Chapter 32: Quiz — Inventory and Supply Chain Analytics

Instructions: 20 questions total. Multiple choice questions have one correct answer. True/False questions require a one-sentence justification. Short answer questions should be answered in 3-6 sentences or with a calculation showing your work.

Section A: Multiple Choice (Questions 1–12)

Question 1

A distributor reports annual COGS of $4,800,000 and average inventory value (average of beginning and ending inventory) of $960,000. What is the inventory turnover ratio?

A) 2.0× B) 5.0× C) 20.0× D) 0.2×

Question 2

A company's inventory turnover is 6.0×. What is its Days Inventory Outstanding?

A) 6 days B) 30.4 days C) 60.8 days D) 365 days

Question 3

The reorder point formula is:

A) EOQ × Lead Time B) Average Daily Demand × Safety Stock C) (Average Daily Demand × Average Lead Time) + Safety Stock D) Safety Stock / Average Daily Demand

Question 4

In EOQ analysis, what happens to the optimal order quantity if the annual holding cost rate increases while all other parameters stay constant?

A) EOQ increases — order more to reduce ordering frequency B) EOQ decreases — holding is more expensive, so carry less per order C) EOQ is unchanged — holding costs do not affect optimal order size D) EOQ doubles — total cost increases proportionally

Question 5

In ABC inventory analysis, Class A items typically represent what share of SKUs and total annual consumption value?

A) 10-20% of SKUs, 70-80% of value B) 50% of SKUs, 50% of value C) 80% of SKUs, 20% of value D) 5% of SKUs, 95% of value

Question 6

Supplier A has an average lead time of 14 days with a standard deviation of 6 days. Supplier B has an average lead time of 18 days with a standard deviation of 2 days. Assuming the same product and service level, which supplier typically requires more safety stock?

A) Supplier A — lower average lead time always means less safety stock B) Supplier B — longer average lead time always means more safety stock C) Supplier A — higher lead time variability (CV ≈ 0.43) drives more safety stock than Supplier B's lower variability (CV ≈ 0.11) D) Both require the same safety stock — service level is the only driver

Question 7

Which metric most directly quantifies the working capital cost of carrying too much inventory?

A) Fill rate B) On-time delivery rate (OTDR) C) Days Inventory Outstanding (DIO) D) Stockout rate

Question 8

A SKU had its last recorded sale 220 days ago. You are using thresholds of 90 days for "slow-moving" and 180 days for "obsolete." How would this SKU be classified?

A) Active B) Slow-Moving C) Obsolete D) Cannot be determined without current stock quantity data

Question 9

The EOQ formula is Q* = sqrt(2DS/H). If annual demand D doubles while all other parameters remain constant, what happens to the EOQ?

A) EOQ doubles B) EOQ increases by a factor of approximately 1.41 (square root of 2) C) EOQ is unchanged D) EOQ is halved

Question 10

Which statement best explains why lead time variability matters more than average lead time for calculating safety stock?

A) Average lead time is already embedded in the base reorder calculation; it is the variability around that average that creates the risk of stockout B) Variability is always more important than the mean in any statistical context C) Average lead time has no effect on safety stock under any formula D) Lead time variability only matters for Class A items, not B or C

Question 11

Acme's supply chain dashboard shows that 60% of their SKUs are classified as C items and account for only 5% of annual inventory spend. Which conclusion is best supported by this finding?

A) Acme has a well-balanced catalog with appropriate distribution of inventory investment B) Class C items are generating proportionally more profit than Class A items C) Most of Acme's operational complexity is devoted to items that drive very little business value — a case for simplification or rationalization D) Acme should increase safety stock for all Class C items to ensure availability

Question 12

A supplier has achieved an 81% on-time delivery rate over the past 12 months (based on 40 purchase orders). What is the most appropriate first action?

A) Immediately switch all orders to an alternate supplier B) Request a performance review meeting to understand root causes and establish a 90-day improvement plan C) Increase safety stock for all items from this supplier by 30% and take no further action D) Reduce order quantities to minimize financial exposure while the situation resolves itself

Section B: True/False with Justification (Questions 13–16)

For each statement, write True or False and provide one sentence explaining your reasoning.

Question 13

True or False: A higher inventory turnover ratio is always better, regardless of industry or business context.

Question 14

True or False: The Economic Order Quantity formula tells you exactly when to place a purchase order.

Question 15

True or False: If a product is classified as a Class C item in ABC analysis, it should be removed from the catalog.

Question 16

True or False: A supplier with a longer average lead time always requires more safety stock to be held than a supplier with a shorter average lead time for the same product.

