Off-Peak Analysis

Off-Peak Period: Two Possible Approaches

1. Based on Peak Revenue (PR)

A time period is off-peak if its revenue is below a certain percentage of the peak revenue.

Formula:

$$OPR_t < \alpha \cdot PR$$

where:

• $OPR_t$ = Off-Peak Revenue at time ( t )

• PR = Peak Revenue

• $\alpha$ = Threshold percentage (e.g., 70% of PR)

2. Based on Average Revenue (AR)

A time period is off-peak if its revenue is significantly below the daily or weekly average revenue.

Formula:

$$OPR_t < \beta \cdot AR$$

where:

• $\beta$ is the threshold factor (e.g., 80% of AR)

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Deriving Revenue Difference Between Off-Peak and Normal Days

To quantify the financial impact of off-peak periods, we need to determine the difference in revenue between off-peak and normal periods.

Revenue Difference Formula

$$\Delta R = (AR - OPR) \times T_{off}$$

where:

• $\Delta R$ = Lost revenue due to off-peak periods

• AR = Average Revenue per unit time (hour, day, week)

• OPR = Off-Peak Revenue per unit time

• $T_{off}$ = Total duration of off-peak periods

Percentage Revenue Loss Due to Off-Peak Periods

$$\text{Loss Percentage} = \left( \frac{AR - OPR}{AR} \right) \times 100$$

This formula helps estimate how much revenue is lost during off-peak times.

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Example Calculation

Let’s assume:

• Peak Revenue (PR) = $10,000 per day

• Average Revenue (AR) = $7,000 per day

• Off-Peak Revenue (OPR) = $4,500 per day

• Off-Peak Time Share ($T_off$) = 5 hours out of a 12-hour business day

Revenue Difference Calculation

$$\Delta R = (7,000 - 4,500) \times \frac{5}{12} = 2,500 \times 0.4167 = 1,041.67$$

Thus, the revenue shortfall per off-peak period is $1,041.67.

Percentage Revenue Loss

$$\left( \frac{7,000 - 4,500}{7,000} \right) \times 100 = \left( \frac{2,500}{7,000} \right) \times 100 = 35.71\%$$

So, off-peak periods account for 35.71% revenue loss compared to normal periods.

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Using This Formula for Forecasting

By adjusting the ( $\alpha$ ) and ( $\beta$ ) values, a business can:

• Predict revenue differences for different off-peak time scenarios.

• Determine discount rates or incentives needed to reduce the impact of off-peak losses.

• Optimize pricing strategies for subscription models based on expected revenue fluctuations.