Allocation tradeoffs and service rules

Understand the constraint

There are twenty four good bottles available before all due dates. Group A requests eighteen and has contribution six currency units per bottle. Group B requests twelve and has contribution ten. Shipments cannot exceed demand and cannot be negative. Pure contribution maximization gives twelve to B and twelve to A, worth one hundred ninety two. A rule that protects at least fifteen for A gives fifteen to A and nine to B, worth one hundred eighty. The policy costs twelve units of contribution in this case.

A proportional allocation based on demand shares gives A twenty four times eighteen divided by thirty, or fourteen point four. B receives nine point six. Bottles are indivisible, so a rounding rule is required. Giving floors first leaves fourteen for A and nine for B, with one bottle remaining. Awarding the remainder to the largest fractional remainder yields fourteen A and ten B. Its contribution is one hundred eighty four. This is a transparent rule, not a mathematical proof that every customer considers it fair.

Interpret the result

Service goals can be hard constraints, weighted scores, or ordered priorities. A hard minimum of fifteen A has a different meaning from a preference for A. If the requested minimum rises above available supply, the model should flag infeasibility rather than silently weaken the rule. Record who may change a priority, which orders it covers, and how customers are informed. Do not treat revenue, contribution, strategic importance, and lateness penalties as interchangeable amounts unless their definitions and units are explicit.

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

Compare available supply 24, 20, and 16 bottles using the same demands and contributions. For each supply level compute pure contribution allocation, a hard A minimum of 15, and proportional allocation by largest remainder. On an exact fractional tie give the remaining bottle to A. No carry or partial bottles are allowed. Add a fourth stress case with only 14 available and retain the A minimum. 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

• Make the objective and protected commitments explicit.
• 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.