A heuristic approach for solution of MINLP problem for production scheduling in preemptive mode

Chemical engineering problems formulated as mixed integer nonlinear programming (MINLP) model are difficult to solve when the model is non-convex. In order to overcome this difficulty, a semi-heuristic algorithm for production scheduling was developed in this work. Using this approach, the non-convex MINLP problem is first considered as an MILP problem without dividing the orders into units. The order causing prolonged delivery time is thus identified, constraints for this order are then relaxed and MILP problem is re-solved using the new constraints. Having reached the new schedule, the quantitative distribution of the specific order to different units is determined by solving the LP problem that does not contain integer variables since allocation of orders to the units, and processing order are known. The results obtained with three example problems indicate improvements over previously reported schedules and therefore, give promise that the suggested strategy may be used in moderately sized industrial applications.