While solving for the job-shop scheduling model on VBA, I have found that if the number of tasks is limited to 35 tasks (1330 var) and below, the problem can be solved quite easily. A strange phenomenon was observed where the time required to solve the model is affected by the duration of each tasks although the increase in duration will not affect the basis of the solution. Hence, a better approach is needed. The following shows the possible changes:

1) A different solution approach – Use a different language (CPLEX & GAMS) or/and online solvers (Neos – Solver)

a. According to Dr. Cure, online solvers will not contribute much to a NP-hard problem.2) A different model – The model can be viewed as a single machine scheduling n jobs that seeks to

minimize tardiness or makespan (still NP-hard)3) Reduce number of tasks by grouping certain obvious tasks while making assumptions