Purpose Of Assignment: Two Cases In This Assignment

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

Introduction

Statistical decision-making plays a vital role in managerial economics, especially under conditions of uncertainty. This report addresses two distinct cases where statistical tools are employed to facilitate decision-making: the expansion strategy of Bell Computer Company and the inventory re-order point for Kyle Bits and Bytes. In the first case, the focus is on utilizing expected value and variance calculations based on probability distributions to determine the optimal expansion alternative. The second case assesses the appropriate re-order level for printers to avoid stockouts, applying normal distribution principles to real-world inventory management.

Case 1: Bell Computer Company - Expansion Strategy

Expected Value of Profit for Expansion Alternatives

The Bell Computer Company is considering two expansion options, each associated with different profit outcomes under uncertain market conditions. To determine the best course of action, the expected profit for each alternative must be computed. The expected value (EV) provides an average estimate of profit, weighted by the probability of various outcomes.

Suppose the profit outcomes and their probabilities for each alternative are given as follows (values are hypothetical for illustration; actual data should be derived from the provided dataset):

• Alternative 1: Profit outcomes of $50,000 (60% probability) and $80,000 (40% probability).
• Alternative 2: Profit outcomes of $70,000 (50% probability) and $100,000 (50% probability).

Calculating the expected values:

Based on expected profit, Alternative 2 is preferred, offering higher average returns ($85,000 vs. $62,000). This aligns with maximizing expected value as the decision criterion.

Variance and Risk Assessment

The variation or variance of profit indicates the risk or uncertainty associated with each alternative. Variance is computed as the expected value of the squared deviations from the mean:

• Variance for Alternative 1:

σ² = (0.6 × ($50,000 - 62,000)²) + (0.4 × ($80,000 - 62,000)²)
= 0.6 × (−12,000)² + 0.4 × 18,000²
= 0.6 × 144,000,000 + 0.4 × 324,000,000
= 86,400,000 + 129,600,000
= 216,000,000

σ² = 0.5 × (−15,000)² + 0.5 × 15,000²
= 0.5 × 225,000,000 + 0.5 × 225,000,000
= 112,500,000 + 112,500,000
= 225,000,000

While Alternative 2 has a higher expected value, its risk (variance) is slightly greater. If minimizing risk is the priority, Alternative 1 might be preferable despite its lower expected profit.

Decision Criteria: Expected Value vs. Variance

Using expected value as the decision criterion suggests choosing Alternative 2 for maximizing profits. However, when considering risk minimization, the slightly lower variance of Alternative 1 might make it more attractive to risk-averse managers. Ultimately, the decision depends on the firm's risk appetite.

Case 2: Kyle Bits and Bytes - Re-Order Point

Determining the Re-Order Point

The re-order point (ROP) is the inventory level at which a new order should be placed to replenish stock before running out. Calculating the optimal ROP involves analyzing demand variability and lead time.

Suppose Kyle's demand for HP laser printers follows a normal distribution with a mean demand of 20 printers per day and a standard deviation of 4 printers. The lead time from the manufacturer is 5 days. To prevent stockouts with a desired service level (e.g., 95%), the ROP can be computed as follows:

Re-Order Point (ROP) = (average demand per lead time period) + (z-score × standard deviation of demand during lead time)

Calculate average demand during lead time:

• Demand during lead time = 20 printers/day × 5 days = 100 printers

Calculate standard deviation during lead time:

• Standard deviation during lead time = √(lead time) × demand standard deviation per day = √5 × 4 ≈ 8.94 printers

Find z-score for 95% service level (z ≈ 1.645):

Re-Order Point:

ROP = 100 + (1.645 × 8.94) ≈ 100 + 14.73 ≈ 115 printers

Therefore, Kyle should reorder when the inventory level drops to approximately 115 printers, and he should stock around 115 units at the time of reordering to meet demand without stockouts with 95% confidence.

Optimal Stock Quantity at Re-Order

The reorder quantity, often determined by economic order quantity (EOQ), considers ordering costs, holding costs, and demand. Using EOQ models, the optimal stock size minimizes total inventory costs. Assuming the EOQ for Kyle's printers is calculated at 150 units (based on demand, ordering, and holding costs), he should keep around that many printers in stock at the point of reordering.

Conclusion

The analysis for Bell Computer Co. indicates prioritizing expected profit for expansion decisions, with a careful consideration of risk as indicated by variance. For Kyle Bits and Bytes, determining an appropriate re-order point using normal distribution assumptions helps prevent stockouts and optimize inventory levels. These applications highlight how statistical principles underpin critical managerial decisions, emphasizing that understanding probability distributions and related metrics is essential for effective operations and financial management.

References

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