SINGLE MACHINE SEQUENCINGQuestion: Process times and due dates for six jobs in waiting to be processed at a work centre are given in the table below. Determine the sequence of processing according to each of the following rules: (a) FCFS, (b) SPT, (c) DD, (d) CR. Job A B C D E F Solution: FCFS: JOB A B C D E F PROCESSI DUE DATE NG TIME (DAYS) (DAYS) 2 6 8 16 4 4 10 17 5 15 12 18 FLOW TIME 2 10 14 24 29 41 LATENESS 0 0 10 7 14 23 Processing time (days) 2 8 4 10 5 12 Due date (days) 7 16 4 17 15 18

STP: JOB A C E B D F PROCESSI DUE DATE NG TIME (DAYS) (DAYS) 2 7 4 4 5 15 8 16 10 17 12 18 FLOW TIME 2 6 11 19 29 41 LATENESS 0 2 0 3 12 23

DUE DATE: JOB C A E B D F PROCESSI DUE DATE NG TIME (DAYS) (DAYS) 4 4 2 7 5 15 8 16 10 17 12 18 FLOW TIME 4 6 11 19 29 41 LATENESS 0 0 0 3 12 23

CRITICAL RATIO: JOB C F D B E A PROCESSI NG TIME (DAYS) 4 12 10 8 5 2 DUE DATE (DAYS) 7 18 17 16 15 4 FLOW TIME 4 16 26 34 39 41 CRITIC LATENES AL S RATIO 1 0 1.5 0 1.7 9 2 18 3 24 3.5 37

EVALUATION OF SEQUENCING: AVERAGE FLOW TIME:

RULES FCFS SPT CR

AVERAGE FLOW TIME 20 18 26.66

RANK 2ND 1ST 3RD

AVERAGE NO.OF JOBS IN THE SYSTEM: RULES FCFS SPT CR AVERAGE FLOW TIME 2.92 2.63 3.90 RANK 2ND 1ST 3RD

AVERAGE JOB LATENESS: RULES FCFS SPT CR AVERAGE FLOW TIME 9 6.67 14.67 RANK 2ND 1ST 3RD

Two Machine Scheduling Problem:In the two machine problem, two centers are there and every job has to pass through both the machines. The best algorithm for this sequencing which gives minimum make span time for the jobs was put forth by

Johnson. This method is named after him and is called Johnson rule.

Example:The times required to complete each of the eight jobs on two machines are shown below. Each job must follow the same sequence, beginning with machine A and moving to machine B. (A) determine the sequence that minimizes the throughout time. (B) construct a chart of the resulting sequence , and find Bs idle time JOB A B C D E F G H SOLUTION: E-B-G-H-D-C-A-F MACHINE A(HRS) 16 13 9 8 2 12 18 20 MACHINE B(HRS) 5 13 6 7 14 4 14 11

JOB SHOP SCHEDULING: The n-job m-machine problem can be divided into four broad groups:

Flow shop Job shop Dependent shop

Open shop