# Rowan Plan
## What It Is
The Rowan Plan is an incentive bonus scheme where the bonus is not a fixed percentage of time saved (unlike Halsey). Instead, the bonus depends on the worker's efficiency ratio — the proportion of standard hours actually used.
## Key Variables (same as Halsey)
| Symbol | Meaning |
|---|---|
| AH | Actual Hours worked |
| SH | Standard Hours allowed for units produced |
| R | Normal Time Rate per hour |
| (SH − AH) | Time Saved |
## Formulas
Bonus under Rowan Plan
$$\text{Bonus} = \frac{AH}{SH} \times (SH - AH) \times R$$
Total Earnings under Rowan Plan
$$\text{Total} = \underbrace{AH \times R}_{\text{Normal pay}} + \underbrace{\frac{AH}{SH} \times (SH - AH) \times R}_{\text{Bonus for time saved}}$$
Effective Hourly Rate
$$\text{Effective Rate per Hour} = \frac{\text{Total Amount}}{\text{Actual Hours Worked}}$$
## Intuition Behind the AH/SH Factor
The ratio AH/SH caps the bonus. As the worker becomes increasingly efficient (AH falls relative to SH), this fraction shrinks, dampening the bonus. This protects the employer from over-rewarding extreme efficiency that may reflect lax standards. The bonus peaks when AH/SH = 0.5 (i.e., worker takes exactly half of standard time).
## Halsey vs Rowan — Quick Comparison
| Feature | Halsey | Rowan |
|---|---|---|
| Bonus base | 50% of time saved | (AH/SH) × time saved |
| Bonus pattern | Linear in time saved | Parabolic — peaks at AH/SH = 0.5 |
| Risk to employer | Higher (unlimited 50% share) | Lower (self-capping) |
## Types of Questions Asked
1. Direct computation — calculate earnings/effective rate under one or both plans.
2. Reverse problem — one plan's data given, find missing data of the other.