KKT在运输成本有体积折扣的运输问题中的应用
Application of KKT to Transportation Problem with Volume Discount on Shipping Cost
摘要：
非线性规划问题在设计和分配工作计划以及将货物和服务从已知来源运输到指定目的地方面是有用的。目标函数可以是线性的或非线性的，这取决于运输的模式或路线。在紧急情况下提供货物和服务时，目标费用函数总是假定为非线性的。本研究的目的是研究运输问题的费用函数的性质，并提供求解此类非线性费用函数的算法。运输的每一单位商品的成本可能不是固定的，因为大宗货物和服务有时可以获得批量折扣。这将使费用函数成为分段线性的、可分离的凹函数或凸函数。解决这些问题的方法是应用现有的一般非线性规划算法，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，算法的非线性费用函数和状态条件下，实现稳定的充分和必要的情况下。
英文摘要：
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.
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