create a categorical refusal condition. A real missing delegation must be addressed in the operating decision record.

Illustrative. Weak-data similarly keeps the same selected set while adjusted assumed annual benefit becomes 230.05 USD thousands. Data-dependent planning remains selected because the declared graph and resource ranking still permit it. That is not a quality acceptance. A sponsor should retain the use-specific data gate and decide whether the available evidence permits the intended commitment. The exact calculation is useful because it demonstrates how a low readiness score can coexist with selection.

Operations-ready changes the later bundle and exhausts the declared effort envelope. Its remaining effort is 0.00 person-months and remaining budget is 50.00 USD thousands. The result shows a sensitivity-driven switch under a fixed full envelope. It directs attention to the assumed readiness of operations, but does not supply that evidence. In chapter nineteen the uplift is rejected as an approval basis while remaining a valid sensitivity case.

These cases also reveal a modelling omission that matters to operating design. Lowering data or ownership readiness changes their direct adjusted benefit. It does not automatically reduce every dependent capability's benefit or enforce an acceptance gate on the dependent service. The author must not assume such propagation merely because an arrow exists. If the intended proposition requires a changed dependent benefit or a different scope, that must be declared in a separate comparison input.

The practical lesson is to document what each multiplier actually does. A sponsor should be able to distinguish a scalar assumption, a hard prerequisite and a mandatory acceptance condition. The app implements the first two within its narrow method. The third belongs to the authorised operating record. The frozen cases supply an exact demonstration of why combining the categories into one maturity colour can mislead a decision.

Effort-constrained and budget-constrained select the same capabilities but leave different resources. The effort case retains budget 230.00 USD thousands and effort 0.00 person-months. The budget case retains budget 30.00 USD thousands and effort 16.00 person-months. Their identical names should not conceal distinct causes. An intervention directed at more funding does not address an exhausted declared effort envelope, and an intervention directed only at capacity does not resolve a cost constraint.

Illustrative. Zero-envelope returns total cost 0.00 USD thousands, total effort 0.00 person-months and adjusted assumed annual benefit 0.00 USD thousands. The selected set is empty. This is a valid conditional outcome, not a failed computation or a recommendation that the enterprise has no useful capabilities. It states that no positive bundle can be selected under the authored unavailable envelopes. A real mandatory obligation would need an authorised resource or scope decision outside that result.

Illustrative. Zero-benefit-enabler selects ROOT and VALUE. ROOT has no direct benefit and no cost in the authored input, but requires effort and is a prerequisite for VALUE. The complete selected bundle costs 100.00 USD thousands, requires 7.00 person-months and yields adjusted assumed annual benefit 200.00 USD thousands. The case demonstrates that the target closure can include an enabler whose standalone benefit is absent. It does not imply that all governance or identity work has zero real cost.

The boundary also challenges a superficial benefit ranking of individual rows. A prerequisite can be necessary for a valuable target even if its own direct effect is difficult to monetise. The app includes it because the author declares a hard dependency. The operating record should still explain the dependency and the cost scope. A zero-cost authored row is an assumption, not a licence to treat real authority or maintenance work as free.

The cases show why valid zero and null states need informative presentation. An empty selection, a zero benefit and a null ratio are distinct meanings. Replacing them with an upbeat generic recommendation or an unqualified score would reduce the transparency of the method. The reader should retain the output's actual state and use the operating record to decide whether resources, scope or a different method must change.

Greedy-trap selects A, whose cost is 6.00 USD thousands and adjusted assumed annual benefit is 12.00 USD thousands. The remaining budget is 4.00 USD thousands. B requires 5.00 USD thousands and C requires 5.00 USD thousands, so neither fits individually after A is selected. The engine's first choice therefore blocks both smaller alternatives under the remaining envelope.

Illustrative. Feasible-alternative removes only A. B and C then fit together under the unchanged budget, costing 10.00 USD thousands and yielding adjusted assumed annual benefit 19.80 USD thousands. The comparison is causal within the declared deterministic method: the highest first ratio consumes budget in a way that prevents the better combined alternative. No uncertainty, overlap or dependency difference is needed to produce this failure.

The counterexample does not prove that every greedy result is poor. The reference may be useful as a transparent candidate, and the heuristic's simplicity can make its reasoning easy to inspect. The case proves the narrower and important proposition that the method does not guarantee the largest additive benefit under the declared envelopes. A reader should not label its result globally optimal. That would be contradicted by an actual retained feasible comparison.

The author also avoids claiming that the restricted alternative is an optimisation algorithm. It is a deliberately supplied menu demonstrating a feasible set. The engine executes that menu exactly. A rigorous optimiser for a different decision would need its own objective, constraints, method and review. The operating synthesis can accept the counterexample as a reason to challenge a candidate without pretending that the current tool has solved the broader portfolio problem.

The full slate therefore demonstrates advantages and limits together. It exposes marginal resource use, clarifies the effect of assumptions and makes a greedy failure reproducible. The companion app remains a useful analytical instrument when the sponsor respects that scope. The manuscript's commitment record then determines what can be accepted, held, revised or rejected on the available evidence.

Two additional complete miniature studies isolate decimal resource admission. The positive-commitment case supplies the minimum supported positive cost and effort beneath zero envelopes. Its capability has positive adjusted assumed benefit, but neither resource may be credited as free. The equality case supplies a foundation and its receiving-service prerequisite relationship whose decimal costs and efforts exactly exhaust the stated envelopes. Both can be admitted without a negative remainder. These cases challenge only the resource account; their benefits, effort and costs remain authored assumptions. The complete input and JSON output accompany each study so a reader can inspect exact decimal resource strings rather than infer feasibility from a rounded chart.