Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is ___________ (correct to two decimal places).

Job	Processing time (days)	Due date (days)
A	3	8
B	7	16
C	4	4
D	9	18
E	5	17
F	13	19

To find the average tardiness using the Shortest Processing Time (SPT) rule, we follow these steps:

Step 1: Arrange the jobs in increasing order of their processing times.
The given jobs and their details are:
• Job A: Processing Time = 3, Due Date = 8
• Job B: Processing Time = 7, Due Date = 16
• Job C: Processing Time = 4, Due Date = 4
• Job D: Processing Time = 9, Due Date = 18
• Job E: Processing Time = 5, Due Date = 17
• Job F: Processing Time = 13, Due Date = 19

Sorting by processing time (shortest first), the scheduling sequence is:
A → C → E → B → D → F

Step 2: Calculate the completion time (flow time) and tardiness for each job in the sequence.
Tardiness (T) for any job is defined as:
$T\; =\; max(0,\; C\; -\; D)$
where $C$ is the completion time of the job and $D$ is its due date.

• Job A:
Completion Time ($C\_A$) = 3 days
Due Date ($D\_A$) = 8 days
Tardiness ($T\_A$) = $max(0,\; 3\; -\; 8)\; =\; 0$ days

• Job C:
Completion Time ($C\_C$) = $3\; +\; 4\; =\; 7$ days
Due Date ($D\_C$) = 4 days
Tardiness ($T\_C$) = $max(0,\; 7\; -\; 4)\; =\; 3$ days

• Job E:
Completion Time ($C\_E$) = $7\; +\; 5\; =\; 12$ days
Due Date ($D\_E$) = 17 days
Tardiness ($T\_E$) = $max(0,\; 12\; -\; 17)\; =\; 0$ days

• Job B:
Completion Time ($C\_B$) = $12\; +\; 7\; =\; 19$ days
Due Date ($D\_B$) = 16 days
Tardiness ($T\_B$) = $max(0,\; 19\; -\; 16)\; =\; 3$ days

• Job D:
Completion Time ($C\_D$) = $19\; +\; 9\; =\; 28$ days
Due Date ($D\_D$) = 18 days
Tardiness ($T\_D$) = $max(0,\; 28\; -\; 18)\; =\; 10$ days

• Job F:
Completion Time ($C\_F$) = $28\; +\; 13\; =\; 41$ days
Due Date ($D\_F$) = 19 days
Tardiness ($T\_F$) = $max(0,\; 41\; -\; 19)\; =\; 22$ days

Step 3: Calculate the Total Tardiness and Average Tardiness.
Total Tardiness = $0\; +\; 3\; +\; 0\; +\; 3\; +\; 10\; +\; 22\; =\; 38$ days

Average Tardiness = $38\; /\; 6\; \approx \; 6.33$ days

Thus, the average tardiness using the shortest processing time rule is 6.33 days.