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Answer First
EOQ and newsvendor models optimize inventory decisions by balancing cost tradeoffs. EOQ minimizes annual ordering and holding costs for stable demand, while the newsvendor model chooses an order quantity that balances overage and underage costs under uncertain demand.
Problem Setup
The classic EOQ formula is: \[ Q^* = \sqrt{\frac{2DS}{H}} \] where \(D\) is annual demand, \(S\) is ordering cost, and \(H\) is holding cost per unit per year.
The newsvendor optimal order quantity is: \[ Q^* = F^{-1}\left(\frac{C_u}{C_u + C_o}\right) \] where \(C_u\) is underage cost, \(C_o\) is overage cost, and \(F^{-1}\) is the inverse demand distribution.
Step-by-Step Explanation
1. EOQ balances ordering and holding costs
Ordering too frequently increases ordering cost; ordering too infrequently increases holding cost. EOQ finds the minimum total cost point.
2. EOQ assumes stable demand
It works best when demand is constant and lead times are predictable.
3. Newsvendor handles uncertain demand
It chooses the quantity that minimizes expected cost when demand is random and unsold inventory has a penalty.
4. The critical fractile drives the newsvendor solution
The ratio \(\frac{C_u}{C_u + C_o}\) determines the optimal service level.
5. Both models appear on mid-semester exams
Students must compute optimal quantities, interpret cost tradeoffs, and explain assumptions.
Intuition
EOQ is about finding the “sweet spot” between ordering too often and holding too much. Newsvendor is about choosing the best bet when demand is uncertain and mistakes cost money.
Common Exam Mistakes
- Using EOQ when demand is uncertain.
- Forgetting to compute underage and overage costs.
- Misinterpreting the critical fractile.
- Ignoring units (annual vs per-period demand).
Final Summary
EOQ and newsvendor models optimize inventory decisions by balancing cost tradeoffs under stable or uncertain demand. They are essential tools in operations management and supply chain analytics.
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