Key Industrial Engineering Formulas and Examples

Formula #1: Calculating the Daily Production Target of a Line

Formula:
$\text{Daily Line Target} = \frac{\text{Total Shift Hours} \times 60 \times \text{No. of Operators in a Line} \times \text{Line Efficiency (\%)}}{\text{Garment SMV}}$

Example:

• Daily Shift Hours: 8 hours
• Number of Operators: 30
• Line Efficiency: 60%
• Garment SMV: 20

Calculation:

$$\text{Daily Line Target} = \frac{8 \times 60 \times 30 \times 60}{20} = \frac{43200}{20} = 432 \, \text{pieces/day}$$

---

Formula #2: Operator-Wise Production Target

Formula:
$\text{Individual Operator Target} = \frac{\text{Total Working Minutes in a Day} \times \text{Line Efficiency (\%)}}{\text{Operation SMV}}$

Example:

• Factory Shift: 8 hours (480 minutes)
• Line Efficiency: 60%
• Operation SMV: 0.5 

Calculation:

$$\text{Individual Operator Target} = \frac{480 \times 60}{0.5} = \frac{28800}{0.5} = 576 \, \text{pieces/day}$$

Note: If operator efficiency is considered individually, the target is based on their performance.

---

Formula #3: Calculating Operator Efficiency

Formula:
$\text{Operator Efficiency (\%)} = \frac{\text{Units Produced} \times \text{Operation SMV} \times 100}{\text{Total Minutes Worked}}$

Example:

• Units Produced: 500 pieces
• Operation SMV: 0.6 
• Total Minutes Worked: 480 minutes

Calculation:

$$\text{Operator Efficiency} = \frac{500 \times 0.6 \times 100}{480} = \frac{300}{480} \times 100 = 62.5\%$$

---

Formula #4: Line Efficiency

Formula:
$\text{Line Efficiency (\%)} = \frac{\text{Line Output} \times \text{Garment SMV} \times 100}{\text{No. of Operators} \times \text{Minutes Worked}}$

Example:

• Line Output: 600 units
• Garment SMV: 20 minutes
• Number of Operators: 30
• Shift Time: 8 hours

Calculation:

$$\text{Line Efficiency} = \frac{600 \times 20 \times 100}{30 \times 8 \times 60} = \frac{1200000}{14400} = 83.33\%$$

---

Formula #5: Machine Productivity

Formula:
$\text{Machine Productivity} = \frac{\text{Line Output}}{\text{No. of Machines Used}}$

Example:

• Line Output: 600 units
• Machines Used: 27

Calculation:

$$\text{Machine Productivity} = \frac{600}{27} = 22.22 \, \text{units/machine}$$

---

Formula #6: Labor Productivity

Formula:
$\text{Labor Productivity} = \frac{\text{Line Output}}{\text{Total Manpower (Operators + Helpers)}}$

Example:

• Line Output: 600 units
• Operators: 30
• Helpers: 5

Calculation:

$$\text{Labor Productivity} = \frac{600}{30 + 5} = \frac{600}{35} = 17.14 \, \text{units/labor}$$

---

Formula #7: Line WIP (Work in Process)

Formula:
$\text{Line WIP} = \text{Total Pieces Loaded} - \text{Total Pieces Out}$

Note: This formula is used to track the current work in process on a production line.

---

Formula #8: Standard Time

Formula:
$\text{Standard Time} = (\text{Observed Time} \times \text{Observed Rating}) + \text{Allowances}$

---

Formula #9: Machine Utilization

Formula:
$\text{Machine Utilization (\%)} = \frac{\text{Actual Machine Running Time} \times 100}{\text{Time Available}}$

---

Formula #10: Cost Per Minute

Formula:
$\text{Cost Per Minute} = \frac{\text{Total Cost Incurred in Labor}}{\text{Total Available Working Minutes} \times \text{No. of Labor}}$

---

Formula #11: Production Cost Per Unit

Formula:
$\text{Production Cost Per Unit} = \frac{\text{Total Production Cost in a Day}}{\text{No. of Garments Produced in a Day}}$

---

Formula #12: Man-to-Machine Ratio

Formula:
$\text{Man-to-Machine Ratio} = \frac{\text{Total Manpower}}{\text{Total No. of Sewing Machines}}$

---

Formula for Calculating SMV

Formula:
$\text{SMV} = (\text{Cycle Time} \times \text{Performance Rating}) + \text{Allowances}$

Where:

• Allowances = $(\text{Bundle Allowance}) + (\text{Machine and Personal Allowance})$

---

Example Question:
An industrial engineer finds the cycle time is 0.83 minutes, and the performance rating of an operator is 80% for a basic T-shirt shoulder joining operation. Find the SMV for that operation.

Solution:

$$\text{SMV} = (\text{Cycle Time} \times \text{Performance Rating}) + \text{Allowances}$$ $$= (0.83 \times 0.8) + \left[(\text{Bundle Allowance}) + (\text{Machine and Personal Allowance})\right]$$

Assume:

• Bundle Allowance = 10%
• Machine and Personal Allowance = 20%

Step-by-Step Calculation:

1. Calculate the basic time:

   $$\text{Basic Time} = \text{Cycle Time} \times \text{Performance Rating} = 0.83 \times 0.8 = 0.664 \, \text{minutes}$$

2. Calculate allowances:

   $$\text{Bundle Allowance} = \text{Basic Time} \times 10\% = 0.664 \times 0.1 = 0.0664$$ $$\text{Machine and Personal Allowance} = \text{Basic Time} \times 20\% = 0.664 \times 0.2 = 0.1328$$

3. Add allowances to the basic time:

   $$\text{SMV} = 0.664 + 0.0664 + 0.1328 = 0.832 \, \text{minutes}$$

Answer:
The SMV for the shoulder joint operation is 0.832 minutes.

Additional Formulas

1. Efficiency:
   $\text{Efficiency (\%)} = \frac{\text{Earned Minutes} \times 100}{\text{Available Minutes}}$

2. Earned Minutes:
   $\text{Earned Minutes} = \text{Production Units} \times \text{Garment SMV}$

3. Factory Capacity:
   $\text{Factory Capacity} = \frac{\text{Work Hours} \times \text{Total Workers} \times \text{Working Days} \times \text{Efficiency (\%)}}{\text{Garment SMV}}$

4. Cycle Time:
   $\text{Cycle Time} = \frac{60}{\text{Team Target}}$

5. Target Per Hour:
   $\text{Target Per Hour} = \frac{60}{\text{SMV}} \times \text{Efficiency (\%)}$

6. Daily Output:
   $\text{Daily Output} = \frac{\text{Work Hours}}{\text{SMV}}$

---