Section C: Short Answer (Questions 17–20)

Question 17 — Calculation

A product has the following characteristics: - Average daily demand: 20 units - Demand standard deviation: 4 units per day - Average lead time: 12 days - Lead time standard deviation: 3 days - Target service level: 95% (z = 1.645)

Calculate (showing your work): 1. Safety stock 2. Reorder point

Question 18 — Interpretation

A company's inventory management team presents the following headline metrics: - Inventory turnover: 3.8× (industry benchmark: 7.0×) - DIO: 96 days - Percentage of SKUs below reorder point: 18% - Average supplier OTDR: 87%

In 4-6 sentences, explain what these numbers tell you about this company's supply chain health. What are the two most important problems to address first, and why?

Question 19 — Concept Explanation

Explain in your own words what safety stock is, why a business holds it, and what the tradeoff is between holding more versus less safety stock. Use a concrete example from the chapter or from your own business experience. (4-6 sentences)

Question 20 — Scenario Analysis

Priya runs Acme's supply chain dashboard and finds three CRITICAL items in the West region (fewer than 3 days of supply remaining) and one supplier with a 71% OTDR. In 4-6 sentences, describe the two separate action plans she should recommend: one for the immediate stockout risk and one for the supplier performance issue.

Answer Key

Section A: Multiple Choice

Q1: B — 5.0× Inventory Turnover = COGS / Average Inventory = $4,800,000 / $960,000 = 5.0. This means the company sells through its entire average inventory value five times per year, or roughly every 73 days.

Q2: C — 60.8 days DIO = 365 / Turnover = 365 / 6.0 = 60.8 days. Option B (30.4 days) corresponds to 12× turnover. At 60.8 days DIO, the company is holding approximately two months of supply at any given time.

Q3: C — (Average Daily Demand × Average Lead Time) + Safety Stock The first term covers expected demand during the replenishment period; safety stock provides a buffer against variability in both demand and lead time. Without safety stock, the formula gives you the bare minimum to order exactly when you would run out under average conditions — no margin for error.

Q4: B — EOQ decreases — holding is more expensive, so carry less per order In Q = sqrt(2DS/H), H is in the denominator. As H increases, Q decreases proportionally to 1/sqrt(H). The intuition is correct: when it costs more to hold inventory, the optimal strategy is to order more frequently in smaller quantities, reducing average inventory on hand.

Q5: A — 10-20% of SKUs, 70-80% of value This is the Pareto principle applied to inventory. The proportions vary by industry, but the pattern is remarkably consistent: a small minority of SKUs drive the vast majority of value. At Acme, 7.5% of SKUs (47 items) drove 80% of annual consumption value.

Q6: C — Supplier A — higher lead time variability drives more safety stock Safety stock is driven by the combined variability of demand and lead time, not by lead time alone. Supplier A's coefficient of variation (6/14 ≈ 0.43) is much higher than Supplier B's (2/18 ≈ 0.11). A less predictable supplier requires more safety stock to achieve the same service level, even if their average lead time is shorter.

Q7: C — Days Inventory Outstanding (DIO) DIO directly measures how many days of sales are locked up in inventory as working capital. A high DIO means the company has cash tied up in product rather than available for operations, debt reduction, or investment. Fill rate and stockout rate measure service level; OTDR measures supplier reliability — these do not directly quantify the working capital cost of over-stocking.

Q8: C — Obsolete 220 days exceeds the 180-day obsolete threshold. The classification is time-based (days since last sale), not quantity-based — even one unit on hand with no sales in 220 days qualifies as obsolete. Knowing the quantity on hand is needed to calculate the dollar value at risk, but not to make the classification itself.

Q9: B — EOQ increases by a factor of approximately 1.41 Q = sqrt(2DS/H). If D becomes 2D: Q_new = sqrt(2 × 2D × S/H) = sqrt(2) × sqrt(2DS/H) = sqrt(2) × Q_old ≈ 1.414 × Q_old. This square root relationship is important: it means EOQ does not scale linearly with demand. Doubling demand increases optimal order size by only 41%, not 100%.

Q10: A — Average lead time is already embedded in the base reorder calculation; variability creates stockout risk The standard reorder point formula (Avg Daily Demand × Avg Lead Time) already accounts for the typical replenishment delay. Safety stock exists specifically to protect against the cases where lead time is longer than average — it is the buffer against variability, not against the average. A perfectly consistent supplier with zero lead time variability needs zero lead-time safety stock, regardless of how long their average lead time is.

Q11: C — Most of Acme's operational complexity is devoted to items that drive little business value If 60% of SKUs generate only 5% of annual inventory spend, those 60% are consuming disproportionate operational resources (purchase orders, receiving, counting, storage space) relative to their contribution. This is a rationalization opportunity — either simplify how Class C items are managed, or evaluate whether some should be discontinued.

Q12: B — Request a performance review meeting 81% OTDR is below industry target (typically 95% for business-to-business distributors), but the appropriate first response is diagnosis, not drastic action. A performance review establishes facts, communicates expectations, and gives the supplier an opportunity to explain root causes and commit to improvement. Switching suppliers immediately has real costs — qualification time, potential price increases, relationship disruption. If the supplier cannot achieve acceptable performance within a defined improvement timeline, then escalating to switching becomes appropriate.

