Answer First

EOQ and newsvendor models balance cost tradeoffs by identifying the order quantity that minimizes total cost. EOQ applies when demand is stable and predictable, while the newsvendor model applies when demand is uncertain and unsold inventory or stockouts create asymmetric costs.

Problem Setup

1. EOQ Model
EOQ minimizes annual ordering and holding costs: \[ Q^* = \sqrt{\frac{2DS}{H}} \] where:
\(D\) = annual demand,
\(S\) = ordering cost per order,
\(H\) = annual holding cost per unit.

2. Newsvendor Model
The optimal order quantity balances underage and overage costs: \[ Q^* = F^{-1}\left(\frac{C_u}{C_u + C_o}\right) \] where:
\(C_u\) = underage cost (lost sales or stockout penalty),
\(C_o\) = overage cost (leftover inventory or markdown loss).

Step-by-Step Explanation

1. EOQ finds the cost-minimizing balance

Ordering too often increases ordering cost; ordering too much increases holding cost. EOQ finds the minimum 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 varies from period to period.

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 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.
• Mixing annual and per-period demand.

Final Summary

EOQ and newsvendor models balance cost tradeoffs under stable or uncertain demand. They are essential tools in operations management and supply chain analytics for determining optimal order quantities.

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