Question

A machine shop processes custom orders from variety of clients. A machining centre in a job shop for a local manufacturing company has five unprocessed jobs remaining at a particular point in time. The jobs are labeled $J_1,J_2,J_3,J_4$ and $J_5$ in the order they entered the shop. The respective processing times and due dates are given in the table below:

Job	Processing time (in days)	Due date (in days)
$J_1$	13	65
$J_2$	32	48
$J_3$	34	34
$J_4$	4	36
$J_5$	5	35

When the jobs are assumed to enter the shop in the sequence of SPT (shortest Processing Time), the mean flow time and average tardiness, respectively, are

• A. 41.4 and 15
• B. 39.4 and 14
• C. 35.4 and 12
• D. 37.4 and 13

Answer 1

The correct option is C 35.4 and 12

Shortest processing time (SPT) rule

$J_4-J_5-J_1-J_2-J_3$

Job (J)	Processing time $\left(t_j\right)$	Flow time $\left(f_j\right)$	Due date $\left(d_J\right)$	Lateness $\left(L_J\right)$	Tardiness $\left(T_J\right)$
$J_4$	4	4	36	-32	0
$J_5$	5	9	35	-26	0
$J_1$	13	22	65	-43	0
$J_2$	32	54	48	6	6
$J_3$	34	88	34	54	54
		$\sum F_J=177$			$\sum T_J=60$

$\text{Mean flow time,}{\overline{F}}_m=\frac{177}{5}=35.4$

Average Tardiness,

$\overline{T}=\frac{\sum T_J}{n}=\frac{60}{5}=12$