Unit 09 — Inventory Control: Reorder Point & Quantity Discounts

1. Reorder Point (Constant Demand) Core syllabus concept

1Concept — What Is It Solving?

The EOQ family of models (Unit 8) answers "how much to order." The reorder point answers the other half of the question every continuous (Q) inventory system must answer: "when to order." Since it takes time (lead time) for a new order to arrive after it's placed, the order must be triggered before stock actually reaches zero — specifically, while there's still enough stock left to cover expected demand during the lead time.

2Formula

3Variables

• R = reorder point (inventory level that triggers a new order)
• d = demand rate per period (e.g., per day)
• L = lead time (time between placing and receiving an order, in the same period units as d)

4When to Use It

Use this basic formula only when demand and lead time are both reasonably constant/known. When demand fluctuates, this formula must be extended with a safety stock term (see the next concept) — using the plain R = dL formula under uncertain demand would leave no cushion against stockouts.

5Textbook Example — Example 13.5

6Common Mistakes

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2. Safety Stock and Service Level Core syllabus concept

1Concept — What Is It Solving?

The plain reorder point formula (R = dL) assumes demand during lead time is perfectly predictable. In reality, demand fluctuates — sometimes it will run higher than average during the lead time, and if the reorder point doesn't account for that, the firm risks a stockout before the new order arrives. A safety stock is extra inventory carried specifically as a buffer against this uncertainty. The service level is the policy choice behind how big that buffer should be: it's the probability that available inventory will be sufficient to meet demand during the lead time (equivalently, 1 − probability of a stockout).

2Formula

3Variables

• z = number of standard deviations corresponding to the chosen service level (from the normal distribution table — e.g. z = 1.65 for a 95% service level)
• σ_d = standard deviation of daily demand
• L = lead time

4When to Use It

Use this whenever demand is uncertain (given as a mean and standard deviation) and management has chosen — or been given — a target service level. A higher desired service level requires a higher z-value, and therefore a larger safety stock (and higher carrying cost) — this is the direct cost of reducing stockout risk.

5Worked Example

6Important Points

• Higher service level → higher z → larger safety stock → higher carrying cost. Service level is fundamentally a cost/risk trade-off decision.
• Safety stock depends on demand variability (σ_d), not just the average demand rate.
• A service level of 90% means a 10% chance of stocking out during any given lead-time period — not a 10% shortfall in units.

7Common Mistakes

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3. Reorder Point with Variable Demand Core syllabus concept

1Concept — What Is It Solving?

This combines the two previous concepts into the complete, practical reorder-point formula: the reorder point must cover both the average demand expected during lead time (dL) and the safety stock needed to protect against demand variability at the chosen service level.

2Formula

(The first term, dL, is the plain reorder point from Concept 1; the second term, zσ_d√L, is the safety stock from Concept 2.)

3When to Use It

This is the formula to use for any real-world reorder-point question that gives you a standard deviation of demand and a desired service level — which is to say, almost every realistic version of this problem. The plain R = dL from Concept 1 is really just this formula's special case when demand has zero variability.

4Textbook Example — Example 13.6

5Important Points

• R = dL + safety stock — always compute the two terms separately, then add.
• This is the formula tested in almost every realistic reorder-point exam question — memorise it over the simpler R = dL version.

6Common Mistakes

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4. Order Quantity for a Periodic Inventory System Core syllabus concept

1Concept — What Is It Solving?

Recall from Unit 7 that in a periodic (P) system, inventory is checked only at fixed time intervals, and the order size varies each time to bring stock back up to a target level. Because inventory is not monitored between review points, the order must cover demand for the entire review period plus the lead time to receive the new order — a longer exposure window than the continuous system's reorder point, which is why periodic systems need a bigger safety stock.

2Formula

3Variables

• d = average demand rate; t_b = fixed time between orders (review period); L = lead time
• σ_d = standard deviation of demand; z = service-level factor
• I = inventory currently in stock at the moment of review

The first term, d(t_b+L), is the average demand expected to occur before the next order after this one arrives; the second term is the safety stock for that combined period; I is subtracted because you only need to order enough to make up the shortfall against what's already on the shelf.

4When to Use It

Use this whenever a question describes a periodic/fixed-interval review system (a vendor visiting on a schedule, a stock count every N days) and asks how much to order at a given review point.

5Textbook Example — Example 13.7

6Important Points

• Order-up-to quantity covers the review period plus lead time — not lead time alone (unlike the continuous system's reorder point).
• Always subtract I (stock on hand at the time of review) at the very end.
• A periodic system's order quantity varies every cycle; only t_b is fixed.

7Common Mistakes