Review — Chapter 20

Inventory Management
in 15 Minutes

Click each question to reveal the answer. From "why hold inventory?" → models → practical tools.

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1

Inventory Basics — Why & What

Before the formulas, understand why inventory exists and what it costs.

1
What's the difference between independent and dependent demand — and why does it matter?
Independent demand comes from external customers — it must be forecasted (e.g., how many pizzas a restaurant will sell). Dependent demand is calculated from the parent product (e.g., if you're making 100 pizzas, you need exactly 100 × 2 = 200 cups of cheese).

This matters because Chapter 20's models (EOQ, safety stock) are for independent demand. Chapter 21's MRP handles dependent demand through explosion calculations — no forecasting needed.
🎓 Campus Example
Independent: How many students will buy coffee at the campus café tomorrow? (Must forecast.)
Dependent: If 500 coffees are planned, you need exactly 500 cups, 500 lids, and 500 sleeves. (Calculated.)
2
What are the three main inventory cost categories, and what's the tradeoff?
1. Purchase cost — What you pay per unit. May decrease with quantity discounts.
2. Ordering cost (S) — Fixed cost per order: paperwork, shipping, setup. Ordering more often = higher total ordering costs.
3. Holding cost (H) — Cost of keeping inventory: storage, insurance, obsolescence, capital tied up. More inventory = higher holding costs.

The fundamental tradeoff: Order frequently in small batches → low holding cost but high ordering cost. Order rarely in big batches → low ordering cost but high holding cost. EOQ finds the sweet spot where these two balance.
💼 Interview tip: "The EOQ balances ordering and holding costs" is a sentence you should be able to say in your sleep. It's the #1 inventory concept interviewers test.
3
What is the single-period (newsvendor) model, and when do you use it?
Use it for perishable or one-shot items — products that lose all/most value after the selling period ends. You get one chance to order before demand happens.

The model balances two costs:
Cu (underage) = cost of ordering too few = lost profit per unit = Revenue − Cost
Co (overage) = cost of ordering too many = wasted money per unit = Cost − Salvage value

Critical Ratio: Service Level = Cu / (Cu + Co)

Order the quantity where the probability of selling all of them equals that ratio.
🎓 Campus Example
A student org selling event T-shirts for $25, cost $10, unsold shirts donated (salvage = $0).
Cu = $25 − $10 = $15 (missed profit), Co = $10 − $0 = $10 (wasted cost).
Critical Ratio = 15/(15+10) = 0.60 → stock enough to satisfy 60% of expected demand.
2

Multi-Period Models — EOQ, Safety Stock, P vs. Q

The core models you need to know cold for the quiz (and for interviews).

4
What is EOQ, what does the formula look like, and what's the average cycle stock?
EOQ (Economic Order Quantity) = the order size that minimizes total ordering + holding costs.

Q* = √(2DS / H)

Where D = annual demand, S = ordering/setup cost, H = annual holding cost per unit.

Average cycle stock = Q/2. Since inventory goes from Q down to 0 in a sawtooth pattern, on average you're holding half the order quantity.

Total annual cost: TC = (D/Q)·S + (Q/2)·H
At EOQ, the ordering cost line and holding cost line cross — they're equal.
💼 Interview tip: Know that average cycle stock = Q/2. If asked "what happens to inventory if we double the order size?" the answer is average on-hand doubles too.
5
What is the reorder point, and what changes when demand is uncertain?
The reorder point (R) is the inventory level that triggers a new order. You need enough to cover demand during the lead time while waiting for the order to arrive.

Certain demand: R = d̄ × L (average daily demand × lead time in days)

Uncertain demand: R = d̄L + z·σ_L
The extra term z·σ_L is safety stock — a buffer against demand variability during lead time. The z-value comes from your desired service level (e.g., 95% service → z = 1.65).
🎓 Campus Example
The campus bookstore sells ~40 hoodies/day. Restocking takes 3 days.
Certain: R = 40 × 3 = 120. Reorder when you hit 120 hoodies.
Uncertain (95% service): If σ_L = 15, then R = 120 + 1.65(15) = 145. The extra 25 hoodies are safety stock — insurance against selling more than expected while waiting for the shipment.
6
Fixed-Order Quantity (Q-model) vs. Fixed-Time Period (P-model) — what's the difference?
Q-Model (Fixed-Order Quantity / EOQ):
✓ Order a fixed quantity Q every time
✓ When you order varies — triggered when inventory hits R
✓ Requires continuous monitoring (perpetual system)
✓ Event-triggered

P-Model (Fixed-Time Period / Periodic):
✓ Order at fixed intervals (e.g., every Monday)
✓ How much you order varies — enough to bring stock back up
✓ Only count inventory at review time
✓ Time-triggered

q = d̄(T + L) + z·σ_(T+L) − I

Key insight: The P-model needs more safety stock because you can only react at the next review — you must protect against stockouts during the review period plus lead time.
🎓 Everyday Examples
Q-Model: Your printer alerts you at 10% ink — that's your "reorder point." You always buy the same cartridge.
P-Model: Every Sunday you check your fridge and buy whatever groceries you need to refill. The timing is fixed, but the shopping list changes.
7
How do price-break (quantity discount) models work?
Suppliers offer lower unit prices if you order larger quantities. The challenge: buying more saves on unit cost but increases holding cost (since H is often a % of unit price).

