Start with something familiar
If a shared dinner has fewer servings than guests, the host needs a rule before handing out plates. First arrivals, equal shares, and priority for people with special needs produce different results. None can create more food. A supply planner faces the same social and commercial choice with scarce bottles. The arithmetic should implement an agreed rule and make its effect visible, rather than allowing whoever asks loudest to quietly take the stock.
Words to know: Allocation, Pegging, Fill rate.
Distinguish policy from arithmetic
Northstar has twenty-four good bottles and two same-date requests: account A wants eighteen and B wants twelve. Total need is thirty. Proportional shares are twenty-four times eighteen over thirty, or 14.4, and twenty-four times twelve over thirty, or 9.6. Whole bottles require a rounding rule. Use largest remainder: floor to fourteen and nine, then give the remaining unit to B.
The final allocation is fourteen and ten, totaling twenty-four. A priority rule could instead fill A first, giving eighteen and six. Both satisfy the physical limit but distribute shortages differently. Management must choose the policy using contracts and service goals. The spreadsheet should not make an ethical or commercial priority decision by accident.
Protect traceability
Attach each allocation to a specific supply record and demand record. This is pegging. If a five-unit receipt is used to promise five units to A, it cannot also promise five to B. Keep unallocated supply, allocated but unshipped supply, and shipped quantity separate. Reconcile the categories back to physical availability after every change.
A frozen allocation may be necessary once picking starts. If reallocating would require unpacking or delaying a truck, include that cost and timing in the decision. A future recovery receipt can reduce eventual backlog, but it should not be presented as current available-to-promise stock unless the promise date genuinely follows its usable date.
Make service effects explicit
Under proportional largest-remainder allocation, A misses four and B misses two. Under A-first priority, A misses zero and B misses six. Total shortage stays six. Report both totals and customer-level effects. A policy can improve one account’s service while leaving overall unit fill unchanged.
For more than two accounts, specify how ties are broken and whether minimum shipment sizes apply. Calculate raw shares first, then round in a reproducible way. If a minimum shipment makes the requested policy infeasible, show the conflict instead of allocating fractional bottles. The lab extends the comparison across weeks to expose cumulative fairness and repeat deferral.
- Define units and event
- Reconcile eligible inputs
- Apply the stated rule
- Check feasibility
- Explain the decision
Northstar worked decision
All quantities and costs below are fictional and self-contained. Apply the stated timing and unit conventions.
| Input | Value |
|---|---|
| Available bottles | 24 |
| Account A need | 18 |
| Account B need | 12 |
- 1. Raw proportional shares are 14.4 and 9.6.
- 2. Floors fourteen and nine allocate twenty-three; largest remainder gives last unit to B.
- 3. Final fourteen and ten leaves shortages four and two.
Proportional allocation is A 14, B 10.
Assumptions
- Use only the quantities and timing stated; no hidden receipts, losses, or substitutions.
- Fractional mathematical results are rounded only where whole-unit or pack rules are explicitly stated.
Where this can fail: This is a transparent teaching model. Confirm calendars, data definitions, and operating constraints before using an analogous policy in practice.
Build, test and explain a plan
Build four independent weekly allocations with no carryover. A needs 18, 10, 16, 12; B needs 12, 20, 14, 18; available supply is 24, 21, 25, 27. Compare largest-remainder proportional allocation with A-first. For tied remainders give the last unit to B. All demands have the same weekly cutoff and partial shipment is allowed. The eight-hour allocation is a self-paced estimate, not experimentally validated; it includes model building, scenario testing, a memo, and teach-back.
Use paper or a spreadsheet. The estimates below include the study and worked example already on this page.
| Estimated hours | Activity |
|---|---|
| 0.5 | Study the reading and make a one-page definition sheet. Mark every unit, date convention, and inclusion rule. Explain the difference between the policy input and the outcome being measured. |
| 0.5 | Recalculate the worked example independently, without copying the displayed result. Show intermediate arithmetic and reconcile the answer to the physical story. Note one assumption that could change the decision. |
| 3 | Build a reusable multi-period spreadsheet from the supplied lab data. Build four independent weekly allocations with no carryover. A needs 18, 10, 16, 12; B needs 12, 20, 14, 18; available supply is 24, 21, 25, 27. Compare largest-remainder proportional allocation with A-first. For tied remainders give the last unit to B. All demands have the same weekly cutoff and partial shipment is allowed. Keep inputs separate from formulas, add a clear output table, and include a check column that flags any quantity or timing inconsistency. Walk through the first and last rows manually. |
| 2 | Create separate named scenario tabs. Reduce each week’s available supply by three. Then add a minimum shipment of eight for any served account; identify where proportional output violates the minimum and propose an explicit feasible policy. Preserve the baseline and record both changed inputs and changed outputs. Explain any outcome that stays the same, since a binding constraint or a measurement rule can make an intervention ineffective. |
| 1 | Write a 400-word decision memo naming your recommended action, evidence, assumptions, responsible role, and next check. Compare at least two alternatives using your table. State one limitation that could reverse the recommendation and what additional evidence would resolve it. |
| 1 | Teach the result aloud in five minutes using an original diagram. Then review every formula, answer the module questions relevant to this lesson, and write a short correction log. Use the remaining time to reproduce the key calculation from a blank sheet. |
Your deliverables
- An auditable multi-period workbook with baseline and named stress cases.
- A decision memo with numerical evidence and explicit limitations.
- An original explanatory diagram and a correction log.
Check your practice work
- Proportional allocation is A 14, B 10.
- A-first allocation is A 18, B 6.
- Both allocate twenty-four and leave total shortage six.
- Baseline proportional A allocations 14,7,13,11; B allocations 10,14,12,16. A-first gives A 18,10,16,12 and B 6,11,9,15.
- Baseline A totals 45 proportional versus 56 priority; B 52 versus 41. Both allocate 97 of 120 demand.
- After reducing supply by three, proportional A 13,6,12,10 and B 8,12,10,14. Week 2 violates an eight-unit minimum for A; an explicit feasible adjustment is A 8,B 10. Other policies are possible if justified.
Keep these three ideas
- Compare proportional and priority allocation while keeping commitments traceable.
- Keep the unit, timing, and denominator visible.
- Treat model outputs as conditional on their stated assumptions.
Common mistakes
- Changing an input definition without changing all affected formulas.
- Presenting an expected or proposed quantity as confirmed usable supply.
Optional video study
Compare proportional and priority allocation while keeping commitments traceable.
- Distinguish policy from arithmetic
- Protect traceability
- Make service effects explicit
Second half: application, contrasting scenario, and handoff.
Open the module media & quizPut this idea to use
Carry your assumptions into a practical tool, then compare your result with a short guide.
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