Question

Question No.2: Table below provides the processing times in hours of seven jobs to be processed on four machines in the order Mi-M2-M3-M4. Obtain the sequence that minimises the total processing time, calculate the minimum time taken to process these seven jobs on four machines, and calculate the minimum value of idle time for each of the machines Data on processing times in hours Job Machine MI 12 M2 MO 9 M4

Answer 1

ANSWER * Here To apply jhonson's rule of sequencing we need to convert the problem for the a machines. 1. e. from y machines to a machines. * To convert the machine 4 to machine a following conditions need to be satisfied. probleme condition - mins time on me 1 z max of [max. time in machine a 3) And/or condition - mins time on mlc u z max of (max. a time on machine 2,3] Here, In This problem ; minsimum time on me = 3 max. of (max. time on me 2,3)= 9 mis time on mle a=9

here, as per conditions ; condition - - 329 Hence, condition is not satistied. condition - 9 29 Here Honce condition is salisted. - Hence, we can convert this problem into problems having a 2 machines. where. processing time on mle 10 = sum of processing time on machine 1,283 Processing time on mle q = sum of Prousting time on machine 2,3,4 Hence, below enuivalent two machine problem is obtalned.

М-1 3, т во 1, 1, ( a5 43 44 3, е 13 41 5, 14 14 , 15 14 16 аз м - а Hence, as per Thomsons rule following sequence can be achived. - Hence Job sequence will be .... З, Т, Э, Т, , , , , , ,

Machine Time Caluclation

Total Idl Time = 56 hours

B C D E F G H I | Machine -1 IN OUT Machine-2 IN OUT Machine-3 IN OUT 6 11 Machine-4 IN OUT 0 33 10 4 11 12 Idle Time 46 50 50 59 40 85 38 0 46 50 20 25 11 15

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