Key takeaway
When a project must be completed as a whole, compare feasible combinations. The highest standalone contribution per hour need not produce the best total under the entered assumptions.
The four hours left over matter
An owner has ten reviewer hours available next week and three optional data projects competing for them. Project A has the largest contribution per reviewer hour. Choosing it feels efficient, but it leaves four hours that cannot complete either remaining project. The apparently strongest individual choice can therefore leave the business with a smaller total contribution.
The question here is which complete combination fits one scarce resource. A schedule for one project answers whether its dependencies can finish in time. An incremental-cost calculation answers which costs change if another license proceeds. This example takes those earlier decisions as inputs and tests a separate problem: selecting indivisible projects.
MIT’s 0–1 knapsack teaching model chooses zero or one of each item, within a total capacity, to maximize the entered values. That is a useful mathematical analogy. Real permissions, customer work and uncertain receipts remain outside an optimizer unless someone represents them honestly in the assumptions.
Price the same paid scenario for each option
Hypothetical example: three compatible, one-package licenses would all need the same internal reviewer next week. Assume their rights, named recipients and delivery feasibility have separately been resolved for this illustration. Each project must be completed in full; partial work earns no receipt. All money is GBP, and every amount is an invented planning input, not a buyer quote.
Preparation cash includes outside engineering and review. A separate fictional third-party delivery fee is payable only after that project completes and is paid. The reviewer’s salary is already committed for the week and is excluded from these incremental cash costs; the reviewer’s hours still constrain the choice. No recurring service, tax, financing or other external fee is entered.
| Project | Reviewer hours | Conditional receipt | Preparation; conditional delivery | Conditional contribution |
|---|---|---|---|---|
| A | 6 | GBP 1,300 | GBP 200; GBP 200 | GBP 900 |
| B | 5 | GBP 1,000 | GBP 150; GBP 150 | GBP 700 |
| C | 5 | GBP 1,000 | GBP 150; GBP 150 | GBP 700 |
Compare the combinations that actually fit
For the hypothetical projects, A contributes GBP 900 / 6 = GBP 150 per reviewer hour. B and C each contribute GBP 700 / 5 = GBP 140. A ratio ranking therefore places A first. After allocating its six hours, four remain; neither B nor C fits. The entered paid-outcome contribution is GBP 900.
B plus C uses all ten hours and produces GBP 1,400: GBP 2,000 receipts less GBP 300 preparation and GBP 300 conditional delivery. A plus either smaller project requires eleven hours. Taking all three requires sixteen. Enumerating the eight possible subsets leaves B+C as the unique maximum among the feasible combinations in this example.
ACCA explains scarce-resource return rankings in its limiting-factor teaching and distinguishes contribution from throughput return. Preserve that distinction when naming your figures. The original counterexample here adds an indivisibility condition; it does not claim that a production-mix ranking alone solves this different selection problem.
The conditional maximum is not an expected payoff
The result says what wins in the entered paid scenario. It supplies no probability that either license will happen. If B and C both fail to produce receipts after their preparation is spent, the hypothetical outflow is GBP 300; their conditional delivery costs do not occur. A’s corresponding no-receipt preparation exposure is GBP 200. Those downside amounts belong beside the paid totals.
Change the model if projects share preparation, compete for different specialists, require mutually incompatible grants or have different deadlines. Shared work makes simple addition unreliable. Divisible work may let a partial project use the remaining hours. A second capacity constraint can invalidate a combination that fits the reviewer alone.
Also ask what the reviewer would otherwise do for the core business. This example does not value displaced customer work or authorize sacrificing it. A computed maximum over an incomplete list of choices can still be a poor management decision.
Give the sponsor the combination, not just a rank
The completed choice card is concise: under the stipulated ten-hour capacity and full-payment assumptions, B+C fits and contributes GBP 1,400; A alone contributes GBP 900. It should retain the GBP 300 preparation exposure and every assumption that made the projects compatible. A changed assumption requires a new comparison.
The sponsor can now explain why B+C beats A within this model and what it risks before a receipt. Authorizing that combination remains separate from obtaining permission for any package or recipient. A computed rank should not be handed to an operator as a release instruction.