A Bayesian approach to batch process scheduling

The problem of decision timing in the context of batch scheduling is addressed in this paper. The representation of time in any scheduling model affects the number of integer variables and the convexity of the model. The usual procedure in batch process scheduling is to divide the scheduling horizon into equal size intervals to achieve the required accuracy. This construction generates a formulation with a potentially large number of binary variables. In this paper, the time events arising in the schedule are modeled directly, and thus the use of binary variables over periods during which no changes in system state occur is avoided. The problem is formulated as a mixed integer nonlinear program. The Bayesian heuristic (BH) approach is used to implement a global optimization algorithm which effectively solves the resulting model. Computational comparisons using two text examples are made against a UDM (uniform discretization model) formulation. The results suggest that the BH approach combined with the nonuniform time discretization formulation shows promise for the solution of batch scheduling problems.