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Flow Shop Scheduling - Absolute-Beginner Level: core concept mastery Flow Shop Scheduling ABSOLUTE BEGINNER

This skill primer 🌟 worksheet focuses on Flow Shop Scheduling - a key topic in Scheduling. You'll solve 20 absolute-beginner-level problems (Worksheet 1 of 10). The primary focus is on core concept mastery. Master flow shop scheduling problems, flow shop scheduling reasoning questions, and flow shop scheduling practice through systematic practice.

📝 Worksheet 1 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Absolute Beginner level

What you'll learn in this worksheet:
Your progress through Flow Shop Scheduling
Worksheet 1 of 10 (0% complete)

Question 1

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (11, 47) - Job B: (30, 26) - Job C: (25, 46) - Job D: (19, 10) - Job E: (45, 39) - Job F: (28, 10) 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 F → Job D → Job A → Job C
3. Calculate makespan: 226

Answer: 226

Question 2

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (13, 23) - Job B: (15, 47) - Job C: (11, 14) - Job D: (45, 31) 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: 160

Answer: 160

Question 3

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (46, 41) - Job B: (10, 31) - Job C: (35, 48) - Job D: (20, 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 A → Job B → Job D → Job C
3. Calculate makespan: 203

Answer: 203

Question 4

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (49, 37) - Job B: (10, 14) - Job C: (27, 21) - Job D: (35, 27) - Job E: (40, 10) 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 E → Job B
3. Calculate makespan: 175

Answer: 175

Question 5

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (26, 27) - Job B: (29, 15) - Job C: (32, 34) - Job D: (24, 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 B → Job D → Job A → Job C
3. Calculate makespan: 146

Answer: 146

Question 6

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (22, 43) - Job B: (34, 13) - Job C: (12, 47) - Job D: (23, 37) - Job E: (16, 22) - Job F: (30, 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 B → Job C → Job E → Job A → Job D → Job F
3. Calculate makespan: 232

Answer: 232

Question 7

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (27, 22) - Job B: (21, 28) - Job C: (19, 32) - Job D: (28, 31) - Job E: (14, 31) - Job F: (49, 14) 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 F → Job E → Job C → Job B → Job D
3. Calculate makespan: 212

Answer: 212

Question 8

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (18, 38) - Job B: (34, 16) - Job C: (43, 17) - Job D: (33, 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 C → Job D → Job B → Job A
3. Calculate makespan: 166

Answer: 166

Question 9

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (14, 14) - Job B: (20, 16) - Job C: (10, 37) - Job D: (42, 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 A → Job D
3. Calculate makespan: 135

Answer: 135

Question 10

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (29, 35) - Job B: (29, 39) - Job C: (34, 41) - Job D: (14, 25) - Job E: (43, 17) - Job F: (44, 26) 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 E → Job D → Job A → Job B → Job C
3. Calculate makespan: 245

Answer: 245

Question 11

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (47, 44) - Job B: (17, 18) - Job C: (41, 22) - Job D: (46, 25) - Job E: (22, 50) - Job F: (42, 35) 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 F → Job D → Job C → Job B → Job E
3. Calculate makespan: 266

Answer: 266

Question 12

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (32, 21) - Job B: (43, 28) - Job C: (21, 24) - Job D: (23, 20) - Job E: (48, 35) - Job F: (14, 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 E → Job B → Job A → Job D → Job F → Job C
3. Calculate makespan: 226

Answer: 226

Question 13

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (13, 25) - Job B: (17, 12) - Job C: (34, 13) - Job D: (28, 47) - Job E: (44, 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 B → Job A → Job D → Job E
3. Calculate makespan: 185

Answer: 185

Question 14

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (15, 50) - Job B: (49, 32) - Job C: (43, 35) - Job D: (35, 31) - Job E: (42, 39) - Job F: (12, 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 E → Job C → Job B → Job D → Job F → Job A
3. Calculate makespan: 291

Answer: 291

Question 15

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (23, 50) - Job B: (15, 46) - Job C: (35, 31) - Job D: (23, 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 C → Job D → Job B → Job A
3. Calculate makespan: 179

Answer: 179

Question 16

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (34, 48) - Job B: (34, 41) - Job C: (36, 38) - Job D: (29, 45) 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 A → Job B → Job C
3. Calculate makespan: 201

Answer: 201

Question 17

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (22, 42) - Job B: (24, 34) - Job C: (17, 36) - Job D: (22, 35) - Job E: (33, 29) - Job F: (46, 24) 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 F → Job C → Job A → Job D → Job B
3. Calculate makespan: 250

Answer: 250

Question 18

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (35, 35) - Job B: (10, 36) - Job C: (40, 32) - Job D: (23, 48) - Job E: (34, 37) - Job F: (28, 43) 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 B → Job D → Job F → Job E → Job A
3. Calculate makespan: 271

Answer: 271

Question 19

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (46, 31) - Job B: (15, 41) - Job C: (28, 32) - Job D: (30, 35) 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 C → Job D
3. Calculate makespan: 185

Answer: 185

Question 20

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (11, 45) - Job B: (44, 15) - Job C: (23, 37) - Job D: (41, 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 D → Job B → Job A → Job C
3. Calculate makespan: 182

Answer: 182
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