While a range of models have been proposed for the multiperiod blend scheduling problem (MBSP), solving even medium-size MBSP instances remains challenging due to the presence of bilinear terms and binary variables. To address this challenge, we develop solution methods for MBSP focusing on the cost minimization objective. We develop a novel preprocessing algorithm to calculate lower bounds on stream flows. We define product dedicated flow variables to address product specific features involved in MBSP. Bounds on stream flows and new product dedicated flow variables are then used to generate tightening constraints which significantly improve the solution time of the mixed integer nonlinear programming models as well as models based on linear approximations.

尽管针对多周期混合调度问题（MBSP）提出了一系列模型，但由于存在双线性项和二进制变量，因此即使求解中等大小的MBSP实例仍然具有挑战性。为了应对这一挑战，我们针对MBSP开发了解决方案方法，重点是降低成本。我们开发了一种新颖的预处理算法来计算流的下限。我们定义产品专用流程变量以解决MBSP中涉及的产品特定功能。然后使用流的界限和新产品专用的流变量来生成紧缩约束，这将显着缩短混合整数非线性规划模型以及基于线性近似的模型的求解时间。