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This assignment revolves around making decisions on customer discounts using Excel functions such as IF statements, random number generation, and histogram analysis. The core task involves calculating whether customers are eligible for specific discounts based on probabilistic conditions, and visualizing the distribution of profit data through histograms derived from binning data points. Additionally, the problem considers a Newsvendor scenario with various order quantities, demanding an understanding of expected profit and probability loss calculations across different inventory levels.

Paper For Above instruction

The application of Excel functions and statistical tools is essential in modern business decision-making, especially in contexts like discount strategies and inventory management. This paper explores the integration of logical functions, probability assessments, and data visualization to optimize sales and profit outcomes.

In the context of discount determination, applying logical functions such as IF statements enables businesses to rationally decide which customers should receive discounts based on predefined criteria, like probability thresholds. For example, in the sample provided, a common approach involves generating a random number using Excel's RAND() function— which produces a uniform distribution between 0 and 1—and then comparing this random value against a probability cutoff, such as 0.63, to decide discount eligibility. This process is mathematically expressed as:

=IF(RAND() 
This formula creates a binary indicator—1 indicating a discount and 0 indicating no discount—effectively turning the probabilistic decision into a straightforward boolean value. This approach can be used to simulate real-world scenarios where only a subset of customers receive discounts, reflecting targeted marketing strategies or limited promotional allowances.
Implementing such probabilistic models is crucial for managing retail pricing, especially when aiming to balance customer acquisition and profit margins. Businesses might decide to offer a 4% or 7% discount depending on customer segmentation, purchasing history, or random sampling to increase perceived fairness and engagement.
Once discounts are decided, calculating these discounts involves multiplying the purchase amount by the discount percentage. For example, if a customer’s purchase amount is $100 and they qualify for a 7% discount, the discount amount would be $7, resulting in a discounted purchase price of $93. The model can be extended by multiplying the discount indicator (1 or 0) by the discount amount, ensuring that discounts are only applied where appropriate.
Mathematically, this can be summarized as:
Discounted Purchase = Purchase – Discount Amount
Discount Amount = Purchase × Discount Percentage × Discount Indicator
In scenarios where only 63% of customers are eligible for discounts, the above probabilistic approach effectively "turns off" the discount for the remaining 37%, by assigning a zero value when the random number exceeds the cutoff threshold. This method emulates real-world conditions where discount eligibility is probabilistic rather than deterministic.
Transitioning to data visualization, histograms serve as crucial tools for analyzing and illustrating the distribution of profits or sales data. In Excel, creating histograms involves selecting your data and binning parameters, then utilizing the Data Analysis Toolpak to generate both the histogram table and accompanying chart. This process provides a clear visual summary of how sales or profit figures are distributed across different ranges, which is particularly helpful in identifying patterns, outliers, and decision thresholds.
For example, in the newsvendor problem context, multiple order quantities are considered (e.g., q = 100, 120, 140, 160, 180). Each scenario's expected profit and probability of loss are calculated based on demand variability. The Excel setup includes defining demand parameters, calculating expected profits per day, and estimating the probability of incurring a loss. The histogram data bins are then used to visualize the frequency distribution of the profit or demand data, which aids in making optimal inventory decisions.
The process of generating histograms within Excel involves several steps:

Select the data set and the bin range (the bins or buckets).
Navigate to the Data tab and choose the Analysis Toolpak's Histogram function.
Configure the dialog box to produce the histogram in the current worksheet.
Interpret the resulting histogram chart to assess the distribution characteristics.

Understanding this distribution enables managers to optimize order quantities that maximize expected profit, considering the trade-off between excess inventory and stockouts. The newsvendor model offers a framework for quantifying these trade-offs, emphasizing the importance of demand forecasting, cost analysis, and probabilistic reasoning.
Specifically, the expected profit calculations aggregate daily profit data across different order quantities, integrating demand distribution, sales revenue, and salvage or scrap prices. Probabilistic analysis pinpoints the likelihood of surplus or shortfall, guiding decisions on optimal stock levels. The interplay between these factors underscores the necessity of both robust data analysis and effective visualization in supply chain optimization.
References

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