Product mix and changing resource pressure

Understand the constraint

Call the plain bottle A and the decorated bottle B. A uses ten machine minutes and six labor minutes. B uses twenty machine minutes and four labor minutes. The shift supplies two hundred machine minutes and one hundred twenty labor minutes. With demand caps of twelve A and ten B, a proposed mix of twelve A and four B uses all two hundred machine minutes but only eighty eight labor minutes. That mix is feasible. The machine is binding while labor has thirty two minutes of headroom.

Now compare ten A and five B. Machine load remains two hundred minutes, while labor falls to eighty minutes. Equal machine load does not imply equal product counts or value. If contribution is six currency units per A and fourteen per B, twelve A plus four B contributes one hundred twenty eight, while ten A plus five B contributes one hundred thirty. This value comparison assumes contribution already subtracts the relevant variable costs. It says nothing by itself about promised customer service.

Interpret the result

A single average time is risky when the product mix moves. Fifteen A need one hundred fifty machine minutes and ninety labor minutes; fifteen B need three hundred machine minutes and sixty labor minutes. Both are fifteen bottles but have very different feasibility. Resource use per product should remain visible in the model. Contribution per bottleneck minute can guide a simple one-resource comparison, but it does not replace checking all constraints, product demand caps, or a policy that protects a minimum allocation.

Create one row for each resource or stock position and one column for each time bucket. Put the unit in the row label and keep inputs separate from calculated results. Begin with the smallest case you can verify by hand, then extend the same equations across periods. Give every receipt a usable date and every requirement a due date. Preserve the baseline before changing an assumption so the effect of an action is visible.

Validate and explain

Use a second check that follows the physical story. Count what enters, what is used, what waits, and what leaves. A plan that balances in total can still fail at an earlier cutoff. Mark any unavailable input as an assumption rather than filling it with a convenient zero. A zero means a known absence; an unknown value means the promise remains conditional. This difference belongs in both the model and the decision note.

A calculation becomes useful when it changes a choice. Compare the baseline with at least two scenarios, identify the first limiting condition in each, and explain what additional resource would actually change delivered output. Keep a service measure alongside any cost or value measure. State whether the choice maximizes value, protects a commitment, or reduces the worst shortfall. A different goal can produce a different sensible answer from the same facts. Finish by testing one deliberately wrong proposal, such as a receipt used before arrival or a quantity above a resource ceiling. Your table should make that error visible. Save the rejected proposal with a short explanation, because it teaches a reviewer how the checks work. The eight hours include rebuilding, scenario work, writing, and teach-back; they are self-paced estimates rather than measured completion times. Faster readers should deepen the checks instead of merely rereading the text.

Build, test and explain a plan

Use the stated A/B data for three shifts, each with machine capacity 200 and labor capacity 120. Demand caps per shift remain A12/B10 with no carry. Evaluate mixes 12/4, 10/5, and 0/10 in every shift. Then reduce labor to 70 in shift two and machine time to 180 in shift three. Add a service requirement of at least six A per shift and find a feasible integer mix for each shift. The eight-hour estimate covers an original workbook or paper model, scenario calculations, checks, and communication; it is not experimentally validated.

Use paper or a spreadsheet. The estimates below include the study and worked example already on this page.

Your deliverables

• A reproducible planning table with inputs, formulas, units, and checks.
• A scenario comparison with service and resource consequences.
• A decision memo and short teach-back outline.

Keep these three ideas

• Compare products using their actual resource requirements.
• Keep quantities, resource units, and due times explicit.
• Recheck all constraints after a change, and report remaining uncertainty.

Common mistakes

• Treating capacity in a later time bucket as available before the due gate.
• Calling an expected or conditional quantity a guaranteed shipment.