容器约束的吉普问题

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 348-357.

容器约束的吉普问题

程序^1,²,丁义明³,华香颖^3,*()

¹ 中国科学院大学北京 100049
² 中国科学院武汉物理与数学研究所武汉 430071
³ 武汉理工大学数学科学研究中心, 理学院武汉 430070

收稿日期:2017-11-06 出版日期:2019-04-26 发布日期:2019-05-05
通讯作者: 华香颖 E-mail:huaxiangying@whut.edu.cn
基金资助:
中央高校基本科研业务费专项资金(2017IVA073)

Jeep Problems with Container Restriction

Xu Cheng^1,²,Yiming Ding³,Xiangying Hua^3,*()

¹ University of Chinese Academy of Sciences, Beijing 100049
² Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071
³ Center for Mathematical Sciences, School of Science, Wuhan University of Technology, Wuhan 430070

Received:2017-11-06 Online:2019-04-26 Published:2019-05-05
Contact: Xiangying Hua E-mail:huaxiangying@whut.edu.cn
Supported by:
the Fundamental Research Funds for Central Universities(2017IVA073)

摘要/Abstract

摘要：

研究无容器约束和容器约束的吉普问题.对无容器约束吉普问题，给出单向及往返的最优行驶策略.对容器约束吉普问题，给出单向及往返行驶策略并证明吉普有能力行至无穷远处.在容器约束下，得到吉普最优行驶策略是一个有挑战性的问题.

关键词: 吉普问题, 容量, 容器约束, 单向行驶, 往返行驶

Abstract:

Jeep problems with and without container restriction are studied. Optimal strategies of problems without container restriction are obtained for one-way and round trip. Strategies of jeep problems with container restriction are also given for one-way trip and round trip respectively, from which we prove that jeep with container restriction can travel any distance if enough fuel is available. To get optimal strategy of jeep problems with container restriction is a challenging task.

Key words: Jeep problem, Capacity, Container restriction, One-way trip, Round trip

中图分类号:

O221

程序,丁义明,华香颖. 容器约束的吉普问题[J]. 数学物理学报, 2019, 39(2): 348-357.

Xu Cheng,Yiming Ding,Xiangying Hua. Jeep Problems with Container Restriction[J]. Acta mathematica scientia,Series A, 2019, 39(2): 348-357.

图/表 1

参考文献 9

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燃料数量	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
单向无约束行驶距离	1.00	2.00	2.33	2.67	2.87	3.07	3.21	3.35	3.46	3.57	3.67	3.76	3.83	3.91	3.98	4.04	4.10	4.16	4.21	4.27
单向有约束行驶距离	1.00	2.00	2.33	2.67	2.81	2.95	3.10	3.24	3.30	3.37	3.44	3.50	3.57	3.64	3.70	3.77	3.80	3.84	3.87	3.90
往返无约束行驶距离	0.50	1.00	1.25	1.50	1.67	1.83	1.96	2.08	2.18	2.28	2.37	2.45	2.52	2.59	2.66	2.72	2.77	2.83	2.88	2.93
往返有约束行驶距离	0.50	1.00	1.25	1.50	1.63	1.75	1.88	2.00	2.06	2.13	2.19	2.25	2.31	2.38	2.44	2.50	2.53	2.56	2.59	2.63

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