Count usable hours
A full order book can leave you choosing what to make first. Start by checking which operation actually restricts output. Scheduled hours can disappear into downtime, changeovers and waiting for materials. Ask the people doing the work where time goes; compare their explanation with operating records before assuming another machine is needed.
BDC’s bottleneck guidance recommends measuring the causes. The hours below are stipulated, not verified factory capacity.
Fictional Canadian-dollar week: 100 usable machine hours; other resources initially unconstrained.
A: Per unit, price 200, incremental cost 120 and 2 machine hours. Sales ceiling: 50.
B: Per unit, price 150, incremental cost 90 and 1 machine hour. Sales ceiling: 60.
Count costs that change
Incremental costs here include every cost changed by producing another unit. Fixed spending stays unchanged, with no additional fixed outlay caused by this choice. Allocating existing overhead differently does not change the decision’s cash costs.
Existing payroll is not automatically an extra cost: available time and displaced work matter. ACCA’s relevant-cost guidance explains this distinction. The calculations measure contribution before unchanged fixed costs—not profit, cash receipts or business value.
Check the model’s limits
Prices, costs and unit times stay constant; resource use and contributions add together. Inputs are assumed known. This example excludes setup charges, batch minima, joint-product interactions and quantity discounts.
UT Dallas’s model explanation also distinguishes continuous variables, which allow fractions, from indivisible products. Our example checks whole units; rounding a fractional answer is not a substitute. If your production conditions differ, the model needs revisiting before its answer becomes useful.
Start with one constraint
Contribution per unit: A, 200 − 120 = 80; B, 150 − 90 = 60. Per machine hour: A, 80 ÷ 2 = 40; B, 60 ÷ 1 = 60.
Meeting both sales ceilings requires 160 hours. OpenStax’s constrained-resource method ranks B first here. Its 60-unit sales ceiling uses 60 hours; the remaining 40 permit 20 A. Contribution: 60 × 60 + 20 × 80 = 5,200.
Making 50 A first uses 50 × 2 = 100 hours for 50 × 80 = 4,000: 1,200 less.
All selected units sell at stated prices; there are no minimum-order or product-bundle commitments.
Now allow only 60 finishing hours, one per unit. The old 20 A/60 B mix needs 80: infeasible.
Add a second constraint
Seek the largest contribution, 80 A + 60 B, within:
Machine: 2 A + B ≤ 100.
Finishing: A + B ≤ 60.
Sales: A ≤ 50; B ≤ 60. Both quantities are whole and nonnegative.
The best mix fills both production resources: subtract A + B = 60 from 2 A + B = 100: A = 40, then B = 20.
Check: 2 × 40 + 20 = 100 machine hours; 40 + 20 = 60 finishing hours. Contribution: 40 × 80 + 20 × 60 = 4,400. Feasible alternatives: 50 A alone gives 4,000; 60 B alone gives 60 × 60 = 3,600. Ranking one resource alone no longer selects the best mix.
Turn the answer into a production plan
The calculated mix remains provisional. BDC’s production-planning guidance adds checks the arithmetic cannot supply: materials at the point of use, available tools and equipment, trained staff, and standard working times that fit the schedule. Long-lead materials, special tools or training may need arranging before work begins.
Check individual order priorities and allow for unexpected changes. Fully consuming a modeled resource does not establish that your actual reserve is sufficient; no universal buffer percentage follows from this example.
Once readiness is established, communicate the schedule to the people implementing it. Changed orders require a revised plan and communication, not just a new total in a spreadsheet.
Fictional decision record
Capacity — production lead. Basis: 100 usable machine hours. Unresolved: logs and downtime. Action: recompute if available time differs.
Costs — controller. Basis: incremental costs A 120 and B 90; fixed spending unchanged. Unresolved: cost completeness. Action: recalculate after additional spending.
Release — planner. Basis: provisional mix. Unresolved: inventory, tools, staffing, timing and reserve. Action: withhold release until checked; revise changed orders.
Model — operations analyst. Basis: constant, additive whole-unit model. Unresolved: production interactions. Action: reformulate if assumptions fail.
For general information and education, not legal, tax, investment or valuation advice. Examples are illustrative and do not predict your business’s value, financing terms or sale outcome. Consult qualified advisers about your situation.
Subscribe to Deal Flow Canada for practical owner guides and Canadian deal updates.