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Flow Shop Scheduling - Expert Level: conceptual clarity Flow Shop Scheduling EXPERT

This skill evaluation ⚡ worksheet focuses on Flow Shop Scheduling - a key topic in Scheduling. You'll solve 20 expert-level problems (Worksheet 9 of 10). The primary focus is on conceptual clarity. Master flow shop scheduling ssc cgl, flow shop scheduling reasoning tricks, and fast flow shop scheduling solving through systematic practice.

📝 Worksheet 9 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Flow Shop Scheduling
Worksheet 9 of 10 (88% complete)

Question 1

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (44, 49) - Job B: (26, 35) - Job C: (13, 18) - Job D: (10, 38) - Job E: (36, 14) - Job F: (32, 44) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job E → Job D → Job C → Job B → Job F → Job A
3. Calculate makespan: 234

Answer: 234

Question 2

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (46, 44) - Job B: (27, 18) - Job C: (16, 19) - Job D: (19, 27) - Job E: (40, 17) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job A → Job B → Job E → Job C → Job D
3. Calculate makespan: 176

Answer: 176

Question 3

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (37, 50) - Job B: (29, 10) - Job C: (38, 50) - Job D: (43, 18) - Job E: (34, 27) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job E → Job D → Job B → Job A → Job C
3. Calculate makespan: 243

Answer: 243

Question 4

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (36, 46) - Job B: (20, 30) - Job C: (28, 43) - Job D: (40, 16) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job D → Job B → Job C → Job A
3. Calculate makespan: 179

Answer: 179

Question 5

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (32, 18) - Job B: (27, 26) - Job C: (11, 27) - Job D: (37, 45) - Job E: (49, 38) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job E → Job B → Job A → Job C → Job D
3. Calculate makespan: 203

Answer: 203

Question 6

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (31, 45) - Job B: (48, 27) - Job C: (49, 15) - Job D: (26, 12) - Job E: (21, 21) - Job F: (26, 37) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job B → Job C → Job D → Job E → Job F → Job A
3. Calculate makespan: 252

Answer: 252

Question 7

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (15, 23) - Job B: (44, 49) - Job C: (12, 43) - Job D: (31, 46) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job C → Job A → Job D → Job B
3. Calculate makespan: 173

Answer: 173

Question 8

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (10, 44) - Job B: (49, 50) - Job C: (42, 18) - Job D: (47, 48) - Job E: (40, 22) - Job F: (22, 32) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job E → Job C → Job A → Job F → Job D → Job B
3. Calculate makespan: 274

Answer: 274

Question 9

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (23, 26) - Job B: (12, 26) - Job C: (20, 46) - Job D: (32, 20) - Job E: (42, 47) - Job F: (39, 40) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job D → Job B → Job C → Job A → Job F → Job E
3. Calculate makespan: 237

Answer: 237

Question 10

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (50, 17) - Job B: (31, 45) - Job C: (23, 35) - Job D: (31, 43) - Job E: (24, 45) - Job F: (44, 33) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job F → Job A → Job C → Job E → Job B → Job D
3. Calculate makespan: 285

Answer: 285

Question 11

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (15, 27) - Job B: (22, 18) - Job C: (31, 17) - Job D: (41, 39) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job D → Job B → Job C → Job A
3. Calculate makespan: 142

Answer: 142

Question 12

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (12, 28) - Job B: (27, 48) - Job C: (42, 16) - Job D: (38, 45) - Job E: (27, 42) - Job F: (38, 25) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job F → Job C → Job A → Job B → Job E → Job D
3. Calculate makespan: 259

Answer: 259

Question 13

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (13, 16) - Job B: (27, 36) - Job C: (26, 21) - Job D: (16, 48) - Job E: (32, 43) - Job F: (17, 28) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job C → Job A → Job D → Job F → Job B → Job E
3. Calculate makespan: 218

Answer: 218

Question 14

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (43, 17) - Job B: (14, 14) - Job C: (37, 35) - Job D: (47, 36) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job D → Job C → Job A → Job B
3. Calculate makespan: 158

Answer: 158

Question 15

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (37, 12) - Job B: (18, 29) - Job C: (20, 38) - Job D: (15, 17) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job A → Job D → Job B → Job C
3. Calculate makespan: 137

Answer: 137

Question 16

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (27, 11) - Job B: (31, 45) - Job C: (46, 30) - Job D: (29, 41) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job C → Job A → Job D → Job B
3. Calculate makespan: 188

Answer: 188

Question 17

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (34, 36) - Job B: (26, 11) - Job C: (17, 24) - Job D: (30, 48) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job B → Job C → Job D → Job A
3. Calculate makespan: 157

Answer: 157

Question 18

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (42, 30) - Job B: (33, 34) - Job C: (12, 24) - Job D: (25, 11) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job A → Job D → Job C → Job B
3. Calculate makespan: 146

Answer: 146

Question 19

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (33, 13) - Job B: (48, 18) - Job C: (44, 47) - Job D: (17, 28) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job B → Job A → Job D → Job C
3. Calculate makespan: 189

Answer: 189

Question 20

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (24, 42) - Job B: (41, 35) - Job C: (41, 20) - Job D: (17, 28) - Job E: (13, 25) - Job F: (28, 44) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job B → Job C → Job E → Job D → Job A → Job F
3. Calculate makespan: 241

Answer: 241
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