Acta mathematica scientia, Series B >
OPTIMAL LOGISTICS FOR MULTIPLE JEEPS
Received date: 2009-04-24
Revised date: 2010-01-31
Online published: 2010-09-20
Supported by
This work is partially Supported by National Natural Science Foundation of China (70571079, 60534080) and China Postdoctoral Science Foundation (20100471140).
We consider variations of the classical jeep problems: the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented.
Key words： jeep problem; logistics; dynamic program principle
CHEN Wen-Lei , DING Yi-Ming , FAN Wen-Tao . OPTIMAL LOGISTICS FOR MULTIPLE JEEPS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1429 -1439 . DOI: 10.1016/S0252-9602(10)60135-X
[1] Always G C. Crossing the desert. Math Gazette, 1957, 41: 209
[2] Bellman R E. Dynamic Programming. Princeton University Press, 1957
[3] Ding Yiming, Fan Wentao. The optimal sequence of jeep problem. Systems Engineering-Theory and Practice, 2000, (2): 97--103
[4] Ding Yiming, Fan Wentao. The jeep-fuel station problems. Acta Mathematica Scientia, 2000, 20(1): 85--94
[5] Fine N J. The jeep problem. Amer Math Monthly, 1947, 54: 24--31
[6] Gale D. The jeep once more or jeep by the dozen. Amer Math Monthly, 1970, 77: 493--501
[7] Hausrath A, Jachson B, Mitchem J, Schmeichel E. Gale's round-trip jeep problem. Amer Math Monthly, 1995, 105: 299--309
[8] Phipps C G. The jeep problem, a more general solution. Amer Math Monthly, 1947, 54: 458--462
[9] Li Xiaoya, Cui Jinchuan. Efficient algorithm for kind of exploration problem with N vehicles. Journal of Systems Engineering, 2008, 23(4): 444--448
[10] Przemyslaw Klesk. The jeep problem, searching for the best strategy with a genetic algorithm. Information Processing and Security Systems, 2005: 453--464
/
| 〈 |
|
〉 |