MINLP model for cyclic multiproduct scheduling on continuous parallel lines

A computational scheme based on valid outer-approximations of the nonlinear part of the problem is proposed to strengthen the bounds of the master problem and therefore achieve fast convergence.

Abstract

This paper addresses the problem of cyclic multiproduct scheduling on continuous parallel production lines. This plant configuration is typically used in the manufacturing of specialty chemicals. The problem involves a combinatorial part (assignment of products to lines and their sequencing in each li and a continuous part (duration of production runs and frequency of production). To account for these two elements, a large-scale mixed integer nonline program (MINLP) is developed and an exact reformulation technique is applied to linearize it in the space of the integer variables. The Kuhn-Tucker optimality conditions are exploited in the resulting model in order to effectively apply generalized Benders decomposition. This avoids the explicit solution of extremely large nonlinear subproblems. At the same time, a computational scheme based on valid outer-approximations of the nonlinear part of the problem is proposed to strengthen the bounds of the master problem and therefore achieve fast convergence. Despite the nonlinear nature of the model, special but important cases are identified for which certain convexity conditions are satisfied and the suggested procedure guarantees the globa optimality of the solution. The proposed technique was applied to a real world problem for a polymer production plant. The corresponding MINLP containe 780 binary variables, 23,000 continuous variables and 3200 constraints.