CAJ | 학술논문

针对二层线性规划问题，结合灰色系统的特性，提出了一般灰色二层线性规划问题，并给出了该问题的模型及相关的定理．针对漂移型灰色二层线性规划，基于单纯形法提出了一种具有全局收敛性质的算法来求解该问题．用下层的Kuhn—Tucker条件代替下层问题，将灰色二层线性规划转化为灰色单层规划问题，利用对偶理论将该单层规划转化为一系列灰色线性规划问题，从而用单纯形法求解该问题来得到灰色二层线性规划问题的解．最后，通过算例验证了文中算法的有效性．
침대이층선성규화문제，결합회색계통적특성，제출료일반회색이층선성규화문제，병급출료해문제적모형급상관적정리．침대표이형회색이층선성규화，기우단순형법제출료일충구유전국수렴성질적산법래구해해문제．용하층적Kuhn—Tucker조건대체하층문제，장회색이층선성규화전화위회색단층규화문제，이용대우이론장해단층규화전화위일계렬회색선성규화문제，종이용단순형법구해해문제래득도회색이층선성규화문제적해．최후，통과산례험증료문중산법적유효성．
Based on the bilevel linear programming and the characteristic of grey system, a general gray bilevel linear programming problem with its model and theorem are given. A globally convergent algorithm based on simplex method is given to solve the drifting grey bilevel linear programming problem. Replacing the lower level problem by its Kuhn-Tucker condition, the gray bilevel linear programming is transformed into a gray single level programming problem, which can be transformed into a series of gray linear programming problem by use of the dual theory. So these problems can be solved by simplex method to obtain the solution of the gray bilevel linear programming problem. Finally, an example is adopted to verify the effectiveness of the proposed algorithm.