The method:
1. Calculate EOQ for each price break.
2. If the EOQ falls within that price range, keep it. If it falls below the minimum quantity for that price, adjust up to the minimum.
3. Calculate total cost (purchase + ordering + holding) for each feasible option.
4. Pick the option with the lowest total cost.
🎓 Bulk Buying Analogy
Costco vs. the campus store: You can buy 1 pack of ramen for $1 or a 48-pack for $30 ($0.63 each). The per-unit savings are real, but you need storage space and it ties up $30 of your budget. If you eat ramen twice a week, the 48-pack lasts 6 months — and some might expire. Same tradeoff companies face.
3

Practical Tools — ABC, Turnover, Cycle Counting

How companies manage thousands of SKUs without losing their minds.

8
What is ABC classification, and what are the rough percentages?
ABC is the Pareto principle applied to inventory — not all items deserve equal attention.

A items ≈ 20% of SKUs → ~80% of annual dollar volume. Tight control, frequent reviews.
B items ≈ 30% of SKUs → ~15% of dollar volume. Moderate control.
C items ≈ 50% of SKUs → ~5% of dollar volume. Loose control, order in bulk.

Dollar volume = Annual demand × Unit cost. A cheap item sold in huge volumes can be an A item.
💼 Interview tip: Companies like Amazon manage millions of SKUs. ABC tells them where to focus. "A" items get the prime warehouse spots and real-time tracking; "C" items sit in the back and get replenished loosely.
9
Inventory Turnover and Weeks of Supply — what do they tell you?
Inventory Turnover = COGS / Avg Aggregate Inventory Value

Higher turnover = faster flow. You're selling and replacing inventory more times per year. Generally a good sign.

Weeks of Supply = (Avg Inventory / COGS) × 52
Or equivalently: Weeks of Supply = 52 / Turnover

Lower weeks = leaner operation. You're carrying fewer weeks' worth of product.
🎓 Quick Example
A company has $5M in COGS and $1M average inventory.
Turnover = 5M/1M = 5 turns/year.
Weeks of supply = 52/5 = 10.4 weeks.
They're carrying about 2.5 months of inventory at any time.
10
What is cycle counting, and why does it beat annual physical inventory?
Cycle counting means auditing a small subset of inventory items every day or week, rather than shutting down the warehouse once a year for a full count.

Why it's better: Catches errors sooner, doesn't disrupt operations, and pairs perfectly with ABC — count A items more often (e.g., monthly), B items quarterly, C items annually. The tolerance for A items is tighter because their value is higher.
🎓 Real-World Parallel
Think of cycle counting like checking your bank balance regularly via an app (catching issues early) vs. only reconciling once a year at tax time (big surprise potential). Amazon counts portions of its warehouses every single day.
✓

Check Your Understanding

5 quick questions — tap to answer, get instant feedback.

1. In the EOQ model, average cycle stock (on-hand inventory) equals:
Q
Q / 2
D / Q
R
Inventory follows a sawtooth pattern from Q down to 0, so the average on-hand inventory is Q/2.
2. The reorder point under uncertainty adds what to expected demand during lead time?
Cycle stock
Safety stock (z·σ_L)
Order quantity Q
Holding cost H
R = d̄L + z·σ_L. The z·σ_L term is safety stock — a buffer against demand variability during the lead time.
3. A vending machine on campus is restocked every Monday regardless of how much was sold. This is a:
Fixed-order quantity model (Q)
Single-period model
Fixed-time period model (P)
ABC classification
Fixed time interval (every Monday) with variable order quantity = P-model. The vending company checks at a fixed schedule and tops up whatever is needed.
4. In the newsvendor (single-period) model, the critical ratio formula is:
Cu / (Cu + Co)
Co / (Cu + Co)
Cu × Co
Co / Cu
Critical Ratio = Cu / (Cu + Co). Higher underage cost (Cu) relative to overage cost (Co) means you should stock more to avoid missing sales.
5. In ABC classification, "A" items represent roughly what % of SKUs and what % of dollar volume?
50% of SKUs, 80% of value
80% of SKUs, 20% of value
20% of SKUs, 80% of value
30% of SKUs, 50% of value
"A" items are the vital few: ~20% of items account for ~80% of total dollar volume. This is the Pareto (80/20) principle applied to inventory.
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