In this paper, we focus on multiobjective two-level simple recourse programming problems, in which multiple objective functions are involved in each level, shortages and excesses arising from the violation of the constraints with discrete random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, a concept of Pareto Stackelberg solutions based on the reference objective levels is introduced. Using the Kuhn–Tucker approach in two-level programming, we formulate as a mixed integer programming problem, and propose an interactive algorithm to obtain a satisfactory solution of the leader from among a Pareto Stackelberg solution set based on the reference objective levels. A numerical example illustrates the proposed algorithm for a multiobjective two-level stochastic programming problem with simple recourses under the hypothetical leader.

在本文中，我们关注于多目标两级简单资源规划问题，其中每级涉及多个目标函数，对离散随机变量违反约束而产生的不足和过度进行惩罚，并求和功能和对罚款金额的期望最小化。为了解决此类问题，引入了基于参考目标水平的Pareto Stackelberg解决方案的概念。在两层编程中使用Kuhn-Tucker方法，我们将其公式化为混合整数规划问题，并提出了一种交互式算法，可以从基于参考目标水平的Pareto Stackelberg解决方案集中获得满意的领导者解决方案。