If (R) is the base rate guaranteed per hour, (S) is the standard time for the job and (T) is the actual time, then according to Rowan plan, wages for the job will be-
TR + [(S - T)/S] × R
Calculating Wages under the Rowan Plan
The Rowan plan is a type of premium bonus plan designed to incentivize workers to complete tasks in less than the standard time allocated for the job. It aims to provide a bonus that increases with time saved, but at a decreasing rate, encouraging both efficiency and quality.
In this plan, wages are calculated based on the actual time taken to complete the job and a bonus based on the time saved.
Let's define the given variables:
- R: The base rate guaranteed per hour.
- S: The standard time allowed for completing the job.
- T: The actual time taken by the worker to complete the job.
The Rowan Plan Wage Formula Explained
According to the structure presented in the options, the formula for wages under the Rowan plan is given by:
\( \text{Wages} = TR + \left[ \frac{S - T}{S} \right] \times R \)
Let's break down this formula to understand each part:
- TR: This part represents the base wage. It is calculated by multiplying the actual time the worker spent on the job (T) by their guaranteed base rate per hour (R). This is the minimum earning the worker receives for the time worked, regardless of whether they finished the job within or beyond the standard time.
- \( S - T \): This term represents the time saved. It is calculated when the actual time taken (T) is less than the standard time (S) allowed for the job. If \( T \ge S \), no time is saved, and consequently, no bonus is typically paid under incentive schemes like this, with the worker earning just the base wage TR.
- \( \frac{S - T}{S} \): This ratio calculates the proportion of time saved relative to the standard time set for the job. For example, if the standard time is 8 hours (S=8) and the worker finishes in 6 hours (T=6), time saved is 2 hours (\(S-T=2\)), and the proportion of time saved is \( \frac{2}{8} = \frac{1}{4} \).
- \( \left[ \frac{S - T}{S} \right] \times R \): This entire term represents the bonus earned for saving time. Based on the structure of the provided formula, the bonus is calculated as the proportion of time saved relative to standard time, multiplied by the base rate per hour (R). This bonus is added to the base wage to determine the total earnings. This bonus is applicable only when \( T < S \).
Therefore, the total wages for the job under this formula are the sum of the base wage for the actual time worked and the bonus calculated based on the time saved relative to the standard time, applied to the base rate.
Comparing this explanation with the given options, option 4 matches this formula structure.
Revision Table: Key Variables and Formula
| Term | Symbol | Description |
|---|---|---|
| Base Rate per Hour | R | Guaranteed earning rate per hour. |
| Standard Time | S | Time allowed for completing the job. |
| Actual Time Taken | T | Time spent by the worker on the job. |
| Time Saved | \( S - T \) | Calculated when \( T < S \). |
| Wages Formula (Rowan Plan) | \( TR + \left[ \frac{S - T}{S} \right] \times R \) | Total earnings = Base Wage + Bonus (for \( T < S \)). |
Additional Information on Premium Bonus Plans
Premium bonus plans are incentive wage systems that aim to reward workers for their efficiency, specifically for saving time compared to a set standard time. Unlike piece-rate systems where payment is based solely on output, premium bonus plans guarantee a base wage for the time worked, providing a level of income security.
The bonus component in these plans is designed to motivate workers to improve productivity. The Rowan plan, along with the Halsey plan, is a well-known example of a premium bonus scheme. These plans differ primarily in how the bonus for time saved is calculated. The Rowan plan's bonus formula results in a bonus that increases with time saved but at a decelerating rate, which is often cited as a feature that discourages rushing excessively and potentially sacrificing quality as standard time is approached.
Important Questions from Line Balancing and Work Study
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