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Product mix optimization with bottlenecks

Can’t make everything the market wants? Enter products, demand and the time each takes on the machines that limit output, and see how much of each item to make to earn the most with the hours you have, and what each extra hour is worth.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Preliminary estimateRevised 11/02/2026
Products and market (per month)
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Net price: after sales taxes, commissions and freight. Variable cost: only what rises with each unit made (material, packaging, power, outside work per part). Current mix: what the plant makes today, for comparison; if blank, the calculator scales demand down proportionally until it fits.

Resources that may limit output (up to 3)
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Time of each product at each resource
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Columns follow the order of the resource list. Product names must match the product list.

Fixed expenses

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—Monthly profit with the optimal mix
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How much to make of each product

Current mix, optimal mix and maximum demand, in units per month.

Tap the chart to see the values.

Monthly production plan

Use of each resource

Hours used as % of hours available, for each mix option.

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Resources and value of an hour

Monthly result by option

Next step

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Method, assumptions and references

Equations used

Unit CM = net price − variable cost; CM per hour of resource r = CM ÷ (minutes on the resource ÷ 60)
Maximize Σ CMᵢ·xᵢ subject to Σ (tᵢᵣ ÷ 60)·xᵢ ≤ Hᵣ for each resource r and minimum demandᵢ ≤ xᵢ ≤ maximum demandᵢ
Shadow price of resource r = optimal profit with Hᵣ + 1 h − optimal profit with Hᵣ (cost of 1 lost h = profit with Hᵣ − profit with Hᵣ − 1 h)
Operating profit = Σ CMᵢ·xᵢ − fixed expenses; single-bottleneck rule: fill in order of CM per hour of the resource with the highest shadow price, respecting all resources

Assumptions and limits

  • Linear program solved by the simplex method (Bland’s rule) with up to 3 resources; the result is the exact optimum of the continuous model and may have fractional units, to be rounded down.
  • Price, variable cost and time per unit are constant; available hours are net of losses; fixed expenses are the same for every mix. Sequence-dependent setups, minimum batches and inventory are not considered.
  • Without a current mix entered, the comparison uses maximum demand scaled down proportionally until it fits every resource.

Standards and technical documents

  • Goldratt, E. M. The Haystack Syndrome: Sifting Information Out of the Data Ocean. North River Press, 1990
  • Corbett, T. Throughput Accounting. North River Press, 1998
  • Hillier, F. S.; Lieberman, G. J. Introduction to Operations Research, 11th ed. McGraw-Hill, 2021 (simplex method and sensitivity analysis)
  • Bland, R. G. New finite pivoting rules for the simplex method. Mathematics of Operations Research 2(2), 1977
  • Horngren, C. T.; Datar, S. M.; Rajan, M. V. Cost Accounting: A Managerial Emphasis, 16th ed. Pearson (product-mix decisions with constraints)

U.S. regulations

  • No statute governs product-mix decisions; they are a management choice.
  • ASC 330 Inventory and IRC §263A (UNICAP): full absorption costing is still required for financial and tax reporting, even when contribution margin drives decisions.

Frequently asked questions

What is product mix optimization with a bottleneck?

It is deciding how much of each product to make in the month when the machines cannot meet all demand. Instead of following percentage margin or price, the calculator looks for the mix that earns the most contribution with the hours available at the resources that limit output (Theory of Constraints and linear programming).

Why is ranking by margin per bottleneck hour not enough?

Because that rule is exact only when a single resource limits output. In the example, the press brake and welding are both full: ranking by margin per press brake hour (safety guard first) jams welding and earns $52,980 of contribution, against $63,840 for the optimal mix found by linear programming.

How do I read the example?

The optimal mix is 300 enclosures, 240 shelves, 900 brackets and 200 guards a month. Contribution rises from $51,900 (current mix) to $63,840, and profit after $45,000 of fixed expenses from $6,900 to $18,840 a month. The laser cutter keeps 38.7 h of slack.

What is the shadow price?

It is how much profit rises with 1 more hour at the resource. In the example, 1 more press brake hour is worth $127.71 and 1 more welding hour $50.57; the laser cutter, which has slack, is worth zero. Overtime or outsourcing pays if it costs less than that per hour, and the same figure is the cost of every hour of downtime there.

Where do I get the data?

Net price: list price less sales taxes, commissions and freight. Variable cost: cost sheet (material, packaging, power, outside work per part). Demand: order book, forecast or sales history. Times: routing or time study, in minutes per unit with setup spread over the batch. Available hours: monthly shift hours × the resource’s OEE.

What is the minimum demand for?

To secure contracted orders, key accounts or spare parts that must ship even at a low margin. The calculator makes at least that minimum and only then spreads the remaining hours. If the minimums do not fit, it shows how many hours are missing at each resource.

What are the limits?

It assumes constant time and margin per unit, available hours already net of losses and fixed expenses that do not change with the mix. It ignores sequence-dependent setups, minimum batches, inventory and due dates within the month; results may come out fractional and should be rounded down. Use capacity planning and job sequencing to check the plan.