CM Per Constraint Unit — Use contribution margin per unit of constraint to prioritize products (intro)

Every firm faces limits—machine hours, labor hours, raw materials, or warehouse space—that prevent it from producing unlimited quantities of every product in its portfolio. For much of early industrial history, managers relied on intuition or simple rules of thumb to decide which products deserved scarce capacity. A product with a higher selling price often received priority, even when it consumed a disproportionate share of the bottleneck resource. The result was sub-optimal profits and, in many cases, outright losses on specific product lines that appeared lucrative but devoured the constraint. The evolution of contribution margin analysis and, later, Theory of Constraints (TOC) formalized a remarkably powerful yet simple idea: rank products not by their total contribution margin per unit, but by the contribution margin they earn per unit of the binding constraint.

The central question that this concept addresses is deceptively straightforward: When capacity is limited, which products should a firm produce more of, and which should it scale back? As we will see, the answer hinges not on the product with the highest per-unit contribution margin, but on the product that squeezes the most contribution margin out of every scarce unit of the binding constraint.

Before diving into calculations, it is essential to anchor the discussion in a few foundational ideas that underpin every product-mix decision under a single binding constraint. Each principle builds on the previous one, culminating in the decision rule that drives optimal prioritization.

The diagram below illustrates the core decision logic. Three products compete for a single binding constraint—machine hours. Although Product B has the highest CM per unit, Product A generates the greatest CM per machine hour and therefore receives top priority in the optimal product mix.

The visual makes a critical lesson concrete: a product's apparent profitability (measured by CM per unit) can be misleading when a scarce resource is involved. The CM per constraint unit metric strips away that illusion by normalizing each product's contribution to the common denominator of the bottleneck. Once ranked, the firm allocates available constraint capacity to the top-ranked product first, filling demand up to its ceiling, and then moves to the second-ranked product, and so on, until the constraint is exhausted.

The mathematical structure of this technique is intentionally accessible, requiring only basic arithmetic once the relevant data have been gathered. Three equations form the analytical backbone, and a fourth expression captures the optimal allocation procedure.

Knowing how to compute CM per constraint unit is necessary but not sufficient; the real payoff comes from applying the ranking to build an optimal production plan. The following diagram walks through the sequential allocation procedure, which mirrors how firms actually schedule production when capacity is tight.

A common error students make is allocating constraint proportionally across products rather than sequentially. Proportional allocation sounds fair, but it sacrifices total contribution margin because it diverts scarce capacity away from the most profitable use per constraint unit. The greedy sequential method is mathematically guaranteed to maximize total CM when there is exactly one binding constraint and demand ceilings are known.

Greenfield Manufacturing produces three products—Alpha, Beta, and Gamma—using a single production line. The binding constraint is machine hours, of which 2,400 hours are available per month. The following data are provided:

Like every managerial tool, CM per constraint unit analysis carries both powerful advantages and important limitations that practitioners must understand before applying it. The table below contrasts the technique's strengths against its boundary conditions.

The introductory CM per constraint unit technique sits at the foundation of a broader family of constrained optimization tools. Understanding where this method ends and more sophisticated tools begin is essential for advanced coursework and real-world applications.

In subsequent coursework, you will encounter scenarios with two or more binding constraints—for example, both machine hours and direct labor hours might be scarce. In those cases, the simple ranking approach breaks down because producing more of the product ranked first on one constraint may consume excessive capacity on the second constraint. Linear programming resolves this by simultaneously satisfying all constraints and identifying the optimal corner-point solution on the feasible region. Goldratt's Theory of Constraints (TOC) extends the idea further by asking not just how to exploit the bottleneck, but how to elevate it—investing to increase bottleneck capacity so the firm can grow total throughput over time.