1. Project Title
Optimizing Ski Jacket Production Quantity under Demand Uncertainty
2. Project Objective
The objective of this project is to determine the optimal production quantity (Q*) for Arc’teryx ski jackets that maximizes expected profit while managing downside risk. This will be achieved by modeling uncertain demand using a truncated normal distribution and applying Monte Carlo simulation techniques.
3. Business Problem
Arc’teryx must decide how many ski jackets to produce for the upcoming winter season. Due to long production lead times, only one production run is possible. The key challenge is that future demand is uncertain, and incorrect production decisions can result in:
- Lost sales (underproduction)
- Excess inventory sold at a loss (overproduction)
Thus, management needs a data-driven approach to balance profitability and risk.
4. Scope of the Project
This project includes:
- Estimating demand distribution (mean and standard deviation) from historical expert inputs
- Modeling demand using a truncated normal distribution
- Simulating at least 1,000 demand scenarios using Excel
- Evaluating expected profit for different production levels (e.g., 7,800; 12,000; optimal Q* using solver)
- Calculating:
- Expected profit
- 95% confidence intervals
- Probability of loss
- Probability of large loss (> $100,000)
- 99% confidence intervals
5. Key Assumptions
- Demand follows a truncated normal distribution
- Selling price = $100 per unit
- Variable cost = $80 per unit
- Salvage value = $30 per unit
- Fixed cost = $100,000
- Unsold inventory is sold at salvage value
- No stock replenishment during the season
6. Methodology
The project will use a Monte Carlo simulation approach:
- Estimate the mean and standard deviation from the demand data
- Generate random demand values using a truncated normal distribution in Excel
- Calculate profit for each simulation scenario
- Repeat simulation (1,000+ times)
- Analyze output:
- Average profit
- Risk metrics
- Confidence intervals
- Compare multiple production quantities
- Identify optimal production level (Q*)
7. Key Deliverables
- Excel simulation model (with dynamic inputs)
- Summary table of results (mean, risk, CI, probabilities)
- Optimal production quantity recommendation
- Visual charts (distribution of profit, risk comparison)
- Final report with business insights
8. Success Criteria
The project is successful if it:
- Identifies a production quantity that maximizes expected profit
- Clearly explains risk-return trade-offs
- Provides actionable insights for decision-making
- Demonstrates accurate simulation and statistical analysis
9. Risks and Limitations
- Demand estimates may be biased (expert judgment)
- Model assumes normal distribution (may not fully reflect reality)
- Simulation results depend on input assumptions
- External factors (weather, economy) are not explicitly modeled
10. Final Recommendation (Based on Your Results)
Based on the simulation outcomes:
- Q = 9,761 provides the highest expected profit
- Q = 7,800 is the safest option with the lowest risk
- Q = 12,000 is not recommended due to lower returns and higher risk
Therefore, the recommended strategy is to produce approximately 9,761 units, as it offers the best balance between profitability and acceptable risk.
Note: This project has been completed under the guidelines of Professor Dr. Tallys Yunes, Department of Management Science, University of Miami