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UPSC MainsMANAGEMENT-PAPER-II20135 Marks
Q27.

Using a weighted average of 0.40, 0.30, 0.20 and 0.10 for week 1, week 2, week 3 and week 4 ago respectively, what is the weighted average forecast for Monday of the current week?

How to Approach

This question requires a straightforward application of weighted average calculation. The approach involves understanding the concept of weighted average, identifying the given weights and corresponding values (which are missing and need to be assumed for demonstration), and then performing the calculation. The answer should clearly show the formula used and the steps involved in arriving at the final weighted average forecast. Since the actual values for each week are missing, we will assume hypothetical values for demonstration purposes.

Model Answer

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Introduction

Forecasting is a crucial aspect of management, enabling informed decision-making in various domains like inventory control, sales projections, and resource allocation. Weighted averages are a common technique used in forecasting, assigning different weights to past observations based on their perceived relevance to the future. This method acknowledges that more recent data often holds greater predictive power. The question asks for the weighted average forecast for Monday of the current week, utilizing specific weights for the preceding four weeks.

Understanding Weighted Average

A weighted average is calculated by multiplying each value in a dataset by a corresponding weight, summing the results, and then dividing by the sum of the weights. The formula is as follows:

Weighted Average = (Value1 * Weight1 + Value2 * Weight2 + ... + Valuen * Weightn) / (Weight1 + Weight2 + ... + Weightn)

Applying the Formula to the Question

In this case, we are given the following weights:

  • Week 1 ago: 0.40
  • Week 2 ago: 0.30
  • Week 3 ago: 0.20
  • Week 4 ago: 0.10

Since the actual sales/demand figures for each Monday of the previous four weeks are not provided, let's assume the following hypothetical values for demonstration:

  • Monday, Week 1 ago: 100 units
  • Monday, Week 2 ago: 110 units
  • Monday, Week 3 ago: 120 units
  • Monday, Week 4 ago: 130 units

Calculation

Now, we can calculate the weighted average forecast for Monday of the current week:

Weighted Average Forecast = (100 * 0.40 + 110 * 0.30 + 120 * 0.20 + 130 * 0.10) / (0.40 + 0.30 + 0.20 + 0.10)

Weighted Average Forecast = (40 + 33 + 24 + 13) / 1.0

Weighted Average Forecast = 110 / 1.0

Weighted Average Forecast = 110 units

Sensitivity Analysis

It's important to note that the accuracy of this forecast heavily relies on the accuracy of the assumed values for the previous Mondays. A sensitivity analysis, where different values are tested, can provide a range of possible forecasts and help assess the potential impact of variations in past data.

Limitations

This method assumes a linear relationship between past and future values. It doesn't account for external factors like seasonality, promotions, or economic changes that might influence demand. More sophisticated forecasting techniques, such as exponential smoothing or regression analysis, may be necessary for more accurate predictions in complex scenarios.

Conclusion

In conclusion, using the provided weights and the assumed values for the previous four Mondays, the weighted average forecast for Monday of the current week is 110 units. This calculation demonstrates the application of a common forecasting technique. However, it’s crucial to remember that the accuracy of the forecast depends on the quality of the input data and the underlying assumptions. A more robust forecasting system would incorporate additional factors and potentially utilize more advanced statistical methods.

Answer Length

This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.

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Additional Resources

Key Definitions

Forecasting
Forecasting is the process of making predictions of the future based on past and present data, and analysis of market trends. It is a key component of planning and decision-making in organizations.
Weighted Average
A weighted average is an average where some elements contribute more than others. The weights represent the importance of each element. It is calculated by multiplying each element by its weight, summing the results, and dividing by the sum of the weights.

Key Statistics

According to a report by Statista, the global market for forecasting software is projected to reach $1.4 billion by 2027.

Source: Statista (as of knowledge cutoff 2023)

A study by McKinsey found that companies that effectively use predictive analytics, including weighted average forecasting, are 23 times more likely to acquire customers and six times more likely to retain them.

Source: McKinsey (as of knowledge cutoff 2023)

Examples

Retail Inventory Management

Retailers use weighted average forecasting to predict demand for products, allowing them to optimize inventory levels and minimize stockouts or overstocking. For example, a clothing store might use sales data from the past four weeks, weighted by their relative importance, to determine how many units of a particular shirt to order for the upcoming week.

Frequently Asked Questions

▶What happens if the sum of the weights is not equal to 1?

If the sum of the weights is not equal to 1, the weighted average needs to be normalized by dividing the numerator (sum of weighted values) by the sum of the weights. This ensures that the weighted average falls within the same range as the original data.

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