Purpose Of Assignment: This Assignment Has Two Cases The Fir

Purpose Of Assignmentthis Assignment Has Two Cases The First Case Is

This assignment has two cases. The first case is on expansion strategy. Managers constantly have to make decisions under uncertainty. This assignment gives students an opportunity to use the mean and standard deviation of probability distributions to make a decision on expansion strategy. The second case is on determining at which point a manager should re-order a printer so he or she doesn't run out-of-stock.

The second case uses normal distribution. The first case demonstrates application of statistics in finance and the second case demonstrates application of statistics in operations management. Assignment Steps Resources: Microsoft Excel®, Bell Computer Company Forecasts data set, Case Study Scenarios Write a 1,050-word report based on the Bell Computer Company Forecasts data set and Case Study Scenarios. Include answers to the following:

Paper For Above instruction

The following report provides a comprehensive analysis of two critical managerial decision-making scenarios faced by Bell Computer Company and Kyle Bits and Bytes. These cases demonstrate the practical application of statistical methods—specifically probability distributions and normal distribution—in making informed decisions under uncertainty, thereby enhancing operational efficiency and financial performance.

Case 1: Bell Computer Company - Expansion Strategy

In the first case, Bell Computer Company needs to evaluate two expansion alternatives using statistical measures to determine which offers the best expected profit while managing risk. The core objective is to utilize probability distributions—namely, mean and standard deviation—to help managers make decisions that maximize expected outcomes and minimize potential losses due to uncertainty.

To compute the expected value (mean) of profits associated with each expansion option, we analyze the profit distribution data provided in the Bell Computer Forecasts dataset. The expected value represents the average profit expected for each alternative, considering the probabilities of different profit outcomes. For each option, the formula involves summing the product of potential profit outcomes and their associated probabilities:

Expected Profit = Σ (Profit_i × Probability_i)

Suppose, for example, Expansion Option A has profit outcomes of $100,000, $150,000, and $200,000 with associated probabilities of 0.3, 0.5, and 0.2 respectively. The expected profit would be calculated as:

Expected Profit_A = (100,000 × 0.3) + (150,000 × 0.5) + (200,000 × 0.2) = $35,000 + $75,000 + $40,000 = $150,000

This process is repeated for each expansion alternative using their respective data. The alternative with the higher expected profit is preferred if the objective is profit maximization.

Next, the variability or risk associated with each alternative is assessed through the standard deviation of profits. The standard deviation quantifies the dispersion of outcomes around the mean, with higher values indicating greater risk or uncertainty. The calculation involves:

Standard Deviation = √[Σ (Profit_i − Expected Profit)² × Probability_i]

By calculating the standard deviation for both options, managers can determine which expansion strategy minimizes risk, aligning with risk-averse decision-making strategies. Typically, the preferred alternative balances a high expected value with manageable risk.

Case 2: Kyle Bits and Bytes - Reorder Point

The second scenario involves determining the optimal reorder point for HP laser printers to prevent stockouts while minimizing inventory costs. When employing normal distribution in operations management, the key is to calculate the reorder point based on the demand variability and lead time.

The reorder point (ROP) considers the average demand during the lead time plus safety stock, which accounts for demand variability. Mathematically, the reorder point is expressed as:

ROP = Average demand during lead time + Z-score × Standard deviation of demand during lead time

To compute this, the average daily demand and standard deviation from historical demand data (provided in the dataset) are used. The Z-score corresponds to the desired service level—e.g., a Z-score of 1.65 for 95% service level, meaning there's a 95% chance stock will not run out during the lead time.

Assuming the average daily demand is 20 printers with a standard deviation of 5 printers, and the lead time is 7 days, the calculations are as follows:

Average demand during lead time = 20 × 7 = 140 printers

Standard deviation during lead time = √7 × 5 ≈ 13.2 printers

The Z-score for a 95% service level is 1.65. Therefore, the safety stock is:

Safety stock = 1.65 × 13.2 ≈ 21.78 printers

Consequently, the reorder point is:

ROP = 140 + 21.78 ≈ 161.78 printers

When Kyle reorders at approximately 162 printers, he maintains a 95% service level, reducing the risk of stockouts.

Conclusion

This analysis underscores the importance of statistical decision-making tools. For Bell Computer Company, understanding expected profits and risk allows for more strategic expansion decisions that balance profitability and risk exposure. For Kyle Bits and Bytes, accurately calculating the reorder point using demand variability and safety stock ensures continuous service while optimizing inventory holding costs. These applications demonstrate how probability distributions and normal distribution models are essential in operational and financial management, guiding managers in making data-driven decisions under uncertainty.

References

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