分枝定界法

To speed up the solution of the problem, a solution method that hybridizes heuristic algorithm with conventional branch and bound method is presented.

文中还讨论了采用启发式算法同传统的分枝定界法相结合以提高问题的求解速度，并给出了一个数值例子。

Reverse logistics ; recycling ; mixed integer linear programming ; branch and bound method

反向物流；再循环；混合整数线性规划；分枝定界法

At first the typical die and mould components and their standard processing technique,and the types of facilities were defined.Then the integer programming model of the facility planning was established and the branch and bound method was used to give a solution to the model cases.

定义了模具典型零件、设备类及模具典型零件标准工艺；建立了设备资源规划的整数规划数学模型；采用分枝—定界法对给定实例进行求解；计算结果证明了模型的有效性及实用性。

The first model is the optimization problems with s linear objective function subject to a system of fuzzy relation equations and a system of fuzzy relation inequalities, which are solved by using path method and 0-1 integer programming with branch and bound method.

第一种为约束为模糊关系方程和模糊关系不等式的具有线性目标函数的优化问题，采用路径法及0-1整数规划中的分枝定界法对其求解；第二种为约束为模糊关系方程和模糊关系不等式的格线性规划问题，采用直接法、路径法及0-1整数规划法对其求解；第三种为模糊关系不等式为模糊的，即约束中有一个可接受的容差，采用容差法及正负理想法对其求解；第四种是一种新的可能性模糊线性规划问题，采用模糊数大小比较法、"切片-粘贴"法及正负理想法，并设计了随机模拟的遗传算法对其求解；第五种为期望值模型，利用期望值将其转化为清晰约束系数的线性规划问题的方法。

For the nonlinear discrete programs the dynamic programming method is used generally, and much time have to be consumed.

其中的线性规划通常用分枝定界法或割平面法，还有图上作业法求解。

Based on the model for FRFS problem,this paper improves the current solution to by combining branch-and-bound algorithm with partan algorithm and by selecting the most optimal schedule.

在 FRFS问题模型的基础上，将分枝定界法与平行切线法相结合，选取最优资源投入量，进而得到最优计划，完善了柔性资源计划问题的解法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。