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Answer First
The EOQ model minimizes total inventory cost by choosing the order quantity where ordering cost and holding cost are perfectly balanced. At this point, the marginal cost of ordering more equals the marginal cost of holding more.
Problem Setup
The EOQ formula is: \[ Q^* = \sqrt{\frac{2DS}{H}}, \] where:
- \(D\) = annual demand,
- \(S\) = ordering cost per order,
- \(H\) = holding cost per unit per year.
Total cost is: \[ TC(Q) = \frac{DS}{Q} + \frac{HQ}{2}. \] The first term decreases with larger orders; the second increases.
Step-by-Step Explanation
1. Ordering cost decreases as order size increases
Fewer orders per year means lower ordering cost.
2. Holding cost increases as order size increases
Larger orders mean more inventory sitting in storage.
3. EOQ finds the balance point
The optimal quantity occurs where: \[ \text{ordering cost} = \text{holding cost}. \]
4. EOQ is robust and easy to compute
It requires only demand, ordering cost, and holding cost.
5. EOQ provides managerial insight
It shows how cost trade-offs drive inventory decisions.
Intuition
EOQ is like choosing the perfect batch size: too small and you order too often; too large and you hold too much inventory. EOQ finds the sweet spot.
Common Exam Mistakes
- Using purchase cost instead of holding cost.
- Forgetting that EOQ assumes constant demand.
- Ignoring lead time (EOQ does not include it).
- Misinterpreting annual vs. monthly demand.
Final Summary
The EOQ model minimizes total inventory cost by balancing ordering and holding costs. It provides a simple, powerful rule for inventory optimization in operations and supply chain management.
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