Question

Six jobs are to be processed through a​ two-step operation. The first operation involves​ sanding, and the second involves painting. Processing times are as​ follows:

JOB	OPERATION 1 (HOURS)	OPERATION 2 (HOURS)
A	4	8
B	10	5
C	3	11
D	14	14
E	6	1
F	7	12

a. Using​ Johnson's rule for​ 2-machine scheduling, the sequence​ is:

Scheduled Order	Job
1	?
2	?
3	?
4	?
5	?
6	?

b. For the schedule developed using Johnson's rule, the total length of time taken to complete the six jobs (including the 2nd operation) = _______ hours (enter. your response as a whole number)

Answer 1

Answer:

a. C A F D B E

b. 54

Explanation:

As per Johnson's rule, first we need to identify the job with the shortest processing time (SPT) , if SPT is for Operation 1 then we need to schedule it as early as possible and if SPT is for Operation 2 then we need to schedule it as late as possible.

Job Operation 1 Operation 2 Scheduled Order 1 Operation 1 Operation 1 Start time End time Operation 2 Operatio 2 Start time End time C 3 11 0 3 3 14 А 4 8 3 7 14 22 2 3 4 F 7 12 7 14 22 34 D 14 14 14 28 34 48 5 B 10 5 28 38 48 53 6 E 6 1 38 44 53 54

Operation 1 Start time for Job 1 = 0

Operation 1 End time for Job 1 = Start time + Operation 1 duration

Operation 2 Start time for Job 1 = Operation 1 End time for Job 1

Operation 2 End time for Job 1 = Operation 2 Start time for Job 1 + Operation 2 Duration

Operation 1 Start time for Job i+1 = Operation 1 End time for Job i

Operation 1 End time for Job i+1 = Operation 1 Start time for Job i+1 + Operation 1 Duration for Job i+1

Operation 2 Start time for Job i+1 = Max(End time of Operation 2 for Job i, End time of Operation 1 for Job i+1)

Operation 2 End time for Job i+1 = Operation 2 Start time for Job io+1  + Operation 2 Duration for Job i+1

Last Scheduled Job E will be completed at the end of 54th hour.