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Successive LP Approximation for Nonconvex Blending in MILP Scheduling Optimization Using Factors for Qualities in the Process Industry
Industrial & Engineering Chemistry Research ( IF 3.8 ) Pub Date : 2018-07-31 , DOI: 10.1021/acs.iecr.8b01093 Jeffrey D. Kelly 1 , Brenno C. Menezes 2 , Ignacio E. Grossmann 2
Industrial & Engineering Chemistry Research ( IF 3.8 ) Pub Date : 2018-07-31 , DOI: 10.1021/acs.iecr.8b01093 Jeffrey D. Kelly 1 , Brenno C. Menezes 2 , Ignacio E. Grossmann 2
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We develop a linear programming (LP) approach for nonlinear (NLP) blending of streams to approximate nonconvex quality constraints by considering property variables as constants, parameters, or coefficients of qualities that we call factors. In a blend shop, these intensive properties of streams can be extended by multiplying the material flow carrying out these amounts of qualities. Our proposition augments equality balance constraints as essentially cuts of quality material flow for each property specification in a mixing point between feed sources and product sinks. In the LP factor formulation, the product blend quality is replaced by its property specification and variables of slacks and/or surpluses are included to close the balance; these are called factor flows and are well known in industry as product giveaways. Examples highlight the usefulness of factors in successive substitution by correcting nonlinear blending deltas in mixed-integer linear models (MILP) and to control product quality giveaways or premium specifications in blend shops.
中文翻译：
基于过程工业质量因素的MILP调度优化中非凸面混合的连续LP逼近
我们通过将属性变量视为常量，参数或质量系数（我们称为因素）来开发一种线性规划（LP）方法，用于流的非线性（NLP）混合，以近似非凸质量约束。在混合车间中，可以通过增加执行这些质量数量的物料流来扩展流的这些密集特性。我们的主张增加了平等平衡的约束条件，因为在原料来源和产品接收者之间的混合点上，每个属性规范的质量材料流实质上都被削减了。在LP因子公式中，产品混合物的质量由其性能指标代替，并包括松弛和/或剩余变量来平衡。这些称为因子流并在行业内被称为产品赠品。示例通过在混合整数线性模型（MILP）中校正非线性混合增量并控制混合车间中的产品质量赠品或优质规格，突出了连续替换中因素的有用性。
更新日期：2018-08-01
中文翻译：
基于过程工业质量因素的MILP调度优化中非凸面混合的连续LP逼近
我们通过将属性变量视为常量，参数或质量系数（我们称为因素）来开发一种线性规划（LP）方法，用于流的非线性（NLP）混合，以近似非凸质量约束。在混合车间中，可以通过增加执行这些质量数量的物料流来扩展流的这些密集特性。我们的主张增加了平等平衡的约束条件，因为在原料来源和产品接收者之间的混合点上，每个属性规范的质量材料流实质上都被削减了。在LP因子公式中，产品混合物的质量由其性能指标代替，并包括松弛和/或剩余变量来平衡。这些称为因子流并在行业内被称为产品赠品。示例通过在混合整数线性模型（MILP）中校正非线性混合增量并控制混合车间中的产品质量赠品或优质规格，突出了连续替换中因素的有用性。
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