Start with something familiar
Buying a giant bag of coffee saves shopping trips, but some coffee may sit for a long time and lose value. Tiny bags take little shelf space but require more trips. The best choice depends on the cost of each trip and the cost of keeping unused coffee. Bottles do not have to spoil quickly for this tradeoff to matter: money, storage, and handling can still make stock expensive.
Words to know: EOQ, Safety stock, Review period.
Separate annual cost terms
Northstar uses 1,200 replacement lids per year. Each replenishment order costs $12 to process, regardless of its size. Holding one lid costs $3 per year. Under constant demand and instantaneous replenishment, a lot of Q creates average cycle stock Q divided by two and about 1,200 divided by Q orders per year. Annual relevant cost is 12 times 1,200 divided by Q plus 3 times Q divided by two.
Purchase cost is excluded here only because every feasible policy buys the same annual quantity at the same unit price. If discounts change unit price, include annual purchase cost. A fixed warehouse lease that does not change with the decision is not an incremental holding cost. Keep cash spent buying stock distinct from annual expense used in this simplified comparison.
Find and test the basic optimum
The economic lot is the square root of two times annual demand times cost per order divided by annual holding cost. Here it is sqrt(9600), about 97.98 lids. This is a continuous mathematical result, not an instruction to buy a fraction of a lid. With pack size twenty, compare nearby feasible quantities eighty and one hundred.
At eighty, annual ordering cost is $180 and cycle-stock holding cost is $120, totaling $300. At one hundred, these are $144 and $150, totaling $294. A lot of one hundred is better among those candidates. If storage caps receipts at eighty, the feasible choice changes even though the unconstrained optimum does not.
Explain the model’s boundary
This basic model assumes stable demand, fixed order cost, constant price, no shortages, and immediate replenishment of a lot. It does not model gradual production, uncertain demand, supplier minimums, or a capacity bottleneck. Use it as a transparent comparison, then bring real constraints back into the decision.
Safety stock is separate from cycle stock. A constant buffer of twelve adds $36 annual holding cost to each policy at $3 per unit-year, without changing the basic ordering tradeoff. It changes total inventory and budget. Avoid claiming that a lower batch cost proves better service; service depends on timing, uncertainty, and the replenishment policy as well.
- 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 |
|---|---|
| Annual demand lids | 1200 |
| Order cost dollars/order | 12 |
| Holding dollars/lid/year | 3 |
| Pack size lids | 20 |
- 1. EOQ = sqrt(2 × 1200 × 12 / 3) = 97.98 lids.
- 2. Q 80: 1200/80 × 12 + 80/2 × 3 = $300/year.
- 3. Q 100: 1200/100 × 12 + 100/2 × 3 = $294/year.
EOQ about ninety-eight; feasible pack choice one hundred under no storage cap.
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
Compare lots 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200 for annual demand 1,200, order cost $12, holding $3/unit-year. Build a twelve-month receipt and stock illustration for Q 100, monthly demand 100, receipts before demand, opening stock zero and no safety stock. Explain why month-end stock alone misses average within-month cycle stock. 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. Compare lots 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200 for annual demand 1,200, order cost $12, holding $3/unit-year. Build a twelve-month receipt and stock illustration for Q 100, monthly demand 100, receipts before demand, opening stock zero and no safety stock. Explain why month-end stock alone misses average within-month cycle stock. 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. Double order cost to $24; separately raise holding cost to $6; then impose an eighty-unit storage cap on each case. Compare feasible costs, not just rounded formulas. 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
- EOQ about ninety-eight; feasible pack choice one hundred under no storage cap.
- Q 120 costs $120 + $180 = $300/year.
- A constant twelve-unit buffer adds $36/year to every candidate.
- Base lowest listed cost is$294 at Q 100. The month-end stock illustration is zero every month although average cycle stock is fifty under uniform within-month consumption.
- With order cost$24, EOQ 138.56; feasible Q 140 costs$415.71, while Q 120 costs$420. With holding$6, EOQ 69.28; Q 60 andQ 80 both cost$420.
- An eighty-unit cap gives base Q 80 costing$300; doubled order cost Q 80 costing$480; doubled holding cost Q 60 orQ 80 each costing$420.
Keep these three ideas
- Calculate a basic economic lot and test feasible pack and storage alternatives.
- 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
Calculate a basic economic lot and test feasible pack and storage alternatives.
- Separate annual cost terms
- Find and test the basic optimum
- Explain the model’s boundary
First half: foundation and first worked check.
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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