COURSE INDUSTRIAL ENGINEERING LESSON : N JOB 2 MACHINE (SEQUENCING)
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N JOBS 2 MACHINES Machine A Machine B Jobs Ai Bi B2 A4 B4 An Bn
N JOBS2 MACHINES In this problem 2 machines A and B are involved and each job is numbered.i 1,2,3,...N. and each job has its processing time on machine A and B denoted by Ai and Bi respectively. The problem is to find a processing order for different jobs so that the idle time for both the machines is minimised. This is done by using Johnson's Rule or Johnson's algorithm The steps involved are: l. Find out the minimum of Ai and Bi. 2. If minimum is for Ar i.e. for the rth job on machine A then do the rth job first. 3. If minimum is for Bs i.e.for the sth job on machine B then do the sth job at the last. 4. In case of tie between Ar and Bs. Perform the rth job first and the sth job at the last. 5. After a job is assigned in a sequence, strike it off so that it can't be considered again. 6. Continue in this manner until all the jobs are assigned.
QUESTION Apply Johnson's algorithm and find the optimal sequence for the following set of jobs. Also find the make span time, idle time for each machine, percentage utilisation of each machine and prepare Gantt chart for both the machine. Jobs Machine A Machine B 4 C B D EA F
SOLUTION Machine A Machine B Jobs In Out In Out . Percentage utilisation of Machine A 35/36 * 100 97.2% Percentage utilisation of Machine Be 28/36 * 100 = 77.7% 20 27 35 26 30 36 20 27 27 35 idle time for machine A Idle time for machine B 2+1+5-8 Make Span Time = 36 04 2 3 4 S6789 lo ll 12131Y/SIGI :" 20212223242526, 729 2930 a2833d 6
IMPORTANT EXAMPLE If Jobs A Here we have to decide for machine A and for machine A minimum is from eginning 4 13 9 13 If Jobs A Here we have to decide for machine B and for machine B minimum is from last 13
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