ฮฃ

OM / SCM / BA

Interactive Learning Module

Chenhao Zhou
PhD Candidate | Lecturer

The Newsvendor Model: Decision-Making Under Uncertainty

Single-Period Inventory Optimization with Stochastic Demand

๐Ÿ“š Learning Objectives

1

Understand the trade-off between overage costs (excess inventory) and underage costs (lost sales) in single-period inventory decisions

2

Apply the critical ratio formula to determine the optimal order quantity Q* that maximizes expected profit

3

Analyze how changes in cost structure, demand variability, and service level requirements impact optimal ordering decisions

4

Develop intuition for risk-return trade-offs in operations and strategic implications for capacity planning

โš™๏ธ Model Parameters
$20 $50 $100
$5 $30 $80
$0 $10 $25
50 100 units 200
10 25 units 50

Critical Ratio Formula

The optimal order quantity Q* satisfies:

F(Q*) = (p - c) / (p - s)
CR = Cแตค / (Cแตค + Cโ‚’)

Where Cแตค = underage cost, Cโ‚’ = overage cost

Stochastic Demand Single-Period Risk-Pooling Service Level
๐Ÿ“Š
0
Round
๐Ÿ“ฆ
0
Order Qty
๐Ÿ‘ฅ
0
Demand
โœ…
0
Units Sold
๐ŸŽฏ
0
Optimal Q*
๐Ÿ“ˆ
0%
Critical Ratio
๐Ÿ“ˆ Profit Analysis Over Rounds
๐Ÿ“Š Order vs Demand Distribution
๐ŸŽฎ Game Mode
๐Ÿ‘ค Your Decision $0
Cumulative Profit:$0
Avg. Fill Rate:0%
๐Ÿค– Optimal Strategy (Q*) $0
Order Quantity:Q*
Cumulative Profit:$0
๐Ÿ“‹ Performance Analysis
Critical Ratio (CR) 0.00
Optimal Q* (Z-score) 0.00
Expected Profit at Q* $0
Service Level 0%
๐Ÿ’ก Strategic Insights
๐Ÿ“Œ Configure parameters and enter your order quantity to begin. Compare your performance against the optimal newsvendor solution.

๐ŸŽฏ Key Managerial Insights

The Overage-Underage Trade-off

The newsvendor model captures the fundamental tension between ordering too much (overage cost: holding unsold inventory) and ordering too little (underage cost: lost profit from unmet demand). The optimal order quantity balances these competing risks.

Profit Margin Drives Risk Appetite

Higher profit margins (larger p-c relative to c-s) justify higher service levels and larger order quantities. Low-margin products require conservative ordering to minimize inventory risk.

Demand Variability Matters

Higher demand variability (ฯƒ) increases the importance of getting the order quantity right. Risk-pooling strategies, better forecasting, and flexible supply arrangements become more valuable as uncertainty grows.

๐Ÿ“š Academic References

Cachon, G., & Terwiesch, C. (2013). Matching Supply with Demand: An Introduction to Operations Management (3rd ed.). McGraw-Hill. โ€ข Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory Management and Production Planning and Scheduling. Wiley. โ€ข Porteus, E. L. (2002). Foundations of Stochastic Inventory Theory. Stanford University Press. โ€ข Chopra, S., & Meindl, P. (2016). Supply Chain Management: Strategy, Planning, and Operation (6th ed.). Pearson.