Three products manufactured must be routed through three machines and each has t

Question

Three products manufactured must be routed through three machines and each has to be processed in the same sequence on each machine: machine 1, machine 2, and finally on machine 3. The times required to perform the work on item i (i=1,2,3) by machine j (j=1,2,3) are given in the following table:

           machine1    machine2   machine3

item 1    1 hour        2 hours      3 hours

item 2    2 hours       1 hour       4 hours

item 3    4 hours       2 hours      1 hour

Formulate an integer programming problem to minimize the total time necessary to process all products.

Explanation / Answer

let there be x,y,z amount of items i=1,2,3

total time by machine 1=x+2*y+4*z=a

total time by machine 2=2*x+y+2*z=b

total time by machine 3=3*x+4*y+z=c

optimize (a+b+c)

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