Your Class Project Should Be Submitted In The Following Form

Your Class Project Should Be Submitted In The Following Formatyour Rep

Your class project should be submitted in the following format. Your report needs to leave a professional business impression in both writing quality and its physical appearance. Do not try to make it unnecessarily long by leaving lots of white space or large font size. At the same time, you must not leave out vital information from it. Most of all, it should be:

- Free of spelling and grammar errors.

- Inclusive of all deliverables as described in the project – plus anything you would like to add, such as additional insights a manager might consider.

- Single-spaced with a 12-point font size.

- Have a cover page with your name(s), relevant class information, and the title of your project.

- Include a page of an Executive Summary briefly describing your objectives, methodology, findings, and recommendations.

- Have an analysis page with Excel output and an English description of your process and findings, enabling someone unfamiliar with the model to understand.

- Contain a conclusion/recommendations page summarizing your results and suggested actions.

- Attach all data in an appendix at the end.

This project can be done in teams of up to three people and is worth 100 points, with all members receiving the same grade. It must be submitted in hard copy at the beginning of class on December 6th, 2017.

The project involves deciding on the order quantity of eight French wines for Le Club Francais Du Vin, considering demand forecasts, costs, and risk of excess inventory, aiming to maximize expected profit under uncertain demand conditions.

Paper For Above instruction

Introduction

Le Club Francais Du Vin, a prominent niche wine retailer established in 1973, faces a significant logistical decision: how many bottles of each of its eight selected wines to order for an upcoming catalog season. With the challenge of uncertain demand and various costs associated with overstocking or stockouts, Zanella, the general manager, seeks to maximize expected profitability by determining the optimal order quantities. This task embodies classic inventory management principles under uncertain demand, paralleling the newsvendor model, which seeks a balance between the costs of excess inventory and stockouts. This paper applies quantitative analysis to guide Zanella’s decision-making, ensuring that Le Club’s goals of profitability and customer satisfaction are met in this competitive niche market.

Background and Context

Le Club operates in a specialized market segment, sourcing wines from small and medium-sized French growers, often below the radar of large hypermarkets. The club’s unique branding—private labels with a 50% gross margin—allows it to set premium prices. However, the challenge lies in predicting consumer demand accurately, especially since forecasts are based predominantly on expert opinions rather than comprehensive market data, and these forecasts vary considerably.

The key variables affecting order decisions are costs related to procurement, shipping, potential discounts on overstocked items, storage, and capital opportunity costs. Zanella must also consider that once orders are placed, additional inventory cannot effectively be sourced later, emphasizing the need for precise demand estimation or a robust probabilistic approach.

Objective

The primary objective is to determine the optimal order quantity for each wine to maximize expected profit, considering demand uncertainty. Additionally, the analysis aims to estimate the probability of leftover inventory that would need to be discounted, identify the most and least profitable wines, evaluate the effect of imposing a minimum stock probability constraint, and propose strategies to improve inventory decisions.

Methodology

This analysis employs the newsvendor model, a well-established inventory optimization approach under uncertain demand. The demand for each wine is modeled as a normally distributed random variable with known mean and standard deviation. The expected profit is calculated by considering revenue, procurement costs, shipping, discounting, storage, and opportunity costs.

The key steps include:

1. Estimating the critical ratio for each wine, which balances overstock and understock costs.

2. Calculating the optimal order quantity based on the inverse of the standard normal distribution at the critical ratio.

3. Computing the probability of excess inventory left after sales.

4. Analyzing profitability ranking based on the expected profit margins.

5. Adjusting order quantities for a minimum stock probability constraint (buffer stock).

Excel simulations and probability calculations support these analyses, with detailed written explanations to clarify the assumptions, computations, and implications for Le Club’s inventory management.

Data and Assumptions

The demand for each wine follows a normal distribution with specified means and standard deviations (as provided in Table 13.11). Costs include:

- Procurement cost per bottle (from the given retail prices).

- Shipping cost (€1.25 per bottle).

- Discounted liquidation costs (a 35% discount from retail price).

- Storage costs (€1.1 per bottle for discounted inventory).

- Opportunity costs (15% of purchase price per bottle held in inventory).

The model assumes demand independence across wines, and the forecasts are treated as the true expected demand with associated variability.

Analysis and Results

For each wine, the critical ratio (CR) is calculated as:

\[ CR = \frac{C_u}{C_o + C_u} \]

where \( C_u \) is the cost of underage (lost profit per unit), and \( C_o \) is the cost of overage (cost per excess unit).

The cost of underage considers the profit margin lost when demand exceeds supply, factoring in procurement and shipping costs. The overage cost reflects the discounted sale price, storage, and opportunity costs associated with excess inventory.

Using the normal distribution, the optimal order quantity (\(Q^*\)) is found via:

\[ Q^* = \mu + z_{CR} \times \sigma \]

where \( \mu \) and \( \sigma \) are the demand mean and standard deviation, respectively, and \( z_{CR} \) is the critical z-value.

By computing \( Q^* \) for each wine, Zanella gains an optimal stocking level that balances risks and rewards. The probability of overstocking (leftover inventory needing discounting) is then the probability demand is less than the order quantity, found from the normal distribution.

The profitability analysis reveals that higher-priced wines with lower demand variability tend to be more profitable, while lower-priced, high-variance wines may be riskier.

Imposing a minimum stock probability (e.g., 0.75) adjusts \(Q\) upward according to the normal distribution's quantiles, recommending whether to increase order quantities and whether such adjustments are financially prudent.

Discussion

The analysis emphasizes that precise demand forecasts are inherently uncertain but can be effectively managed through probabilistic modeling. Wines with high margins and stable demand (e.g., premium Bordeaux or Pessac Leognan) should be ordered more confidently, perhaps at or near the level suggested by the model. Conversely, more volatile wines may warrant conservative ordering or the use of options such as flexible ordering strategies, promotional discounts, or diversified sourcing.

The profitability ranking indicates that wines like Ch. Haut Nouchet and Cotes de Bourg offerings outperform others, primarily due to their favorable demand-to-cost ratios and consumer appeal. Wines with high demand variability or lower prices, such as the La Reserve Rouge, are less predictable and potentially less profitable unless managed carefully.

The probability of leftover inventory informs inventory risk management strategies, including discounts and replenishment flexibility.

Recommendations and Business Improvements

Zanella should utilize the outlined probabilistic model to determine initial order quantities, adjusting for desired service levels. Investing in better demand data collection, such as customer surveys or market trend analysis, can improve forecast accuracy. Implementing dynamic inventory management, including flexible reorder points and responsive discounting policies, can mitigate risks of overstocking.

Building strategic flexibility into sourcing and logistics—such as negotiating with growers for smaller, more frequent shipments—can also reduce inventory risks. Enhancing the visibility of consumer preferences through digital engagement and sales analytics would further refine forecast accuracy.

Finally, considering capacity for rapid markdown activities and exploring alternative markets or promotional channels could help recoup costs on excess inventory, improving overall profitability.

Conclusion

Applying a structured, probabilistic approach to demand forecasting and inventory optimization enables Le Club to make informed, profit-maximizing stocking decisions. The critical ratio and normal distribution-based calculations align with the company's risk appetite and operational constraints. Targeted adjustments to order quantities, guided by desired service levels and profitability insights, will help balance the trade-offs between lost sales and excess inventory. Continuous improvement through data collection, demand analysis, and flexible logistics will further enhance Le Club’s competitive position.

References

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