3
.
You have been asked to balance a flow shop assembly operation to achieve an output rate of
1
5
0
units per eight
-
hour day. Task times and precedence relationships are shown in the table bel

Question

3
.
 ﻿You have been asked to balance a flow shop assembly operation to achieve an output rate of 
1
5
0
 ﻿units per eight
-
hour day. Task times and precedence relationships are shown in the table below. 
 
 ﻿Task Predecessor
(
s
)
 ﻿Duration 
(
minutes
)
 ﻿A 
-
-
 
1
.
4
 ﻿B 
-
-
 
0
.
8
 ﻿C A
,
 ﻿B 
0
.
4
 ﻿D 
-
-
 
1
.
8
 ﻿E 
-
-
 
0
.
4
 ﻿F C 
3
.
0
 ﻿G E
,
 ﻿F 
2
.
0
 ﻿H D
,
 ﻿G 
1
.
2

(
a
)

﻿Draw the precedence diagram.

(
b
)
 
 ﻿Determine the desired cycle time.

(
c
)

﻿Determine the theoretical minimum number of stations needed.

(
d
)
 
 ﻿Balance this line using the smallest processing time heuristic.

(
e
)
 ﻿What is the efficiency of the line obtained in part d
?

give all question answer and give final summary

VIPSolutions · Accepted Answer

# Flow Shop Assembly Line Balancing

## Given Data

| Task | Predecessor(s) | Duration (minutes) |
|------|----------------|-------------------|
| A    | -              | 1.4               |
| B    | -              | .8               |
| C    | A, B           | .4               |
| D    | -              | 1.8               |
| E    | -              | .4               |
| F    | C              | 3.               |
| G    | E, F           | 2.               |
| H    | D, G           | 1.2               |

Required output rate: **150 units per 8-hour day**

---

## (a) Precedence Diagram

```mermaid
graph TD
  A --> C
  B --> C
  C --> F
  E --> G
  F --> G
  D --> H
  G --> H
```
**Alt text:** A flow chart showing the tasks and their precedence relationships, as described in the table.

---

## (b) Desired Cycle Time

1. **Total time available per day:**  
   $8 \text{ hours} \times 60 = 480 \text{ minutes}$

2. **Desired output:**  
   $150$ units per day

3. **Cycle time ($CT$):**  
   $$
   CT = \frac{\text{Total time available}}{\text{Required output}} = \frac{480}{150} = 3.2 \text{ minutes}
   $$

---

## (c) Theoretical Minimum Number of Stations

1. **Sum of all task times:**
   $$
   1.4 + .8 + .4 + 1.8 + .4 + 3. + 2. + 1.2 = 11. \text{ minutes}
   $$

2. **Theoretical minimum stations ($N_{min}$):**
   $$
   N_{min} = \frac{\text{Total task time}}{\text{Cycle time}} = \frac{11.}{3.2} = 3.44
   $$
   Round up: **4 stations**

---

## (d) Line Balancing (Smallest Processing Time Heuristic)

**Heuristic:** Assign available tasks with the smallest duration as early as possible, respecting precedence.

### Step-by-Step Assignment

#### **Station 1** (CT = 3.2 min)
- **Available:** A (1.4), B (.8), D (1.8), E (.4)
  - Assign E (.4) → 2.8 min left
  - Assign B (.8) → 2. min left
  - Assign A (1.4) → .6 min left
  - Can't fit D (1.8)
  - **Total assigned:** E + B + A = .4 + .8 + 1.4 = **2.6 min**
  - Remaining: .6 min (cannot fit next available task)

#### **Station 2** (CT = 3.2 min)
- **Available:** D (1.8), C (.4) [A and B done]
  - Assign C (.4) → 2.8 min left
  - Assign D (1.8) → 1. min left
  - **Total assigned:** C + D = .4 + 1.8 = **2.2 min**
  - Remaining: 1. min

#### **Station 3** (CT = 3.2 min)
- **Available:** F (3.) [C done]
  - Assign F (3.) → .2 min left
  - **Total assigned:** F = **3. min**
  - Remaining: .2 min

#### **Station 4** (CT = 3.2 min)
- **Available:** G (2.) [E, F done]
  - Assign G (2.) → 1.2 min left
  - **Next:** H (1.2) [D, G done]
  - Assign H (1.2) →  min left
  - **Total assigned:** G + H = 2. + 1.2 = **3.2 min**

---

### **Summary Table**

| Station | Tasks           | Total Time (min) |
|---------|-----------------|------------------|
| 1       | E, B, A         | 2.6              |
| 2       | C, D            | 2.2              |
| 3       | F               | 3.              |
| 4       | G, H            | 3.2              |

---

## (e) Line Efficiency

$$
\text{Efficiency} = \frac{\text{Total task time}}{\text{Number of stations} \times \text{Cycle time}} \times 100\%
$$
$$
\text{Efficiency} = \frac{11.}{4 \times 3.2} \times 100\% = \frac{11.}{12.8} \times 100\% \approx 85.9\%
$$

---

# **Final Summary**

- **Precedence diagram** is provided above (see mermaid graph).
- **Desired cycle time:** 3.2 minutes per unit.
- **Theoretical minimum stations:** 4.
- **Balanced assignment (smallest processing time first):**
  - Station 1: E, B, A (2.6 min)
  - Station 2: C, D (2.2 min)
  - Station 3: F (3. min)
  - Station 4: G, H (3.2 min)
- **Line efficiency:** ~85.9%

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Study Help, Fast Answers

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Related Answers

Study Help, Fast Answers