石化企业最优生产计划中的效益曲线分析

Profit curve analysis for optimal production planning in the petrochemical industry

针对一般灵敏度分析存在的不足,提出一种效益曲线分析方法。效益曲线的纵坐标为效益变化,横坐标为某一约束方程的右端项,曲线上任一点切线的斜率则为影子价格。将效益曲线划分为无可行解区、过渡区I、灵敏度分析区、过渡区II和临界区共5个区,并给出相应的算法。实际应用表明,效益曲线可以给出使得效益增加的约束方程右端项参数的最大区间,同时给出模型有可行解的下界值,对于生产计划的参数分析和调整具有重要的意义。

A profit curve analysis method was developed as an improved version of the general sensitivity analysis method. On the profit curve, the ordinate is the change in the profit while the abscissa is the right side of the constraint. The slope at any point is the shadow price. The profit curve can be divided into the infeasible region, transition region I, the sensitivity analysis region, transition region II, and the critical region. An algorithm was developed to identify each region. Examples show that the profit curve gives the maximum range of the constraint where the profit increases and the minimum for where the model is feasible. Profit curve analyses are important for parametric analyses and a production planning.