制造系统负荷配置的非线性优化

Non-Linear Optimization of Load Allocation in a Manufacturing System

基于排队理论,建立制造系统负荷分配的非线性优化模型.该模型以服务负荷为目标函数,包括关于在制品状态的3个不等式约束.设计一种优化变量转换方法,并经适当的约束条件合并,将该非线性模型转换为凸优化模型.推导给出该凸优化模型对应的拉格朗日函数及KKT条件,并引入凸优化内点法作为负荷分配的有效计算工具.实例计算结果表明,模型的优化结果能保证充分利用设备的生产能力及最低的在制品库存,同时凸优化内点算法具有迭代次数少、收敛速度快的优点.实际应用中,可以将非线性的复杂的优化问题凸性化,从而得到其最优解.

Based on the queuing theory, a nonlinear optimization model is proposed, which has the service load as its objective function and includes three inequality constraints of work-in-progres （WIP）. A novel transformation of optimization variables is also devised and the constraints are properly combined so as to make this model into a convex one, from which the Lagrangian function and the Karush-Kuhn-Tucker （KKT） conditions are derived. The interior-point method for convex optimization is presented here as a computationally efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are reached that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method needs fewer iterations with significant computational savings; and it is possible to make nonlinear and complicated optimization problems convexified so as to obtain the optimum.