Elementary solution to the jeep problem with one chief and two supporting vehicles

摘要

The jeep problem is a well known logistics problem. A jeep must cross a desert wider than it can travel on one tank of fuel with the help of optimal arrangement of fuel dumps along the route. The available resources refer, especially, to solutions of two basic variants - the single jeep problem and the convoy of jeeps problem. This contribution deals with one modification of the jeep problem with 3 vehicles and n cans of fuel (n > 3). Elementary solutions to this modification are detailed derived for small amounts n of cans of fuel. General solution to this problem using harmonic numbers is also stated. Numerical solutions for some of the outstanding amounts of fuel and units of distance, computed by the programming language of the computer algebra system Maple, are presented, too.