Jeep Problem - Problem

Problem

There are n units of fuel stored at a fixed base. The jeep can carry at most 1 unit of fuel at any time, and can travel 1 unit of distance on 1 unit of fuel (the jeep's fuel consumption is assumed to be constant). At any point in a trip the jeep may leave any amount of fuel that it is carrying at a fuel dump, or may collect any amount of fuel that was left at a fuel dump on a previous trip, as long as its fuel load never exceeds 1 unit. There are two variants of the problem:

  • Exploring the desert – the jeep must return to the base at the end of every trip.
  • Crossing the desert – the jeep must return to the base at the end of every trip except for the final trip, when the jeep travels as far as it can before running out of fuel.

In either case the objective is to maximise the distance travelled by the jeep on its final trip. Alternatively, the objective may be to find the least amount of fuel required to produce a final trip of a given distance.

In the classic problem the fuel in the jeep and at fuel dumps is treated as a continuous quantity. More complex variations on the problem have been proposed in which the fuel can only be left or collected in discrete amounts.

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