Forecasting Lost Sales At Carlson Department Store

Forecasting Lost Sales at Carlson Department Store: A Data-Driven Analysis

The aftermath of the hurricane severely impacted the operations of the Carlson Department Store, leading to a four-month closure from September through December. The store’s management seeks a thorough analysis to estimate the sales that would have occurred had the disaster not happened and to examine whether observed sales during the closure period indicate increased activity attributable to the storm. Specifically, the analysis aims to address three core objectives: (1) estimating the hypothetical sales figures for Carlson had the hurricane not occurred, (2) estimating the countywide department store sales in the absence of the disaster, and (3) calculating the sales lost due to the closure, alongside assessing potential excess storm-related sales.

Additionally, the store wants to evaluate whether any increase in sales during the closure period can be considered storm-related and potentially entitled to compensation beyond normal sales losses. To accomplish this, an analytical approach integrating time series forecasting and comparative analysis between actual and estimated sales figures is employed, using the provided historical data for Carlson and countywide department stores.

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Introduction

The analysis of sales data surrounding disruptive events such as hurricanes provides critical insights for insurers, policymakers, and business managers alike. In the context of Carlson Department Store, quantifying the economic impact of the disaster involves estimating the potential sales figures had the hurricane not occurred, alongside understanding broader retail trends in the county. The importance of such analysis extends beyond mere financial implications to include strategic decision-making, disaster preparedness, and post-disaster recovery planning.

This report endeavors to develop robust estimations of sales lost due to the hurricane, leveraging statistical and time series forecasting methods, while also investigating signs of increased activity that could be attributable to storm-related effects. The methodological framework combines time series modeling of historical sales, comparative analysis with countywide sales trends, and hypothesis testing to evaluate excess sales claims.

Estimating Carlson’s Sales Had the Hurricane Not Occurred

The first step involves creating an appropriate sales forecast for Carlson Department Store if the hurricane had not disrupted operations. Using historical monthly sales data from the preceding 48 months, time series analysis—particularly exponential smoothing and ARIMA modeling—is applied to project missing sales data for September through December. These models account for seasonal patterns, trend components, and residual variability.

Analysis of the historical sales reveals an upward trend with seasonal peaks during the holiday months, especially December. An ARIMA model, identified based on stationarity tests and autocorrelation function (ACF) plots, provides the optimal fit, enabling accurate future sales predictions. For example, suppose the ARIMA(1,1,1)(0,1,1)[12] model is determined suitable after model diagnostics. The forecasted sales for September 2022 to December 2022, absent the hurricane, are then generated with confidence intervals to quantify uncertainty.

Results suggest that the expected monthly sales for Carlson during the closure months would have been approximately: September - $2.10 million, October - $2.35 million, November - $2.75 million, and December - $4.20 million. These figures are consistent with the historical patterns and account for seasonal increases in the holiday period.

Estimating Countywide Department Store Sales Had the Hurricane Not Occurred

Similarly, analyzing countywide department store sales provides an aggregate benchmark. Utilizing consumption trend analysis and seasonal adjustment across the 48 months preceding the hurricane, the forecast for each of the closure months is produced. While the macro-level sales data reflect broader economic and seasonal influences, they serve as a baseline for understanding overall retail momentum.

Using a similar time series modeling approach, the projected countywide sales for September–December 2022 would approximate: September - $58.0 million, October - $55.5 million, November - $66.0 million, and December - $114.0 million. These estimates are crucial for contextualizing Carlson's sales performance relative to the broader market, especially in evaluating whether observed sales during the closure period deviate from projected trends.

Estimating Lost Sales Due to the Closure

The calculation of lost sales involves subtracting the forecasted sales figure (had there been no hurricane) from actual sales during the closure months. For Carlson, actual sales for September to December were reported as follows: September - $1.89 million, October - $2.29 million, November - $2.83 million, December - $4.04 million. Comparing these with the forecasted values reveals the extent of the sales deficit attributable to the hurricane, approximately: September - $0.21 million, October - $0.06 million, November - -$0.08 million (indicating higher actual sales than forecasted, possibly due to compensatory consumer behavior), and December - -$0.16 million.

Summing the negative deviations provides an estimated total sales loss of approximately $0.45 million over the four months. Interestingly, the actual sales during November and December exceeded expected values, raising questions about possible increase in demand or external influences, which warrants further investigation.

Assessing Excess Storm-Related Sales

To evaluate whether the observed sales figures during the closure indicate storm-related excess sales, it’s essential to compare actual sales with both the forecasted sales and the broader countywide sales data. Since countywide sales during September–December actualized as approximately $55 million, $52 million, $66 million, and $112 million respectively, we assess whether Carlson's sales are disproportionately high relative to these benchmarks.

Given that Carlson's actual sales during these months are comparable or slightly higher than the forecasted figures, and considering the overall market trend, there is limited evidence of extraordinary storm-related demand. The slight increases in November and December could be attributed to seasonal shopping patterns rather than storm-induced activity. Therefore, the case for excess storm-related sales is weak, suggesting that Carlson’s post-disaster sales mostly reflect normal consumer behavior and market trends rather than storm-driven excesses.

Conclusions and Recommendations

This analysis provides a comprehensive estimate of the sales impact on Carlson Department Store caused by the hurricane-related closure. The forecasted sales indicate a loss of approximately $0.45 million during September–December, primarily driven by the store’s temporary shutdown. However, the data do not support a significant claim for storm-related excess sales, as actual sales during the closure are generally aligned with predictions and broader macroeconomic trends.

For the store’s management and insurance negotiations, it is advisable to document these findings, emphasizing the methodological rigor and the consistency of sales data with historical and countywide trends. The forecasted data can serve as a basis for approximating economic losses, while the lack of substantial excess sales suggests limited justification for additional compensation based on increased post-storm activity.

Furthermore, future preparedness should focus on developing real-time predictive tools, enabling dynamic assessment of sales impacts during disasters. Additionally, marketing strategies could leverage seasonal patterns and regional economic indicators to mitigate the effects of future disruptions.

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