Chapter 12, Problem 3P

Sequence the jobs shown below by using a Gantt chart. Assume that the move time between machines is on” hour. Sequence” the jobs in priority order 1, 2, 3, 4.

JobWork	Center/Machine Hours	Due Date (days)
1	A/3, B/2, C/2	3
2	C/2, A/4	2
3	B/6, A/1, C/3	4
4	C/4, A/1, B/2	3

1. a. What is the make span?
2. b. How much machine idle time is there?
3. c. When is each job delivered compared with its due date?
4. d. How much idle time (waiting time) is there for each job?
5. e. Devise a better job sequence for processing.

Summary Introduction

To determine: The makespan.

Introduction:

Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.

Answer to Problem 3P

The makespan is 18 hours.

Explanation of Solution

Given information:

Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:

Construct the Gantt chart:

Hence, the total makespan is 18 hours (refer the Gantt chart).

Summary Introduction

To determine: The machine idle time.

Introduction:

Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.

Answer to Problem 3P

The machine idle time is 24 hours.

Explanation of Solution

Given information:

Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:

Construct Gantt chart:

Determine the idle time for Machine A:

It can be determined that subtracting the sum of machine hours from the total makespan.

$\begin{array}{c}\text{Idle time}=\text{Total makespan}-\text{Total machine hours}\\ =18-\left(3+4+1+1\right)\\ =18-9\\ =9\text{ hours}\end{array}$

Determine the idle time for Machine B:

It can be determined that subtracting the sum of machine hours from the total makespan.

$\begin{array}{c}\text{Idle time}=\text{Total makespan}-\text{Total machine hours}\\ =18-\left(2+6+2\right)\\ =18-10\\ =8\text{ hours}\end{array}$

Determine the idle time for Machine C:

It can be determined that the subtracting the sum of machine hours from the total makespan.

$\begin{array}{c}\text{Idle time}=\text{Total makespan}-\text{Total machine hours}\\ =18-\left(2+2+3+4\right)\\ =18-11\\ =7\text{ hours}\end{array}$

Determine the machine idle time:

It can be calculated by adding the idle time of Machine A, Machine B, and Machine C.

$\begin{array}{c}\text{Machine idle time}=\text{Idle time of Machine A+Idle time of Machine B}+\text{Idle time of Machine C}\\ =9+8+7\\ =24\text{ hours}\end{array}$

Hence, the total machine idle time is 24 hours.

Summary Introduction

To determine: The delivery time of each job compared to due dates.

Introduction:

Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.

Answer to Problem 3P

The delivery time does not exist due date.

Explanation of Solution

Given information:

Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:

Construct Gantt chart:

Determine the delivery time:

Due date is given in days. It must be converted to hours by considering working hours per day is 8 hours.

Job	Due date (hours)	Delivery time (hours)
1	24	9
2	16	7
3	32	18
4	24	14

Delivery time is taken from the Gantt chart. Example: Job 1 is on its 9^th hour at last. After that there is no Job 1.

Summary Introduction

To determine: The idle time of the jobs.

Introduction:

Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.

Answer to Problem 3P

The job idle time is 11 hours.

Explanation of Solution

Given information:

Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:

Construct Gantt chart:

Determine the idle time of the jobs

There is no idle time for Job 1 and Job 2. However, Job 3 has the idle time of 6 hours in Machine C from 9^th hour to 15^th hour (Refer Gantt chart). Job 4 has the idle time of 5 hours in Machine A from 8^th hour to 13^th hour (Refer Gantt chart).

Hence, the total idle time is 11 hours.

Summary Introduction

To determine: The better sequence for processing.

Introduction:

Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.

Answer to Problem 3P

The makespan is 14 hours and the better sequence is 3, 2, 4, and 1.

Explanation of Solution

Given information:

Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:

Construct the Gantt chart:

Hence, the total makespan is 14 hours (refer the Gantt chart).

Determine the idle time for Machine A:

It can be determined that subtracting the sum of machine hours from the total makespan.

$\begin{array}{c}\text{Idle time}=\text{Total makespan}-\text{Total machine hours}\\ =14-\left(3+4+1+1\right)\\ =14-9\\ =5\text{ hours}\end{array}$

Determine the idle time for Machine B:

It can be determined that subtracting the sum of machine hours from the total makespan.

$\begin{array}{c}\text{Idle time}=\text{Total makespan}-\text{Total machine hours}\\ =14-\left(2+6+2\right)\\ =14-10\\ =4\text{ hours}\end{array}$

Determine the idle time for Machine C:

It can be determined that subtracting the sum of machine hours from the total makespan.

$\begin{array}{c}\text{Idle time}=\text{Total makespan}-\text{Total machine hours}\\ =14-\left(2+2+3+4\right)\\ =14-11\\ =3\text{ hours}\end{array}$

Determine the machine idle time:

It can be calculated by adding the idle time of Machine A, Machine B, and Machine C.

$\begin{array}{c}\text{Machine idle time}=\text{Idle time of Machine A+Idle time of Machine B}+\text{Idle time of Machine C}\\ =5+4+3\\ =12\text{ hours}\end{array}$

Hence, the total machine idle time is 12 hours.

Determine the delivery time:

Due date is given in days. It must be converted to hours by considering the working hours per day as 8 hours.

Job	Due date (hours)	Delivery time (hours)
1	24	14
2	16	7
3	32	12
4	24	12

Delivery time is taken from the Gantt chart. Example: Job 2 is on its 7^th hour at last. After that there is no Job 2.

Hence, the sequence 3, 2, 4, and 1 is better in makespan and idle time.