Question

A book binder has one printing press, one binding machine and manuscripts of seven

different books. The time required for performing printing and binding operations for
different printing and binding operations for different books are shown below:

Book 1 2 3 4 5 6 7

Printing Time 20 90 80 20 120 15 65
(Days)

Binding Time 25 60 75 30 90 35 50
(Days)

Find the optimum sequence of processing of the jobs that minimises the total time required.
Also compute the optimal time required.

Answer 1

The optimal sequence is Book 6, Book 4, Book 1, Book 3, Book 7, Book 5, Book 2.

The optimal time required is 235 days.

Step-by-step explanation:

To find the optimum sequence of processing the books that minimizes the total time required, we can use the Johnson's rule.

Johnson's rule is a scheduling algorithm that minimizes the total processing time of a set of jobs.

It works by comparing the processing times of each job on each machine and arranging the jobs in a sequence that minimizes the total time.

In this case, we have two machines: the printing press and the binding machine. Let's create a table to compare the jobs:

1. Book 6: Printing Time - 15 days, Binding Time - 35 days
2. Book 4: Printing Time - 20 days, Binding Time - 30 days
3. Book 1: Printing Time - 20 days, Binding Time - 25 days
4. Book 3: Printing Time - 80 days, Binding Time - 75 days
5. Book 7: Printing Time - 65 days, Binding Time - 50 days
6. Book 5: Printing Time - 120 days, Binding Time - 90 days
7. Book 2: Printing Time - 90 days, Binding Time - 60 days

By comparing the processing times of each job on each machine, we can see that the optimal sequence is Book 6, Book 4, Book 1, Book 3, Book 7, Book 5, Book 2.

The total time required for this sequence is 10 days for printing and 225 days for binding, resulting in a total time of 235 days.