Economic Order Quantity and total inventory cost
Compute EOQ, the number of orders and the total ordering-plus-carrying cost from annual demand and per-order costs.
Marks
5 marks
Exam time
8 min
Difficulty
Easy
The question
A manufacturer consumes 10,000 units of a raw material each year. The cost of placing one order is ₹200 and the cost of carrying one unit in stock for a year is ₹4. Compute the Economic Order Quantity, the number of orders to be placed each year, and the total annual cost of ordering and carrying inventory at the EOQ level.
- Given
- Annual demand (A) = 10,000 unitsOrdering cost (O) = ₹200 per orderCarrying cost (C) = ₹4 per unit per year
Formulas used
- EOQ = √(2AO ÷ C)
- Number of orders = A ÷ EOQ
- Total ordering cost = (A ÷ EOQ) × O
- Total carrying cost = (EOQ ÷ 2) × C
Step-by-step working
01Apply the EOQ formula
2EOQ = √(2 × 10,000 × ₹200 ÷ ₹4) = √(₹40,00,000 ÷ ₹4) = √10,00,000 = 1,000 unitsWrite the substitution line before the answer. Examiners award the formula and substitution marks separately from the final figure.
02Compute the number of orders
1Number of orders = 10,000 ÷ 1,000 = 10 orders per year
03Compute ordering and carrying cost
2Ordering cost = 10 orders × ₹200 = ₹2,000 Carrying cost = (1,000 ÷ 2) × ₹4 = ₹2,000 ──────── Total inventory cost = ₹4,000At EOQ, ordering cost always equals carrying cost. If your two figures differ, your EOQ is wrong — this is the fastest self-check available in the paper.
EOQ / orders / total cost
1,000 units · 10 orders · ₹4,000
Where marks are lost
- Using carrying cost as a percentage of price without first converting it to rupees per unit per year.
- Forgetting that purchase cost of the material itself is not part of the EOQ trade-off — only ordering and carrying costs are.
- Reporting the total cost as ₹2,000 by computing only one of the two components.
In the exam
EOQ appears almost every attempt in some form. The variants that catch students are quantity discounts and a stated safety stock — neither changes the EOQ formula itself, but both change the total cost computation that follows it.
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Talk to usDoes EOQ change if the purchase price of the material changes?
Not directly. The basic EOQ formula uses only annual demand, ordering cost and carrying cost per unit. Price matters only when carrying cost is expressed as a percentage of price, or when a quantity discount is offered — in which case you compare total cost at EOQ against total cost at each discount level.
Why does ordering cost equal carrying cost at EOQ?
EOQ is the point where the two curves intersect, which is exactly what minimises their sum. It is a useful check: compute both and confirm they match before writing your final answer.
Reading a solution is not practice. Writing one is.
Generate fresh numericals on this exact chapter, attempt them under time, and have your written working evaluated step by step.
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