Bottleneck Product Mix with Demand Limits

Contribution per bottleneck hour helps prioritize products when one scarce resource limits output. It is only a starting point when products require separate setups or indivisible production quantities. A product with the better ongoing contribution per hour may still be unattractive in a small batch because introducing it consumes setup capacity. Compare complete feasible schedules, including the option of not introducing that product at all.

Worked decision model

Assume 100 machine hours are available. Product A contributes $40 per unit and uses two machine hours, giving $20 per constrained hour. Product B contributes $30 per unit and uses one hour, giving $30 per constrained hour after setup. Producing any B requires a ten-hour setup during the period; A's setup is already included in available capacity. Demand is at most 50 A units and 60 B units, with no other modeled constraint.

An A-only schedule produces 50 units and $2,000 contribution. If B demand reaches 60 units, its setup plus production uses 70 hours, leaving 30 hours for 15 A units. The resulting contribution is $1,800 from B plus $600 from A, or $2,400. Under this demand case, using B improves the schedule by $400. These are contribution totals before fixed expenses that remain the same across the alternatives.

If B demand is only ten units, introducing it consumes 20 hours including setup and leaves capacity for 40 A units. Contribution becomes $300 plus $1,600, or $1,900, below the $2,000 A-only option. The higher contribution-per-hour ranking did not cover the capacity consumed by setup. At 20 B units and 35 A units the alternatives tie at $2,000. At 21 B units, only 34 whole A units fit, leaving one hour unused and total contribution of $1,990.

The next whole-unit schedule, 22 B and 34 A, contributes $2,020. This illustrates why a continuous threshold is not always sufficient: indivisible units can create small drops between adjacent quantities. Evaluate whole-unit schedules around the threshold instead of rounding a continuous mix independently for each product. An independently rounded A quantity could exceed the capacity limit even when its contribution appears attractive.

The example contains one shared bottleneck and simple demand caps. Multiple machines, minimum production lots, linked customer commitments, or sequence-dependent setups can require a fuller scheduling model. Contribution rates also change if overtime, discounts, or outsourcing become necessary. Keep the productive-hour estimate grounded in downtime and maintenance plans, and distinguish a demand limit from a sales forecast. A mathematically best schedule among supplied scenarios does not guarantee that every planned unit will sell.

Apply and verify the decision

1. Identify the actual bottleneck

   Measure usable time at the limiting process and keep unconstrained labor or equipment out of the scarce-resource denominator.

2. Include product-entry costs

   Add setup hours whenever a product enters the schedule, rather than spreading those hours across a hypothetical unlimited batch.

3. Enumerate feasible schedules

   Check whole units, demand caps, and setups together. Compare the best mixed schedule with the best schedule excluding each optional product.

Method reference: OpenStax: Decisions with Constrained Resources. Accessed October 22, 2026. The reference supports the accounting concept; all scenario prices, rates, probabilities, and worked calculations are independently constructed hypothetical examples.