Abstract: The authors study the solution robustness of the Risk Explicit Interval Linear Programming (REILP) model using numerical experimentations, investigating whether optimal solutions of a REILP would vary under various preferences to different constraints. The first numerical experiment deals with an optimal land use planning subject to nutrient loading constraints. The second one deals with an optimal water resource allocation subject to pollutant loading constraints. The results show that REILP solutions have different sensitivities to constraint preferences in different cases. This phenomenon suggests that in practice it is necessary to conduct thorough analysis on the robustness of REILP solutions to constraint preferences before reaching reliable decision support. In addition, the variability of REILP solutions with regard to various constraint preferences makes it possible to efficiently generate alternative management schemes within the frame work of REILP.

Key words: steady, sensitivity, numerical experimentation, risk explicit interval linear programming, risk preference

摘要： 利用数值试验的方法考察了风险显性区间数线性规划(REILP)模型最优解的稳健性问题, 即其最优解在决策者对不同约束条件存在偏好的情况下是否一致。数值案例一为基于污染物总量控制的土地利用规划问题, 目标是在污染物排放总量符合约束的前提下实现不同农业种植组合的收益最大化; 数值案例二为基于污染物总量控制的水资源优化分配问题, 目标是在污染物排放总量满足约束的前提下, 企业间水资源利用分配所获得的效益最大化。 数值试验结果表明, REILP的解在某些情况下呈现稳健性特征, 但在另一些情况下则呈现出最优解随着决策者对约束条件偏好的不同而产生变化的特征。REILP模型的这种特点表明, 在实际应用中, 建模人员需要特别分析最优解对决策者偏好的响应, 从而产生有效稳健的决策支持。此外, REILP解对决策者偏好的变异性也使其具备能够在不确定性条件下产生多种替代方案的能力。

关键词: 稳健性, 敏感性, 数值模拟, 风险显性区间线性规划, 风险偏好