论文标题
KKT在运输问题上的应用以及量折扣的运输成本
Application of KKT to Transportation Problem with Volume Discount on Shipping Cost
论文作者
论文摘要
非线性编程问题可用于设计和分配工作时间表以及将商品和服务从已知来源运输到指定目的地。目标函数可以是线性或非线性的，具体取决于运输方式。在紧急情况下提供商品和服务时，始终认为客观成本功能是非线性的。这项研究的目的是研究运输问题成本函数的性质，并提供解决方案算法来解决此类非线性成本函数。由于有时可用于大量商品和服务，因此运输的每单位商品成本可能无法固定。这将使成本函数要么分段线性，可分离凹形或凸。解决这些问题的方法是应用现有的一般非线性编程算法，并在必要时进行修改以适应问题的特殊结构。我们从理论上描述了非线性成本函数的算法和状态条件，在足够和必要的情况下可以实现稳定性。
Nonlinear programming problems are useful in designing and assigning work schedule and also in transporting goods and services from known sources to specified destinations. The objective function could be linear or nonlinear depending on the mode or rout of transportation. In supplying goods and services during emergency cases, the objective cost function is always assumed to be nonlinear. The purpose of this research is to study the nature of the cost function of the transportation problem and provide solution algorithms to solve such nonlinear cost functions. The cost per unit commodity transported may not be fixed since volume discounts are sometimes available for large shipments of goods and services. This will make the cost function either piecewise linear, separable concave or convex. The approach to solving such problems as they arise is to apply existing general nonlinear programming algorithms and when necessary make modifications to fit the special structure of the problem. We describe theoretically , algorithms for the nonlinear cost function and state conditions under which stability is achieved with both sufficient and necessary cases.
