摘要
首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.
Firstly, some interrelated conceptions of transportation problem are proposed, in which, the multiple optimal solutions is expanded to broad-sense category, the narrow-sense multiple optimal solutions and the broad-sense multiple optimal solutions are proposed and differentiated. Then some judgment theorem are given and proved, such as the judgment theorem on exclusive optimal solutions, multiple optimal solutions, broad-sense numbered multiple optimal solutions, broad-sense unnumbered multiple optimal solutions. Finally, two formulas are put forward they are the formula for least number of narrow-sense numbered multiple optimal solutions multiple optimal solutions and the formula for most number of broadsense numbered multiple optimal solutions multiple optimal solutions, and one example is given to show correctness of conclusion.
出处
《数学的实践与认识》
CSCD
北大核心
2006年第5期140-146,共7页
Mathematics in Practice and Theory
基金
陕西省自然科学基金项目(2003G11)
西北工业大学研究生创业种子基金项目(Z200589)
关键词
运输问题
多重最优解
狭义多重最优解
广义多重最优解
有限多重最优解
无限多重最优解
transportation problem
multiple optimal solutions
narrow-senseoptimal solutions
broad-sense multiple optimal solutions
numbered multiplesolutions
unnumbered multiple optimal solutions
