Can Overtime Really Boost Productivity? A Mathematical Model Reveals the Truth

Many industries are experiencing intense competition, and the "996" work model has become common, assuming longer hours increase output and efficiency.

However, excessive overtime may not significantly improve productivity and can cause efficiency decline, health issues, and reduced innovation. This article builds a mathematical model to reveal the relationship between overtime and output and quantify overtime costs.

1. Model Setup

We divide an employee's daily total output into three parts: output during regular work hours, output during overtime, and the costs of overtime (health loss, overtime pay, turnover intention, creativity decline, etc.).

Based on these factors, we establish a mathematical model for total daily output.

2. Output During Regular Work Hours

Assuming a stable unit-time work efficiency during the standard 8‑hour workday, let the hourly efficiency be ... The total output of regular work is ... (formula omitted).

This output reflects that employees can maintain relatively high efficiency within a reasonable work duration.

3. Output During Overtime

When employees work overtime, fatigue and reduced attention cause efficiency to decline as overtime increases. We use an efficiency‑decay model, assuming hourly overtime efficiency decays exponentially. The total overtime output is ... (formula omitted).

The formula shows that as overtime lengthens, marginal output decreases and eventually the marginal benefit of overtime diminishes.

4. Overtime Costs

Overtime costs include not only additional wages but also health loss, increased turnover intention, and reduced creativity.

Health Loss Cost

Health loss cost is assumed proportional to overtime hours.

Overtime Wage Cost

Companies must pay extra wages for overtime, also proportional to overtime hours.

Turnover Intention Cost

Longer overtime raises employees' turnover tendency, increasing recruitment and training costs, proportional to overtime hours.

Creativity Loss Cost

Extended overtime harms creativity and innovation, especially in innovation‑required environments, with cost proportional to overtime hours.

Total Cost

The total cost is the sum of all individual costs, simplified as a comprehensive cost coefficient representing the total cost per hour of overtime.

5. Total Output Formula

Combining regular work output, overtime output, and overtime costs yields the complete formula for an employee’s daily total output.

6. Model Analysis and Conclusions

The model shows that moderate overtime can increase output in the short term, but as overtime extends, efficiency drops sharply while costs rise linearly. Beyond a certain threshold, total output may fall below that of normal work, even becoming negative.

In the short term, moderate overtime increases output, but the benefit is limited.

Further overtime leads to rapid efficiency decline, while costs increase linearly.

To maximize output, companies should balance reasonable overtime and mitigate costs with appropriate compensation.

Overall, excessive overtime harms health, reduces efficiency, raises turnover risk, and weakens innovation, ultimately decreasing company productivity.

Companies should control overtime, optimize work hours, and ensure work‑life balance to achieve the highest output.