Scaling Workforce in Building Construction: A Mathematical Insight into Productivity

In the realm of construction, understanding workforce productivity is crucial for efficient project management and budgeting. The given scenario involves a comparison of different workforces and their productivity levels. This article delves into the mathematical analysis of such scenarios, providing a structured approach to scaling workforce and calculating the required time for completing a project.

Introduction to Man-Hours and Workforce Productivity

Workforce productivity in construction is often measured in terms of man-hours. Man-hours are calculated by multiplying the number of workers with the total hours they work over a specific period. This metric is useful for comparing different workforces and predicting outcomes such as the time required to complete a project with varying numbers of workers and working hours.

Calculation and Analysis

The scenario involves determining the number of days required by 18 men, each working 7 hours a day, to build a house initially constructed by 15 men working 10 hours a day over 21 days.

Step 1: Calculating Total Man-Hours in the First Scenario

The initial scenario is straightforward in terms of calculating the total man-hours.

Number of men: 15 Number of hours per day: 10 Number of days: 21

Total man-hours Number of men × Hours per day × Number of days

Text{Total man-hours} 15 Text{ men} × 10 Text{ hours/day} × 21 Text{ days} 3150 Text{ man-hours}

Step 2: Calculating the Daily Output of the Second Scenario

For the second scenario, we first calculate the daily man-hours output.

Number of men: 18 Number of hours per day: 7

Daily man-hours in the second scenario:

Text{Daily man-hours} 18 Text{ men} × 7 Text{ hours/day} 126 Text{ man-hours/day}

Step 3: Calculating the Number of Days Required in the Second Scenario

To find out how many days 18 men working 7 hours a day would take to complete the house, we need to distribute the total man-hours calculated in Step 1 over the daily man-hours output in Step 2.

Number of days Total man-hours / Daily man-hours

Text{Number of days} 3150 Text{ man-hours} / 126 Text{ man-hours/day} ≈ 25 days

Conclusion

Therefore, 18 men working 7 hours a day would take approximately 25 days to build the house. This is 4 days more than the initial 21 days taken by 15 men working 10 hours a day. This analysis helps project managers and construction teams to estimate and plan their workforces accurately.

Mathematical Formula for Comparison

The following formula can also be derived to find the days required in the second scenario:

1 House / (15 men × 10 hours × 21 days) 1 House / (18 men × 7 hours × x days)

15 × 10 × 21 18 × 7 × x

x (15 × 10 × 21) / (18 × 7)

x (15 × 10 div 2 × 21 div 7) / (18 div 2 × 7 div 7)

x (15 × 5 × 3) / (9)

x (15 div 3 × 5 × 3) / (9 div 3)

x (5 × 5 × 3) / (3)

x (25 × 3 div 3) / (3 div 3)

x 25 days

Further Analysis

To derive the number of days required for 18 men working 7 hours a day, we can also set up the following equation:

15 men × 10 hours × 21 days 18 men × 7 hours × x days

152110 187x

x 152110 / 25 25 days

Therefore, the difference in the number of days is:

25 days - 21 days 4 more days

Key Takeaways

Different workforces can significantly impact the time required to complete a construction project. The concept of man-hours is essential in assessing the productivity of a workforce. Mathematical calculations can provide a precise estimate for project timelines and resource allocation.

Keyword Optimization

Man-hours, construction efficiency, productivity analysis