化学工艺的最优化方法Chapter1.ppt

Example1.4 Multiplant product distribution A single product (Y) manufactured at several plant locations. The product needs to be delivered to several customers located at various distances from each plant. Question: How can you arrange the production at various plants? How many factors should we think about? How much Y must be produced at each of m plants (Y1,Y2,Y3,Y4,……Ym)?; How should Ym be allocated to each of n demand point? Transportation Production cost versus capacity curves for each plant (old plant inefficient, new plant more efficient) The essential features of Opt. problem Every optimization problem contains three essential categories: At least one objective function to be optimized; Equality constrains (equations); Inequality constraints (inequatilitis). 有关部门对32D纯棉纱规定的质量指标为棉结不多于70粒，品质指标不小于2900．求最优解。 原料 单价，元/t 混合比，% 棉结粒 品质指标 混和单价 国棉131 8400 25 60 3800 2100 国棉229 7500 35 65 3500 2625 国棉327 6700 40 80 2500 2680 平均合计 100 70 3175 7405 根据问题的需要设置变量：设X1 ， X2和X3分别为国棉131，229，327的棉花配比。得到数学模型： minZ＝（ 8400 X1 +7500 X2 +6700 X3 ） S.t. 60X1 +65X2 +80 X3 ≤70 3800 X1 +3500 X2 +2500 X3 ≥2900 X1 + X2 + X3＝1， X1 ， X2 ， X3 ≥ 0 Analyze the process itself so that the process variables and specific characteristics of interest are defined; that is, make a list of all of the variables. Determine the criterion for optimization, and specify the objective function in terms of the variables defined in step 1 together with coefficients. This step provides the performance model（运用模型）. Using mathematical expressions, develop a valid process or equipment model that relates the input-output variables of the process and associated coefficients. Includes both equality and inequality constraints. Use well-know physical principles (like mass balances, energy balances), empirical relations, implicit concepts and external restrictions. Identify the independent and dependent variables to get the number of degree of freed