Section B: True/False Answers

Q13: FALSE While higher inventory turnover is generally more efficient, extremely high turnover for a business-to-business distributor can indicate dangerously low stock levels that risk frequent stockouts — a high turnover rate combined with a high stockout rate means you are winning the efficiency metric while losing the service level metric. Industry context matters: a grocery store needs much higher turnover than a specialty industrial parts distributor.

Q14: FALSE EOQ tells you how much to order (the optimal order quantity), not when to order. The reorder point formula tells you when to order (the stock level that triggers a purchase order). Both are needed together for a complete ordering policy.

Q15: FALSE Class C classification means a product contributes a small share of total inventory value relative to other items — it does not mean the product is unprofitable or should be discontinued. Some Class C items may serve important customers, complete a product line, or have strategic value. The appropriate response is to manage Class C items with simpler, lower-cost processes — not necessarily to eliminate them.

Q16: FALSE Lead time variability, not average lead time, is the primary driver of safety stock requirements. A supplier with a longer but perfectly consistent lead time (zero standard deviation) needs zero safety stock for lead time variability — you can predict exactly when goods will arrive and plan accordingly. A supplier with a shorter but highly variable lead time can require more safety stock than the longer-lead supplier, because you cannot reliably predict arrival timing.

Section C: Short Answer

Q17 — Calculation

Safety Stock = Z × sqrt(LT × σ_d² + d̄² × σ_LT²) = 1.645 × sqrt(12 × 4² + 20² × 3²) = 1.645 × sqrt(12 × 16 + 400 × 9) = 1.645 × sqrt(192 + 3,600) = 1.645 × sqrt(3,792) = 1.645 × 61.58 = 101.3 units (round up to 102 units)

Reorder Point = (Average Daily Demand × Average Lead Time) + Safety Stock = (20 × 12) + 102 = 240 + 102 = 342 units

Interpretation: When stock drops to 342 units, place a purchase order. Of that, 240 units covers expected demand during the typical 12-day lead time; the remaining 102 units of safety stock provide approximately 95% probability of not stocking out even if demand runs higher than average or the supplier runs late.

Q18 — Interpretation (Sample Answer)

These metrics collectively describe a supply chain that is significantly underperforming. An inventory turnover of 3.8× against a 7.0× industry benchmark, combined with a DIO of 96 days, indicates the company is holding roughly twice as much inventory as it should — approximately $X million in excess working capital is trapped in product on shelves.

The 18% of SKUs below reorder point is equally concerning, because it means that while the company is over-stocked in aggregate, it has stocks of the wrong things — suggesting demand forecasting or replenishment triggers are not working correctly. And an 87% average supplier OTDR means roughly 13% of orders are arriving late, which may be contributing to both problems: late deliveries cause emergency orders that build excess stock while simultaneously leaving some SKUs short.

The two most important issues to address first are the inventory balance (too much of the wrong things, not enough of the right things) and the 18% at-risk SKUs. The supplier performance issue is important but unlikely to be fully resolved in the short term — the immediate priority is ensuring customers can be served.

Q19 — Concept Explanation (Sample Answer)

Safety stock is buffer inventory held in excess of the expected demand during a supplier's lead time, specifically to protect against situations where demand is higher than expected or the supplier delivers later than expected. A business holds it because both demand and delivery timing are uncertain — without a buffer, any deviation from the average would cause a stockout.

The tradeoff is straightforward: more safety stock means better protection against stockouts (higher service level) but higher working capital costs (more cash tied up in inventory, more warehouse space consumed). A business at 99% service level carries significantly more safety stock than one at 90%, and pays for it continuously in the form of holding costs. The goal is to find the service level that appropriately balances the cost of stockouts against the cost of holding safety stock — different products and customer relationships warrant different levels.

Q20 — Scenario Analysis (Sample Answer)

For the three CRITICAL items in the West region, Priya should recommend immediate action: contact the purchasing manager to place emergency purchase orders for those three SKUs today, request expedited shipping from the suppliers, and simultaneously alert the West region sales team so they can proactively communicate with customers about any potential delays. This is a tactical response to prevent an imminent service failure.

For the 71% OTDR supplier, Priya should recommend a formal supplier review meeting with Acme's purchasing and operations leadership. The objective of that meeting is to present the data (47 purchase orders, 71% on-time over 12 months), understand the root cause from the supplier's perspective, and agree on measurable improvement targets with a specific timeline — typically 90 days. If the supplier cannot achieve a minimum acceptable OTDR (typically 90-95%) within that period, Acme should qualify an alternative source for the affected product categories. In the interim, Acme should increase safety stock for all products from this supplier to protect against continued late deliveries.