Five 9s Communications

Inventory Management
Fundamentals

Economic Order Quantity • Reorder Point • Safety Stock

4 SectionsCore Topics
Final Exam20 Questions
80%Passing Score
~45 minEstimated Time
Section 1 of 5
1

Economic Order Quantity (EOQ)

Finding the optimal amount to order — every time

Imagine you manage the supply room at a busy service company. You need to keep printer paper stocked. You have two choices that both cost you money:

📦 Order too often (small amounts)

You're constantly calling suppliers, receiving shipments, and processing invoices. All that time and effort adds up — these are your ordering costs.

🏭 Order too rarely (large amounts)

You're holding mountains of paper in the warehouse. Space, insurance, and the risk of spoilage or damage all cost money — these are your holding costs.

EOQ finds the sweet spot — the order quantity where your total costs (ordering + holding) are at their lowest point.

⚙ The EOQ Formula
Q* = √( 2DS / H )
  • Q* — The optimal order quantity (what you're solving for)
  • D — Annual demand in units (how many you use/sell per year)
  • S — Cost to place one order (shipping fees, purchasing time, admin costs)
  • H — Annual holding cost per unit (storage, insurance, spoilage per unit per year)
📋 Worked Example — Hardware Store

A hardware store sells 2,400 boxes of screws per year. Each order costs $30 to process. Holding one box costs $2.00 per year.

1
Identify values: D = 2,400 | S = $30 | H = $2.00
2
Plug in: Q* = √( 2 × 2,400 × 30 / 2.00 )
3
Simplify: Q* = √( 144,000 / 2 ) = √72,000
4
Q* ≈ 268 boxes per order

At 268 boxes per order, the store would place about 9 orders per year (2,400 ÷ 268), roughly every 40 days.

Why does the formula work? As order quantity increases, ordering costs go down (fewer orders placed) but holding costs go up (more inventory sitting around). EOQ is the quantity where these two costs are exactly equal — the mathematical minimum of total cost.

📌 EOQ Model Assumptions
  • Demand is constant and known (no surprising spikes or drops)
  • Lead time is consistent and known
  • Ordering and holding costs are stable
  • No quantity discounts — price per unit stays the same regardless of order size
  • Items are independent (ordering one item doesn't affect another)
⚠ Real-World Note: These assumptions rarely hold perfectly. EOQ is a starting point — a mathematical foundation you'll refine with safety stock and a good reorder point. Think of it as the anchor, not the entire system.
🧮 EOQ Calculator — Try It Yourself
Optimal Order Quantity (EOQ)
Orders Placed Per Year
Days Between Orders
Annual Ordering Cost
Annual Holding Cost
Total Annual Inventory Cost
Section Quiz

EOQ Knowledge Check

2

Reorder Point (ROP)

Knowing exactly when to place your next order

EOQ tells you HOW MUCH to order. The Reorder Point tells you WHEN.

Here's the problem: when you place an order, it doesn't arrive instantly. Your supplier needs time to process and ship it — this is called lead time. During that waiting period, your inventory keeps being used. If you wait too long to order, you'll run out before the shipment arrives.

🔔 The Basic ROP Formula
ROP = d × L
  • d — Average daily demand (units sold or used per day)
  • L — Lead time in days (time from order to delivery)
  • ROP — When inventory hits this number, place an order immediately

How to think about it: ROP represents the amount of inventory you expect to consume while waiting for your order to arrive. By the time your shipment shows up, you've (ideally) used exactly the ROP quantity — arriving at zero just as the new stock lands.

📋 Worked Example — Parts Warehouse

A parts warehouse uses an average of 25 units per day. Their supplier consistently delivers within 6 days of an order being placed.

1
Identify values: d = 25 units/day | L = 6 days
2
Calculate: ROP = 25 × 6 = 150 units
3
Action: When inventory drops to 150 units, place an order for the EOQ amount.

By the time the shipment arrives 6 days later, the warehouse will have used approximately 6 × 25 = 150 units — landing at zero right as the new stock arrives.

What if you don't hit the ROP in time? You get a stockout — you run out of product before the order arrives. This means frustrated customers, halted operations, or costly emergency orders. That's where safety stock comes in (Section 3).

📈 When Lead Time Increases

Your ROP must increase. You'll consume more inventory during the longer wait, so you need to order earlier.

📊 When Daily Demand Increases

Your ROP must increase. You're burning through inventory faster, so the trigger point needs to come sooner.

⚠ Key Point: The basic ROP formula assumes demand and lead time are perfectly consistent. In reality, both can vary — which is exactly why we'll add safety stock to our ROP in Section 3.
🧮 ROP Calculator
Demand During Lead Time
Safety Stock Buffer
Reorder Point (ROP)
Interpretation
Section Quiz

Reorder Point Knowledge Check

3

Safety Stock

Your buffer against the unexpected

The world doesn't always cooperate. Demand can unexpectedly spike because of a promotion, a seasonal rush, or a competitor going out of stock. Suppliers can run late due to production issues, shipping delays, or weather. The basic ROP assumes everything goes according to plan — safety stock is your insurance policy when it doesn't.

