Chapter 14, Problem 30P

(a)

Summary Introduction

Interpretation:

The best sequence in terms of the average flow time: $\text{EDD}$ ,critical ratio, or $\text{SPT}$

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 tardiness that is required to finish the each job. Similarly do the same for the schedule of $\text{SPT}$ . Then, the lowest shortest processing time can be observed.

Explanation of Solution

Given information:

The table below contains the information about five jobs waiting to be processed at stamping machine $307$ in the Metal Bright Job Shop.

Job	Processing Time (hrs)	Due (hrs)
$A$	$3$	$4$
$B$	$5$	$9$
$C$	$1$	$3$
$D$	$2$	$6$
$E$	$4$	$1$

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

Hours	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
Job	$E$	$C$	$A$	$D$	$B$

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

  $\frac{4hours+5hours+8hours+10hours+15hours}{5}=8.40hours$

Now, calculating the average tardiness, it is given that job $E$ has the tardiness of

  $4hours-1hour=3hour$

The job $C$ has the tardiness of

  $5hours-3hours=2hours$

The job $A$ has the tardiness of

  $8hours-4hours=4hours$

The job $D$ has the tardiness of

  $10hours-6hours=4hours$

The job $B$ has the tardiness of

  $15hours-9hours=6hours$

Adding the delay time of the order and divide it by the number of the orders;

  $\begin{array}{l}AT=\frac{3+2+4+4+6}{5}\\ AT=3.80hours\end{array}$

From the table, it is observed that job $C$ takes the $5$ hours for the completion.

Calculate the critical ratio by dividing the hours until due by the processing time for the each job.

Job	Processing Time (hrs)	Due (hrs)	Critical ratio
$A$	$3$	$4$	$1.33$
$B$	$5$	$9$	$1.80$
$C$	$1$	$3$	$3.00$
$D$	$2$	$6$	$3.00$
$E$	$4$	$1$	$0.25$

Now, schedule the based on the ascending order of the critical ratios.

Hours	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
Job	$E$	$A$	$B$	$D$	$C$

Calculate the average flow time by adding the delay time of the order and divide it by the number of the orders;

  $\frac{4hours+7hours+12hours+14hours+15hours}{5}=10.40hours$

Calculate the tardiness for the each job,

that job $E$ has the tardiness of

  $4hours-1hour=3hour$

The job $C$ has the tardiness of

  $15hours-3hours=12hours$

The job $A$ has the tardiness of

  $7hours-4hours=3hours$

The job $D$ has the tardiness of

  $14hours-6hours=8hours$

The job $B$ has the tardiness of

  $12hours-9hours=3hours$

Adding the tardiness of the order and divide it by the number of the orders;

  $\begin{array}{l}AT=\frac{3+3+3+8+12}{5}\\ AT=5.80hours\end{array}$

From the table, it is observed that the job $C$ has a flow time of $15$ hours.

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

Hours	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
Job	$C$	$D$	$A$	$E$	$B$

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

  $\frac{1hour+3hours+6hours+10hours+15hours}{5}=7hours$

Now, calculating the average tardiness, it is given that job $C$ has no tardiness and the job $D$ has no tardiness.

The job $A$ has a tardiness of,

  $6hours-4hours=2hours$

The job $E$ has the tardiness of

  $10hours-1hour=9hours$

The job $B$ has the tardiness of

  $15hours-9hours=6hours$

Now, calculate the average tardiness,

  $\begin{array}{l}AT=\frac{0+0+2+9+6}{5}\\ AT=3.40hours\end{array}$

Thus, the job $C$ gets completed in $1$ hour.

From the above calculation, the average flow time based on methods:

  $\text{EDD}$ method is $8.40$ hours. And the critical ratio method is $10.40$ hours and the $\text{SPT}$ method takes $7$ hours.

Therefore, shortest processing time gives the lowest average flow time.

(b)

Summary Introduction

Interpretation:

The best sequence in terms of the average tardiness: $\text{EDD}$ ,critical ratio, or $\text{SPT}$ .

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 tardiness that is required to finish the each job.

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. Then, shortest processing time gives the lowest average tardiness.

Explanation of Solution

Given information:

The table below contains the information about five jobs waiting to be processed at stamping machine $307$ in the Metal Bright Job Shop.

Job	Processing Time (hrs)	Due (hrs)
$A$	$3$	$4$
$B$	$5$	$9$
$C$	$1$	$3$
$D$	$2$	$6$
$E$	$4$	$1$

From the above calculation, the average tardiness based on the different methods,

  $\text{EDD}$ method is $3.80$ hours. And the critical ratio method is $5.80$ hours and the $\text{SPT}$ method takes $3.40$ hours.

Therefore, shortest processing time gives the lowest average tardiness.

(c)

Summary Introduction

Interpretation:

The finish time of job $C$ .

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 tardiness that is required to finish the each job.

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. Then, the job $C$ finished time is observed.

Explanation of Solution

Given information:

The table below contains the information about five jobs waiting to be processed at stamping machine $307$ in the Metal Bright Job Shop.

Job	Processing Time (hrs)	Due (hrs)
$A$	$3$	$4$
$B$	$5$	$9$
$C$	$1$	$3$
$D$	$2$	$6$
$E$	$4$	$1$

From the above calculations, the completion of the job $C$ is based on different methods,

  $\text{EDD}$ method is $5$ hours. And the critical ratio method is $15$ hours and the $\text{SPT}$ method takes $1$ hour.