Jeep problem is a kind of model of logistics in extreme situation, which has application in exploration and aircraft problems. The optimal distance and driving strategy of multiple jeeps problem are known. We consider multiple jeeps problem with container restriction, which is more complicated in the proof of feasibility and optimality of a driving strategy. We investigate when it can achieve the same optimal distance as without restriction. Based on the non-restricted optimal distance, a new driving strategy is proposed. We provide the necessary and sufficient condition to ensure the feasibility of the strategy, and obtain the maximal feasible distance.
Xiangying HUA
. MULTIPLE JEEPS PROBLEM WITH CONTAINER RESTRICTION[J]. Acta mathematica scientia, Series B, 2020
, 40(1)
: 75
-89
.
DOI: 10.1007/s10473-020-0106-z
[1] Alway G G. Crossing the desert. The Mathematical Gazette, 1957, 41(337):209
[2] Chen W, Ding Y, Fan W. Optimal logistics for multiple jeeps. Acta Mathematica Scientia, 2010, 30B(5):1429-1439
[3] Cheng X, Ding Y, Hua X. Jeep problems with container restriction. Acta Mathematica Scientia, 2019, 39A(2):348-357
[4] Dewdney A K. Computer recreations. Scientific American, 1987:128-131
[5] Ding Y, Fan W. The optimal sequence of jeep problem. Engineering-Theory and Practice, 2000, 20(2):97-103
[6] Fan W, Ding Y. The jeep-fuel station problem. Acta Math Sci, 2000, 20A(1):85-94
[7] Fine N J. The jeep problem. American Mathematical Monthly, 1947, 54(1):24-31
[8] Franklin J. The range of a fleet of aircraft. Journal of the Society for Industrial and Applied Mathematics, 1960, 8(3):541-548
[9] Gale D. The jeep once more or jeeper by the dozen. American Mathematical Monthly, 1970, 77(5):493-501
[10] Hausrath A, Jackson B, Mitchem J, Schmeichel E. Gale's round-trip jeep problem. American Mathematical Monthly, 1995, 102(4):299-309
[11] Jackson B, Mitchem J, Schmeichel E. A solution to dewdney's jeep problem//Proc 7th International Conference in Graph Theory, Combinatorics, Algorithms and Application, 1992
[12] Kuwata T, Maehara H. Another exploration problem. Discrete Mathematics, 2016, 339(5):1543-1550
[13] Lantz B. Where should captain scott's support parties have turned back? Polar Record, 2018, 54(1):76-78
[14] Oberschelp W. Alcuin's camel and the jeep problem. Charlemagne and His Heritage. 1200 Years of Civilization and Science in Europe, 1998, 2:411-422
[15] Phipps C G. The jeep problem:A more general solution. American Mathematical Monthly, 1947, 54(8):458-462
[16] Yu F, Cui J. Research on the efficient computation mechanism-in the case of n-vehicle exploration problem. Acta Mathematicae Applicatae Sinica, English Series, 2018, 34(3):645-657
