Chapter 14, Problem 29P

(a)

Summary Introduction

Interpretation:

The time period required on an average to finish the job.

Concept Introduction:

Schedule the job on the basis of the $\text{FCFS}$ . Then determine the average flow time for the each job. Calculate the average flow time that is required to finish the each job. Then calculate the average tardiness by adding the delay time of the order.

Explanation of Solution

Given information:

The owner of an in HM Catering Company has four jobs to deliver today, shown in the order in which they are received:

Job	Processing Time (hrs)	Due (hrs)
$W$	$4$	$5$
$X$	$3$	$9$
$Y$	$2$	$2$
$Z$	$1$	$1$

Schedule the jobs based on the first come first served:

Hours	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
Job	$W$	$X$	$Y$	$Z$

From the table, it is observed that the flow time of the job $W$ is $4$ hours which due in $5$ hours. Thus, $W$ has no delay in job.

The flow time of the job $X$ is $7$ hours which due in $9$ hours. Thus, $X$ has no delay in job.

The flow time of the job $Y$ is $9$ hours which due in $2$ hours. Thus, $X$ has $7$ hours delay in job.

In order of the job $Y$ :

The flow time of the job $Z$ is $10$ hours which due in $1$ hour. Thus, it has a delay of $9$ hours.

In order of the job $Z$ :

Thus, calculate the average flow time that is required to finish the each job:

  $\frac{4hours+7hours+9hours+10hours}{4}=7.5hours$

Now, calculating the average tardiness, adding the delay time of the order and divide it by the number of the orders;

  $\begin{array}{l}AT=\frac{0+0+7+9}{4}\\ AT=4hours\end{array}$

(b)

Summary Introduction

Interpretation:

The job that will be late and the average job tardiness.

Concept Introduction:

Schedule the job on the basis of the $\text{SPT}$ . Then determine the average flow time for the each job. Calculate the average flow time that is required to finish the each job. Then calculate the average tardiness by adding the delay time of the order.

Explanation of Solution

Given information:

The owner of an in home meal catering company has four jobs to deliver today, shown in the order in which they are received:

Job	Processing Time (hrs)	Due (hrs)
$W$	$4$	$5$
$X$	$3$	$9$
$Y$	$2$	$2$
$Z$	$1$	$1$

Schedule the jobs based on the $\text{SPT}$ ,

Hours	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
Job	$Z$	$Y$	$X$	$W$

From the table, it can be observed that $Z$ has the $1$ hour flow time which due in $1$ hour. $Z$ will be deliver on time.

  $Y$ has the $3$ hour flow time which due in $2$ hour. $Y$ will be delay $1$ hour of the job.

  $X$ has the $6$ hour flow time which due in $9$ hour. There will be no delay in order of the job $X$ .

  $W$ has the $10$ hours flow time which due in $5$ hours. Thus, there is delay of $5$ hours on job order of $W$

Thus, calculate the average flow time that is required to finish the each job:

  $\frac{1hours+3hours+6hours+10hours}{4}=4hours$

Now, calculating the average tardiness, adding the delay time of the order and divide it by the number of the orders;

  $\begin{array}{l}AT=\frac{0+1+0+5}{4}\\ AT=1.5hours\end{array}$

(c)

Summary Introduction

Interpretation:

The job that will be late and the average job tardiness.

Concept Introduction:

Schedule the job on the basis of the $\text{EDD}$ . Then determine the average flow time for the each job. Calculate the average flow time that is required to finish the each job. Then calculate the average tardiness by adding the delay time of the order.

Explanation of Solution

Given information:

The owner of an in home meal catering company has four jobs to deliver today, shown in the order in which they are received:

Job	Processing Time (hrs)	Due (hrs)
$W$	$4$	$5$
$X$	$3$	$9$
$Y$	$2$	$2$
$Z$	$1$	$1$

Schedule the jobs based on the $\text{EDD}$ ,

Hours	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
Job	$Z$	$Y$	$W$	$X$

From the table, it can be observed that $Z$ has the $1$ hour flow time which due in $1$ hour. $Z$ will be no delay.

  $Y$ has the $3$ hour flow time which due in $2$ hour. $Y$ will be delay $1$ hour of the job.

  $W$ has the $7$ hour flow time which due in $5$ hour. There will be delay of $2$ hours for the job.

  $X$ has the $10$ hour flow time which due in $9$ hours. There will be delay of $1$ hour in order of the job $X$ .

Now, calculating the tardiness, adding the delay time of the order and divide it by the number of the orders;

  $\begin{array}{l}AT=\frac{0+1+2+1}{4}\\ AT=1hour\end{array}$

Thus, calculate the average flow time that is required to finish the each job:

  $\frac{1hour+3hours+7hours+10hours}{4}=5.25hours$

(d)

Summary Introduction

Interpretation:

The most efficient sequence from the $\text{FCFS,SPT,EDD}$ .

Concept Introduction:

The efficiency can be measured as the average tardiness or the number of jobs delayed and the average flow time.

Explanation of Solution

Given information:

The owner of an in home meal catering company has four jobs to deliver today, shown in the order in which they are received:

Job	Processing Time (hrs)	Due (hrs)
$W$	$4$	$5$
$X$	$3$	$9$
$Y$	$2$	$2$
$Z$	$1$	$1$

The efficiency can be measured as the average tardiness or the number of jobs delayed and the average flow time.

Average flow time:

By comparing the average flow time, it is observed that $\text{SPT}$ method gives the lowest average flow time.

Average tardiness:

By comparing the average tardiness, it is observed that $\text{EDD}$ method gives the lowest average tardiness.

Number of jobs delayed:

Both $\text{FCFS}$ and $\text{SPT}$ have the lower number of the jobs delayed as compared to the $\text{EDD}$ method.

Therefore, it depends on the owner which gives the priority to the most efficient method will vary.