Inventory EOQ Model (FM): A Complete Guide

Inventory EOQ Model (FM): A Complete Guide

Economic Order Quantity (EOQ) is a formula used to calculate the optimal order size for inventory that minimises the total costs of ordering and holding stock. It is a fundamental concept in working capital management, balancing the cost of holding inventory against the cost of ordering it from suppliers.

Why this actually matters

You are worried about what to study and what to ignore. The EOQ model is a classic, recurring topic in the FM exam, so focusing on it is a high-yield use of your limited study time. Mastering this guarantees you can pick up marks on a predictable question.

Structured breakdown

The EOQ model is built on a few key components. Understanding them is crucial for applying the formula correctly.

• Holding Costs (Ch): These are the costs associated with storing inventory until it is used. Examples include warehousing costs, insurance, security, and the opportunity cost of the capital tied up in inventory. It is usually expressed as a cost per unit per year.
• Ordering Costs (Co): These are the costs incurred each time an order is placed with a supplier. This includes administrative costs for processing the purchase order, delivery charges, and inspection costs upon arrival. It is expressed as a cost per order.
• Annual Demand (D): This is the total number of units your company expects to use or sell over the year. Predictability of demand is a key assumption of the basic EOQ model.
• The EOQ Formula: The formula itself is what you need to memorise. It is: EOQ = √[(2 * Co * D) / Ch].
• Re-order Level: This is the inventory level at which a new order should be placed. It is calculated as: Maximum Usage x Maximum Lead Time. This ensures you do not run out of stock while waiting for the new order to arrive.
• Total Annual Costs: The goal is to minimise total costs. These are calculated as: Total Holding Cost + Total Ordering Cost. Total Holding Cost = (EOQ/2) * Ch. Total Ordering Cost = (D/EOQ) * Co.

Worked example

A company has an annual demand for 24,000 units of a component. The cost of placing an order is $150. The cost of holding one unit in inventory for a year is $1.20.

Calculate the Economic Order Quantity (EOQ).

Step 1: Identify the variables

• Annual Demand (D) = 24,000 units
• Cost per Order (Co) = $150
• Holding Cost per unit (Ch) = $1.20

Step 2: Apply the EOQ formula

• EOQ = √[(2 * Co * D) / Ch]
• EOQ = √[(2 * $150 * 24,000) / $1.20]
• EOQ = √[$7,200,000 / $1.20]
• EOQ = √[6,000,000]
• EOQ = 2,449.49 units

Answer: The Economic Order Quantity is 2,449 units (rounded to the nearest whole unit).

Marking Logic:

• 1 mark for correctly identifying and substituting all three variables (D, Co, Ch) into the formula.
• 1 mark for the correct calculation and final answer.
• A question might ask you to calculate the total annual costs at the EOQ. You would show: Total Holding Cost = (2449/2) * $1.20 = $1,469.40. Total Ordering Cost = (24000/2449) * $150 = $1,469.98. The small difference is due to rounding the EOQ.

If you're working full-time

Trying to master every inventory model at once is a recipe for burnout. Focus solely on the EOQ formula this week. Spend one 30-minute session just memorising the formula and what each component means (D, Co, Ch). In your next 1-hour weekend session, practice two past exam questions on EOQ. That's it. This is a small, manageable topic you can lock down quickly to build confidence.

Common mistakes

• Mixing up Co and Ch: Confusing the cost per order (Co) with the holding cost per unit (Ch) is the most frequent error. Label them clearly in your workings.
• Using monthly demand: The formula requires annual demand (D). If the question gives you monthly figures, always multiply by 12.
• Incorrect holding cost calculation: Sometimes the holding cost is given as a percentage of the purchase price. Remember to calculate the monetary value per unit before using it in the formula.
• Forgetting the square root: It's a simple mistake under exam pressure. Always double-check you have taken the square root as the final step.
• Rounding too early: Keep the numbers in your calculator as long as possible and only round the final answer to the required precision.
• Ignoring bulk discounts: The basic EOQ model does not account for bulk purchase discounts. A more complex question might require you to compare the total costs at the EOQ with the total costs when ordering a larger quantity to get a discount. You must calculate both scenarios and choose the cheapest.

How examiners think

Examiners want to see that you can apply a formula methodically. It's not just about the final number. They award marks for structure and clear workings. Simply writing the final answer, even if correct, will not get you full marks.

• What scores marks: Stating the formula (√[(2 * Co * D) / Ch]), showing the substitution of the correct numbers into the formula, and then presenting the final answer. Clearly labelling your variables (D=..., Co=..., Ch=...) is a simple way to show the examiner you know what you're doing.
• What doesn't score marks: A jumble of numbers with no explanation. An answer without the formula or workings. Examiners cannot award marks for what they cannot see. They also don't award marks for lengthy written explanations of what the EOQ is, only for the correct application of it in the calculation.

FAQ

Calm summary

This topic does not need to be a source of stress. The EOQ formula is a small, predictable part of the FM syllabus that you can master.

Your next steps for this week:

1. Write the formula down: Write EOQ = √[(2 * Co * D) / Ch] on a flashcard or post-it note. Look at it once a day.
2. Define the terms: On the back of the card, write what D, Co, and Ch stand for.
3. Attempt one question: Find one past exam question on EOQ and attempt it, following the worked example structure above. Check your answer against the official solution. This should not take more than 20-30 minutes.

Completing these small tasks will build certainty and prove you are making progress.