一类完全型区间线性规划的求解

Solution of Complete Style of Interval Linear Programming

在现有研究的基础上,定义了一类完全型的区间线性规划,其目标系数和约束系数均可为区间数,约束条件可包括等式和不等式类型.给出了一种反映决策者满意度的区间数序关系,基于此将区间不等式约束转化为确定型约束.讨论了区间等式约束的含义并将其化为确定型不等式约束,分析了含有区间数的目标函数并将其转化为一个确定性目标函数.在此基础上,将区间线性规划转化为确定型线性规划并进行求解.最后,给出一个算例.

Based on the current related researches, a complete style of interval linear programming was defined. All the coefficients of its objective function and constraints can be interval numbers, and its constraint conditions may be equations or inequations. An order relation between interval numbers reflecting the satisfactory level of decision makers was proposed, and based on this, inequality constraints of interval linear programming were transformed into constraints with exact coefficients. The equality constraints of interval linear programming were discussed and converted into inequality constraints with exact coefficients. In addition, its objective function concluding interval numbers was analyzed and changed into an exact objective function. As a result, an interval linear programming problem was transformed into an exact linear programming problem and solved. Finally, an example was given.