otherwise go to step 4 Step 4 Convert the m machines problem into a two machine problem by introducing two fictious machines H and K such that thi t j t j tk and U tkj 12 t3j tkj Where tj is the processing time of jth job in machine H and tx is the processing time of jth job in machine K Step 5 Determine the optimal sequence for n jobs and 2 machines sequencing problem Problem Find the sequence that minimizes the total elapsed time required to complete the following six jobs on three machines M M and M3 in the order M M M3 Jobs Machines J Jz M 3 12 M 8 M3 13 6 a min ty 2 max t j j 2 5 b min tj 2 max t j j 2 5 M 2 12 14 36 J3 5 M 1 8 4 2 6 Js J6 11 9 3 9 12 8 Solution We are given 6 jobs each of which is to be processed in 3 machines M M2 M3 in the order M M M3 Hence n 6 and m 3 Hence the given problem becomes 6 jobs in 3 machines problem For optimum sequence the required condition is either or both of the following conditions must be true M3 8 14 1 13 Minimum time Maximum time Min t 2 and nt3j 8 Max taj 8 Clearly Min t3 Max t 8 Hence the condition to reduce 3 machines problem to 2 maxhines problem is satisfied Hence the given problem can be converted to an equivalent two machines for six jobs problem Hence we have the processing table for the two machines H and K Jober Let H and K be two fictious machines such that the processing times are got from the following relations H M M z i e H tj tj t j K M 2 M 3 i e K txj tzi t3j Where 1 i 6