Choose a service mix when two different skills limit delivery

A service business can have enough total staff hours and still lack the combination of skills needed to deliver its preferred work. Ranking jobs by contribution per analyst hour may exhaust reviewers first. Ranking by reviewer hour can create the opposite problem. When both resources constrain delivery, model them together.

ACCA's linear-programming guidance describes maximizing contribution subject to resource constraints and interpreting the value of relaxing a constraint. The example below applies that method to two service packages. It is a simplified planning calculation, not a staffing benchmark or a substitute for an actual delivery schedule.

Use contribution that changes with the package delivered. Keep unchanged fixed operating costs outside the comparison while preserving them in the full profit plan. Include any job-specific contractor, travel or other variable cost before calculating the contribution available to cover those fixed costs.

Suppose an invented team sells a detailed-review package, X, and a specialist-assessment package, Y. Each X requires two analyst hours and one reviewer hour, producing $300 of contribution. Each Y requires one analyst hour and two reviewer hours, producing $400 of contribution.

The period has 80 usable analyst hours and 70 usable reviewer hours after other committed duties. Assume sufficient qualified demand for the combinations being compared, consistent quality and no additional setup time. These assumptions matter: the model can allocate only work the business can actually sell and deliver.

The analyst constraint is 2X + Y no greater than 80. The reviewer constraint is X + 2Y no greater than 70. Both quantities must be nonnegative. The objective is to maximize $300X + $400Y while satisfying both limits.

If the same employee supplies both skills, those hours cannot be counted twice as independent capacity. Add the shared time restriction or assign the person's available hours consistently. Skill labels do not create additional working time, even when the employee can perform either task.

Producing only X permits 40 packages before analyst capacity is exhausted. That plan uses 40 reviewer hours and produces $12,000 of contribution. Producing only Y permits 35 packages before reviewer capacity is exhausted, using 35 analyst hours and producing $14,000.

The two resource limits intersect where 2X + Y equals 80 and X + 2Y equals 70. Solving those equations gives X equal to 30 and Y equal to 20. That mix uses all 80 analyst hours and all 70 reviewer hours, producing $17,000 of contribution.

For this two-variable linear model, checking the feasible corner points establishes the best modeled contribution. The zero-work corner contributes nothing, and the mixed corner beats both single-service plans. These quantities are also whole packages, so this particular optimum does not require rounding fractional jobs.

Per analyst hour, X contributes $150 and Y contributes $400. An analyst-only ranking favors Y, but the all-Y plan leaves 45 analyst hours unused because reviewers run out first. Per reviewer hour, X contributes $300 and Y contributes $200, so that ranking favors X and leaves 30 reviewer hours unused.

The mixed plan uses the two resources in a better combination. It gives up some of the service favored by each separate ranking to avoid stranding the other skill. The improvement comes from the resource relationships, not from changing the stated package contribution.

A single-resource ranking can still be appropriate when only one resource binds and the others have enough capacity. The point is to establish which constraints actually limit the proposed plan. Do not add mathematical complexity where a verified single bottleneck already answers the question.

Suppose three additional analyst hours become available while reviewer capacity stays at 70. The revised intersection is 32 packages of X and 19 of Y. Contribution rises to $17,200, a gain of $200 before the extra capacity's incremental cost.

Three additional reviewer hours instead, with analyst capacity unchanged, allow 29 packages of X and 22 of Y. Contribution becomes $17,500, a gain of $500. Around the original optimum, the implied resource values are about $66.67 per analyst hour and $166.67 per reviewer hour.

Those values depend on the objective's cost definition. In this example, regular staff salaries are unchanged and the contribution figures exclude any payment for new capacity. Compare the full additional cash cost of that capacity with the modeled gain. If a model already includes a normal variable resource charge, avoid charging that same amount twice when assessing a premium.

A local resource value does not remain valid for unlimited additional hours. Eventually another constraint, demand limit or zero quantity can change which plan is optimal. Re-solve the actual proposed capacity package rather than multiplying a local shadow value by an arbitrarily large purchase.

Indivisible work and minimum commitments can also matter. A fractional solution may be mathematically valid for divisible activity but impossible for complete customer engagements. Use an appropriate integer model or compare feasible whole-job alternatives where the distinction changes the result.

Check whether the extra specialist hours are usable at the right time. A reviewer available after the promised delivery date does not relax this period's constraint. Supervision, rework, handoffs and a contractor's required onboarding can consume capacity that the simple coefficients omit.

Confirm demand limits, client commitments and any minimum service obligations before adopting the calculated mix. A strategically important contract may justify a different plan, but show its contribution cost explicitly. The financial model informs that choice without pretending all commercial consequences fit its objective.

Retain the approved package definitions, capacity dates and cost assumptions. Compare actual effort with the modeled hours after delivery and investigate changes in complexity or rework. A useful optimization remains connected to the work: it explains which combination can be delivered, what it contributes and what additional capacity would change.