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The range of a fleet of aircraft

Franklin, J. N. (1960) The range of a fleet of aircraft. Journal of the Society for Industrial and Applied Mathematics, 8 (3). pp. 541-548. ISSN 0368-4245. http://resolver.caltech.edu/CaltechAUTHORS:FRAjsiam60

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Abstract

The problem discussed in this paper is to determine the range of a fleet of n aircraft with fuel capacities g gallons and fuel efficiencies ri gallons per mile (i= 1,..., n). It is assumed that the aircraft may share fuel in flight and that any of the aircraft may be abandoned at any stage. The range is defined to be the greatest distance which can be attained in this way. Initially the fleet is supposed to have g gallons of fuel. A theoretical solution is obtained by the method which Richard Bellman [1] calls dynamic programming. Explicit solutions are obtained in the case of two aircraft with different fuel capacities and fuel efficiencies and in the case of any number of aircraft with identical fuel capacities and identical fuel efficiencies. The problem is similar to the so-called jeep problem. The jeep problem was solved rigorously by N. J. Fine [2]. A solution was also obtained by O. Helmer [3, 4]. Fine cited an unpublished solution by L. Alaoglu. The problem was generalized by C. G. Phipps [5]. Phipps informally developed the special result which is deduced in [section] 4 of this paper.


Item Type:Article
Additional Information:©1960 Society for Industrial and Applied Mathematics Received by the editors August 20, 1959 and in revised form March 17, 1960.
Record Number:CaltechAUTHORS:FRAjsiam60
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:FRAjsiam60
Alternative URL:http://dx.doi.org/10.1137/0108039
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4867
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:11 Sep 2006
Last Modified:26 Dec 2012 09:02

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