Product Mix Decision Under Constraints
Pattern: A named solution to a recurring problem.
Rank products by throughput per unit of constraint capacity, then fill the scarce capacity in that order before checking the full T-I-OE effect.
Also known as: P&Q problem, throughput per constraint-unit ranking, T/CU ranking
A product-mix decision is where Throughput Accounting stops being vocabulary and starts overruling the spreadsheet. A plant has more demand than the constraint can handle. The sales report says one product has the better margin. The TOC calculation says another product deserves the scarce constraint minutes. Both rankings can be arithmetically coherent, but only one respects the resource that limits the system.
Understand This First
• Throughput Accounting — the T-I-OE decision frame this pattern applies.
• Throughput — the numerator in the ranking.
• Constraint — the resource whose capacity makes the ranking necessary.
• Capacity-Constrained Resource (CCR) — the usual denominator when a tight resource is not yet the system constraint.
Context
The pattern lives in the Performance Measures section because product mix is where the cost world and the throughput world visibly part company. Throughput Accounting refuses allocated unit cost. Cost-World vs. Throughput-World Thinking names the paradigm conflict. The Product Mix Decision is the simple operating call that makes the conflict testable: which products should consume the constraint this week?
The context is narrower than ordinary assortment planning. This pattern applies when demand exceeds the capacity of one internal constraint, or when a CCR is tight enough that accepting the wrong mix would compromise throughput. If the system doesn’t have an active capacity constraint, the T/CU ranking is the wrong tool. If the system has multiple interactive constraints, the simple ranking is only a first pass. The final decision still comes from the total change in throughput, inventory, and operating expense.
That boundary matters. The TOCICO Dictionary cautions that T/CU should not be used alone. Budd’s TOC Handbook chapter makes the same practical point: the ranking gets the analyst to the right candidate mix quickly, but the final answer is the mix’s total T-I-OE effect.
Problem
Constrained systems usually have more profitable-looking demand than the constraint can serve. Sales wants to protect the product with the highest price. Accounting wants to protect the product with the highest gross margin or lowest allocated unit cost. Operations wants to protect the sequence that keeps the constraint running.
Those rankings can disagree. The high-margin product may consume so much constraint time that it earns less money per scarce minute than a lower-margin product. Filling the constraint with the wrong product mix can make the cost report look sensible while leaving total throughput on the table. The decision is easy to defend in the wrong vocabulary: it followed the margin ranking, so it looks financially disciplined. The problem appears when the period closes and the plant has earned less money than it could have.
Forces
• Constraint time is the scarce resource. Every minute assigned to one product is unavailable to another product.
• Unit margin is visible and politically familiar. It is usually the number the operating review already trusts.
• The constraint can shift. A product-mix change can overload a secondary resource if protective capacity is too thin.
• Demand is not proof of desirability. A customer will buy the product, but the system still has to decide whether that sale is the best use of constraint time.
• The calculation has to survive accounting review. The recommendation must be expressible in T, I, and OE, not only in shop-floor intuition.
Solution
Use throughput per constraint-unit as the first-pass ranking.
For each product competing for the constraint, compute unit throughput as selling price minus totally variable cost. Then divide that unit throughput by the amount of constraint capacity the product consumes. The resulting ratio is T/CU: dollars per constraint-minute, dollars per constraint-hour, shelf dollars per constrained shelf-foot, or whatever unit represents the scarce capacity in the system.
Rank products from highest T/CU to lowest T/CU. Fill available constraint capacity in that order until the constraint is loaded or demand is exhausted. Then run the full decision check: total throughput from the mix, inventory or investment required to support it, changes to operating expense caused by the decision, and any effect on non-constraint protective capacity. If the simple ranking would shift the constraint or cause a secondary resource to fail, don’t treat the ratio as final.
The discipline is a direct application of the Five Focusing Steps. Step 2 asks the system to exploit the constraint, which means putting the constraint’s available time on the work that generates the most throughput. Step 3 asks non-constraints to subordinate, which means their local preferences cannot override the mix that protects the constraint. The product-mix decision is where those two steps meet the finance report.
How It Plays Out
The simplest version uses two products and one binding machine. Product A sells for $120, has $60 of totally variable cost, and requires 12 minutes on the constraint. Its unit throughput is $60, so its T/CU is $5 per constraint-minute. Product B sells for $90, has $50 of totally variable cost, and requires 4 minutes on the same constraint. Its unit throughput is only $40, but its T/CU is $10 per constraint-minute.
| Product | Price | TVC | Unit T | Constraint Minutes | T/CU |
|---|---|---|---|---|---|
| A | $120 | $60 | $60 | 12 | $5/min |
| B | $90 | $50 | $40 | 4 | $10/min |
If the plant has 1,600 constraint minutes and enough demand for 200 units of each product, the unit-throughput ranking puts A first. That fills almost the whole constraint with 133 units of A and earns about $7,980 of throughput. The T/CU ranking puts B first, uses 800 minutes to make 200 units of B, then uses the remaining 792 minutes for 66 units of A. That mix earns $11,960 of throughput before OE.
