## Answered: - Dear Tutor, I need help with these problems. Some of these

Dear Tutor, I need help with these problems. Some of these problems may involve using the "LookUp" excel function. some of the relevant lessons are: scheduling, one machine problem, flow shop, Johnson's algorithm, dynamic programming, branch & bound.?

HOMEWORK

PROBLEM No. 1 (3 points)

Find a good schedule and the corresponding Cmax for this 7/3/P/Fmax problem. The TC is M1, M2, M3.

How good do you think this schedule is?

Why?

Why may it not be optimal?

If you think it is optimal, at least how many optimal schedules are there?

Whether you think you found an optimal schedule or not, how many optimal schedules do you think there are?

Job

p1

1

6

2

5

3

8

4

6

5

3

6

4

7

2

p2

3

2

3

1

2

4

3

p3

4

6

2

3

2

7

2

Page 1

PROBLEM No. 2 (3 ? points)

You have a 4/3/P/Fmax problem with zero ready times. You are to find a solution within 6% of the optimum.

Job

ai

bi

ci

1

7

9

5

2

11

6

4

8

7

8

3

11

6

3

4

Page 2

PROBLEM No. 3 (3 points)

We wish to minimize the maximum penalty for these 5 jobs on a single machine. The processing times,

due dates, precedences and penalty functions are given in the table below. Find the minimum maximum

penalty and indicate the sequence of jobs that will accomplish this.

Job

Processing time

Due date

penalty

Precedence

1

3

6

Tardy

2

4

8

Late

3

2

14

Flow/2

4

5

12

Flow/4

Page 3

5

1

11

Late

before 4

PROBLEM No. 5 (3 points)

Given the 5/1/P/

T

problem, where job 2 must occur before job 1, determine an optimum sequence and the associated

J

p

d

1

3

9

2

2

11

3

4

15

4

8

27

5

7

8

Page 4

T

.

PROBLEM No. 6 (3 points)

Create a Gantt chart for this general job shop problem, using a non-delay schedule and breaking ties with SPT and then

EDD if necessary. Calculate Cmax, Fbar, Tmax and Tbar.

Machine processing time

Job

1

2

3

4

1

1

4

1

3

2

1

2

3

1

3

5

3

4

1

Due

date

13

15

12

10

TC

123

132

213

231

Page 5

PROBLEM No. 7 (2 1/2 points)

A single processor can process many jobs in sequence. You have multiple objectives. You are interested in both the

smallest maximum tardiness as well as the minimum average flow time. There are 6 jobs to be processed with the

processing times and due dates given below (both in days). Find two efficient schedules and their associated measures.

Job

Processing time

Due

date

1

2

3

4

5

6

4

5

2

6

4

8

11

15

20

18

6

7

Page 6

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