Safety stock is extra inventory held above and beyond what's needed to meet expected demand during lead time. It sits in the background, ready to absorb the shock of unpredictable events.

🛡 Basic Safety Stock Formula
SS = (Max Demand – Avg Demand) × Lead Time
  • Max Demand — The highest daily demand you've ever seen (or reasonably expect)
  • Avg Demand — Your normal average daily demand
  • Lead Time — Days between ordering and receiving
  • SS — Units of safety stock to keep on hand
📋 Worked Example — Basic Method

A supply room normally uses 30 units per day, but on busy days it can spike to 50. The supplier takes 5 days to deliver.

1
Max demand = 50 | Avg demand = 30 | Lead time = 5 days
2
SS = (50 – 30) × 5 = 20 × 5 = 100 units
3
Full ROP = (30 × 5) + 100 = 150 + 100 = 250 units

The Statistical Method — For more precise safety stock calculation (used when you have historical demand data), the statistical formula uses standard deviation and a Z-score to hit a specific service level target:

📊 Statistical Safety Stock Formula
SS = Z × σd × √L
  • Z — Service level Z-score (see table below)
  • σd — Standard deviation of daily demand (how much demand varies)
  • √L — Square root of lead time in days
📋 Service Level Z-Score Reference
Target Service LevelMeaningZ-Score
85%85 out of 100 reorder cycles have no stockout1.04
90%90 out of 100 cycles — no stockout1.28
95%95 out of 100 cycles — no stockout1.65
98%98 out of 100 cycles — no stockout2.05
99%99 out of 100 cycles — no stockout2.33

Service Level Trade-Off: A higher service level means fewer stockouts — but it requires more safety stock, which means higher holding costs. Most companies balance between 90%–98% depending on how critical the item is and how severe a stockout would be.

🔗 Full ROP Including Safety Stock
ROP = (d × L) + SS
  • This is the complete, real-world Reorder Point formula
  • When inventory hits this level → place your EOQ-sized order
🧮 Safety Stock Calculator
Safety Stock
Avg Demand During Lead Time (d × L)
Full Reorder Point (d × L) + SS
Formula Used
Section Quiz

Safety Stock Knowledge Check

4

Putting It All Together

EOQ + ROP + Safety Stock working as one system

📦

EOQ

HOW MUCH to order each time

🔔

ROP

WHEN to place the order

🛡

Safety Stock

PROTECTION against variability

Together, these three tools create a complete, automatic inventory management cycle. Once set up, the system tells you exactly when to order and exactly how much — while protecting you from the inevitable bumps along the way.

Here's how the cycle works in practice: Inventory starts high (just received an order). Every day, demand pulls it down. When it reaches the ROP, you immediately place an order for the EOQ quantity. The safety stock sits at the bottom as a final buffer. By the time the order arrives, you've ideally consumed down to just your safety stock level — and the new shipment refills your back up.

🔗 The Complete System — All Three Formulas
  • EOQ: Q* = √( 2DS / H )
  • Safety Stock: SS = (Max Demand – Avg Demand) × L
  • Full ROP: ROP = (d × L) + SS

Full Worked Scenario — Metro Supply Co.

Metro Supply Co. manages industrial cable for field technicians. Here is all the data they need:

  • Annual demand (D): 3,600 spools/year
  • Order cost (S): $45/order
  • Holding cost (H): $3.00/spool/year
  • Average daily demand (d): 10 spools/day
  • Max daily demand: 16 spools/day
  • Lead time (L): 5 days
1

Calculate EOQ — How much to order?

Q* = √( 2 × 3,600 × 45 / 3.00 ) = √(324,000 / 3) = √108,000

EOQ ≈ 329 spools per order
2

Calculate Safety Stock — How much buffer?

SS = (16 – 10) × 5 = 6 × 5

Safety Stock = 30 spools
3

Calculate Full ROP — When to order?

ROP = (10 × 5) + 30 = 50 + 30

Reorder Point = 80 spools
4

The Automated Decision Rule

Metro Supply Co. sets up their system with one simple rule:

When inventory hits 80 spools → Order 329 spools immediately

That's it. The entire inventory management system for this item boils down to a single automated trigger. Review and recalculate these numbers periodically as demand patterns change, supplier performance shifts, or costs are renegotiated.

🧮 Full Integration Calculator
EOQ — Order This Many Units
Safety Stock
Reorder Point (Full)
Orders Per Year
Days Between Orders
Total Annual Inventory Cost

Final Assessment

Covering all three topics — EOQ, Reorder Point, and Safety Stock. Take your time and use the knowledge from all four sections.

20 Questions Passing Score: 80% (16/20) Results emailed on submission

Student Name
Email Address
ModuleInventory Management Fundamentals
Date
Final Score
Section 1 — EOQ
Section 2 — Reorder Point
Section 3 — Safety Stock