The minimum processing time among these jobs is 6 which

Last updated: 10/9/2023

The minimum processing time among these jobs is 6 which corresponds to the job J4 on machine M and job J5 on machine M Hence J4 is placed in the first available position in the sequence as shown below J2 J4 J5 Finally the job J3 is placed as shown below J2 J4 J3 Thus J2J4J3 two machines Sequencing n Jobs on 3 Machines Processing n Jobs in m Machines Machines M M M3 J5 J J5J is the optimal sequence of the five jobs on the Let there be n jobs J IzIn each of which is to be processed in m machines say M M Mm in the order M M Mm The list of job numbers 1 2 n with their processing time is given in the following table Job numbers 1 t11 t21 t31 3 t13 t22 t23 t32 33 2 t12 J En tin tzn t3n Mm tmn tm1 tm3 An optimum solution to this problem can be obtained if either or both of the following conditions are satisfied a min t max ty for i 2 3 k 1 b min tj 2 max ty for i 2 3 k 1 35 If the above condition is satisfied then the problem can be converted to an equivalent two machines and n jobs problem Algorithm for optimum sequence for n jobs in m machines The iterative procedure for determining the optimal sequence for n jobs in m machines is given below Step 1 Find min tij and mintmj Also find the maximum of each of t2j t3j t for all j 1 2 n Step 2 Check the following a min ti 2 max tij for i 2 3 k 1 b min tm max tij for i 2 3 k 1 Step 3 If both the inequalities of step 2 are not satisfied this method fails