(120g) Solution Methods for Multiperiod Blend Scheduling MINLP Models
In this work, we first propose an integrated model for the multiperiod blending and scheduling problem taking into account all three refinery subsystems. We employ a discrete representation of time and, for illustration, we use linear mixing rules resulting in bilinear terms. We show that accounting for all subsystems simultaneously can lead to better solutions.
Second, to solve the resulting MINLP model, we propose a series of preprocessing and tightening methods based on flow and property propagation. The preprocessing algorithms calculate parameters that are then used to generate new tightening constraints. The algorithm runs in seconds. Three types of constraints are generated:
(1) Constraints on property demands. Using the lower bounds of the property specifications of a product and its demand, we propose novel constraints on available streams for blending, which consider the product demand and property specifications simultaneously.
(2) Constraints on single stream flow. For a given product, by examining its property specifications, we determine if there exists a stream that is required to be blended in order to satisfy the property specifications. If such stream exists, we enforce its flowrate to satisfy certain lower bound, which is calculated from product demands.
(3) Constraints on multiple stream flows. For every property specification of a product, we determine a subset of streams, at least one of which is required to be blended. We propose constraints for streams that are involved in these subsets, to ensure both product demand and property specifications are satisfied.
The integrated MINLP model and proposed solution methods are tested on a number of instances of different horizon and process complexity. The addition of the generated constraints leads to significant improvement in computational performance. Some instances that originally cannot be solved to optimality in hours, are solved in a few minutes. To further show the effectiveness of the methods, we test them using two MILP models from the literature .Â Using the proposed methods leads to one order of magnitude improvement in solution times for both models, thus allowing us to address previously intractable instances.
Finally, we study, theoretically, the tightness of these proposed constraints. We show that they are often tighter than the McCormick envelops for the relaxation of the bilinear terms appearing in the âproperty balanceâ constraints. The relaxation of the MILP models is also significantly reduced when adding the proposed tightening constraints.
1. Kolodziej SP, Grossmann IE, Furman KC, Sawaya NW. A discretization-based approach for the optimization of the multi period blend scheduling problem. Comput Chem Eng. 2013; 53: 122â42.