Scheduling n Jobs × m Machines using Jackson's Rule

Sequencing the jobs may not be always in the form of n × 2 or n × 3. In fact in real practice, we often come across with the n jobs to sequence on m machines or men or work centers. However it is not very difficult to sequence in such case. The method we apply here is again based on the Jackson's conditions as explained below.

Let there be n jobs, of which each is to be processed through m work centers/machines

Say   W₁, W₂, W₃ . . . Wm

Now, the iterative procedure is as follows:

Step 1

Find minimum process time of W₁ and W_m series, and maximum process time of all the middle series.

Step 2

Check whether

              Minimum of W₁ series ≥ Maximum of middle series.

              Minimum of W_m series ≥ Maximum of middle series.

Step 3

If the equations of step 2 are not satisfied, the method fails. Otherwise move to next step.

Step 4

Convert m Work center problem to two-work center problem by two fictitious machines say A and B.

A = The algebraic sum of process time of W₁ and all corresponding timings of the mediocre series.

B = The algebraic sum of process time of W_m and all corresponding timings of the mediocre series.

(However in general practice we can find the sequence by taking the timings of W₁ and W_m if the sums of the mediocre series are fixed positive constants).