Expansion Strategy And Establishing A Reorder Point Grade
Expansion Strategy And Establishing A Re Order Point Grading Guideqnt
Write a 1,050-word report based on the Bell Computer Company Forecasts data set and Case Study Scenarios. Include answers to the following: Case 1: Bell Computer Company. Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expected profit? Compute the variation for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of minimizing the risk or uncertainty? Case 2: Kyle Bits and Bytes. What should be the re-order point? How many HP laser printers should he have in stock when he re-orders from the manufacturer? Format your assignment consistent with APA format. Plagiarism Free
Paper For Above instruction
Introduction
Decision-making under uncertainty is a crucial aspect of strategic planning in business operations. This report explores two primary cases: one concerning expansion strategies for Bell Computer Company and another focusing on determining optimal reorder points for Kyle Bits and Bytes regarding HP laser printers. Utilizing statistical tools such as expected value, variance, and the normal distribution, the analysis provides data-driven insights to guide managerial decisions under risk and uncertainty.
Case 1: Bell Computer Company - Expansion Strategy
Expected Value Analysis
The first step involves calculating the expected profits associated with two expansion alternatives—medium-scale and large-scale projects. Given the probability distribution for demand, the expected profit (\(E[P]\)) is calculated by summing the products of each possible profit and its respective probability. The formula used is:
\[E[P] = \sum_{i} P(x_i) \times \text{Profit}_i\]
where \(P(x_i)\) is the probability of demand state \(i\), and \(\text{Profit}_i\) is the profit corresponding to that demand level.
Suppose, based on the firm's forecast data, the profits for the medium-scale expansion at low, medium, and high demand levels are $200,000, $500,000, and $800,000, respectively, with associated probabilities of 0.20, 0.50, and 0.30. Calculating the expected profit yields:
\[
E[P]_{medium} = (0.20 \times 200,000) + (0.50 \times 500,000) + (0.30 \times 800,000) = \$590,000
\]
Similarly, for the large-scale expansion, with profits at these demand levels being $300,000, $700,000, and $1,200,000, the expected profit is:
\[
E[P]_{large} = (0.20 \times 300,000) + (0.50 \times 700,000) + (0.30 \times 1,200,000) = \$760,000
\]
Based on expected values, the large-scale expansion is financially preferable for maximizing expected profit.
Risk Analysis – Variance and Standard Deviation
To assess uncertainty, the variance (\(\sigma^2\)) of profits for each alternative is computed. The variance formula:
\[
\sigma^2 = \sum_{i} P(x_i) \times (x_i - E[P])^2
\]
provides a measure of risk associated with each choice. Calculations yield:
- For the medium-scale expansion, the variance:
\[
\sigma^2_{medium} = (0.20 \times (200,000 - 590,000)^2) + (0.50 \times (500,000 - 590,000)^2) + (0.30 \times (800,000 - 590,000)^2) \approx \$69.4 \text{ million}^2
\]
- For the large-scale expansion:
\[
\sigma^2_{large} = (0.20 \times (300,000 - 760,000)^2) + (0.50 \times (700,000 - 760,000)^2) + (0.30 \times (1,200,000 - 760,000)^2) \approx \$115.2 \text{ million}^2
\]
The standard deviation (\(\sigma\)) is the square root of variance. Choosing the expansion with lower risk aligns with minimizing uncertainty. Here, the medium-scale expansion, with a standard deviation of approximately \$8.33 million, presents less risk compared to the large-scale option (\(\approx \$10.74\) million). Therefore, if risk aversion is a priority, the medium-scale expansion may be more suitable, despite the lower expected profit.
Case 2: Kyle Bits and Bytes - Reorder Point
Determining the reorder point involves applying concepts from the normal distribution. Given the average weekly demand of 200 units, standard deviation of 30 units, and a service level requirement that stock-outs occur at most 6% of the time, the appropriate z-score is determined via standard normal distribution tables. For a 94% service level, the z-score is approximately 1.55.
Reorder Point (ROP)
The ROP formula:
\[
\text{ROP} = \text{Demand during lead time} + (z \times \sigma_{demand})
\]
where demand during lead time is the average weekly demand multiplied by lead time, which is 1 week in this case:
\[
\text{Demand during lead time} = 200 \times 1 = 200
\]
The safety stock is:
\[
\text{Safety Stock} = z \times \sigma_{demand} = 1.55 \times 30 \approx 46.5
\]
Thus, the reorder point:
\[
\text{ROP} = 200 + 46.5 \approx 247
\]
To maintain a 6% stock-out probability, Kyle should reorder whenever inventory falls to approximately 247 units. Similarly, the reorder quantity, or how many units to order each time, could be based on economic order quantity (EOQ) models, but the critical focus here is on the reorder point.
Conclusion
The analysis demonstrates the importance of statistical tools in strategic decision-making. For the expansion, the expected profit favors the large-scale project but with increased risk; hence, managers need to weigh risk tolerance levels. For inventory management, applying the normal distribution to determine reorder points ensures a balance between customer service levels and inventory costs. Integrating these quantitative methods enables more informed and effective managerial decisions.
References
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