Finite capacity with labor and materials

Understand the constraint

Suppose Northstar can run twenty bottles on Monday and twenty on Tuesday by machine time. Qualified labor supports only twelve on Monday and eighteen on Tuesday. Each bottle also needs one cap. Opening caps are eight and a receipt of twenty arrives before Tuesday work. With no initial finished stock, Monday production is limited to eight, despite spare machine and labor capacity. Tuesday can use the twenty received caps, but labor limits production to eighteen. Total production is twenty six, with two caps left.

The daily material balance is opening caps plus receipts minus production use equals closing caps. Do not let physical stock become negative; carry unmet demand as backlog on a separate row. Demand of ten on Monday and twenty on Tuesday gives two units of backlog on Monday and four at the end of Tuesday. These results assume all good production is released before each day’s demand and yield is one hundred percent for this exercise. Different release timing changes service even if total quantities stay the same.

Interpret the result

Extra labor is not always the best recovery. Two more qualified labor units on Tuesday raise output to twenty and reduce final backlog to two. Two more caps arriving before Monday raise Monday output to ten and final total output to twenty eight, also leaving two. Both changes together permit thirty total bottles and clear the stated demand. A useful action log therefore records the timing and resource affected, not just the total quantity purchased. Check competence, shift access, and physical receipt before calling the action firm.

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

Build Monday through Wednesday with machine ceilings 20/20/20, labor ceilings 12/18/16, opening caps 8, receipts 0/20/12 before work, and demand 10/20/10. Serve old backlog first. Test two extra caps before Monday, then two extra qualified labor units Tuesday, then both actions. Keep output at or below all resource limits and do not produce more than due demand plus backlog. 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

• Check all required resources in the same time bucket.
• 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.