Same demand. Same prices. Same machine. The difference is the denominator.
Budd’s TOC Handbook chapter gives the certification-grade version of the same lesson. Her adaptation of Goldratt’s P-Q problem uses three products, a shared Resource 2 constraint, and several accounting rankings. The throughput ranking uses Resource 2 minutes and produces the best operating income. Traditional gross profit, traditional contribution margin, and activity-based cost rankings all select different priorities because they don’t recognize the constraint as the scarce resource.
The pattern generalizes cleanly outside manufacturing, but only if the unit of constraint capacity is chosen honestly. In Wadhwa’s healthcare example, doctor time is the denominator; procedures that look attractive by fee can rank lower once their doctor-hour consumption is counted. In distribution, constrained shelf space or cash can become the denominator. In software, the denominator may be the scarce review, architecture, security, or release-window capacity that gates business-value delivery. The arithmetic travels; the unit must be real.
Do Not Stop At The Ratio: T/CU is a ranking, not a final business case. Before acting, check the total move in throughput, inventory, and operating expense, and verify that the selected mix does not move the constraint to a resource with too little protective capacity.
Consequences
Benefits
• The constraint works on the demand that produces the most throughput per scarce unit.
• The product-mix decision becomes defensible against a margin-ranking spreadsheet because the denominator is explicit.
• The calculation exposes policy errors, especially sales incentives that reward revenue while consuming constraint time badly.
• The result gives DBR, S-DBR, and throughput budgeting a shared finance language.
Liabilities
• The pattern depends on a correct constraint diagnosis. If the wrong resource is used as the denominator, the ranking is false precision.
• The simple ranking assumes one active constraint. Interactive constraints usually require a full mix model, often with linear programming or a direct T-I-OE scenario comparison.
• Product mix can shift the constraint. A ranking that overloads a secondary resource can destroy the very gain it predicted.
• TVC data must be clean. If labor or overhead has been smuggled into TVC, the numerator has already been pulled back into cost-world arithmetic.
• The ranking can provoke organizational resistance because it often tells sales and accounting to favor the product that looks less attractive by their familiar measures.
Related Articles
Complements: Traditional Financial Measures and Their Dilemmas — Traditional Financial Measures and Their Dilemmas explains why the margin and unit-cost rankings that product-mix decisions often inherit are unreliable in constrained systems.
Depends on: Capacity-Constrained Resource (CCR) — A capacity-constrained resource often supplies the denominator in the T/CU calculation and determines which product consumes the scarce minutes.
Depends on: Constraint — The pattern applies only when a binding constraint or capacity-constrained resource makes one unit of capacity scarcer than the others.
Depends on: Operating Expense (TOC Definition) — The calculation works because operating expense is treated as a system-period figure, not allocated into each unit before the ranking is made.
Depends on: Throughput — The ranking uses throughput in the TOC sense, revenue through sales minus totally variable cost, not production volume or allocated gross margin.
Depends on: Throughput Accounting — The product-mix ranking is a Throughput Accounting calculation: throughput per constraint-unit is meaningful only inside the T-I-OE decision frame.
Implements: Five Focusing Steps — The product-mix decision implements exploitation and subordination by deciding what the constraint should work on first.
Prevents: Cost-World Thinking — Ranking by throughput per constraint-unit prevents the cost-world trap of filling scarce constraint time with products that look profitable only under allocated-cost arithmetic.
Tests: Cost-World vs. Throughput-World Thinking — The product-mix decision is the practical test case for the cost-world and throughput-world paradigm split: the two rankings can disagree on the same demand data.
Sources
• Cox, TOCICO Dictionary (2nd ed., 2012), entries “throughput per constraint unit (T/CU)” and “PQ problem” — the certification-grade definitions, cautions, and simple example this entry cross-checks against. The Dictionary is distributed through TOCICO membership rather than the trade book channel and does not carry an Open Library record.
• Cox and Schleier, Theory of Constraints Handbook (2010), Ch. 13 (Budd, “Traditional Measures in Finance and Accounting, Problems, Literature Review, and TOC Measures”) — the canonical contemporary treatment of the product-mix ranking, including the three-product adaptation of Goldratt’s P-Q problem and the comparison against traditional gross profit, contribution margin, and activity-based cost rankings.
• Goldratt, The Haystack Syndrome (1990) — the original book-length Throughput Accounting source for the P-Q problem and the broader argument that product-mix decisions must be made against the system constraint rather than against allocated unit cost.
• Goldratt and Cox, The Goal (1984) — the originating business-novel treatment of the constraint, the NCX-10, and the move from local efficiency to constraint-based scheduling; the product-mix logic is the financial form of the same exploitation discipline.
• Corbett, Throughput Accounting (1998) — practitioner treatment of product-mix, make-versus-buy, and special-order decisions in the Throughput Accounting frame.