An ode to Phipps' jeep convoys

TL;DR

This paper refines Phipps' convoy approach to the jeep problem, extending it to more general scenarios including single jeeps and Maddex's variant, providing new solutions and insights.

Contribution

It advances the convoy method for the jeep problem, offering a more general framework and solutions for various jeep convoy configurations.

Findings

Refined Phipps' convoy approach for the jeep problem.

Extended solutions to single jeep and Maddex's jeep problem.

Unified framework for different jeep convoy variants.

Abstract

The jeep problem was first solved by O. Helmer and N.J. Fine. But not much later, C.G. Phipps formulated a more general solution. He formulated a so-called convoy or caravan variant of the jeep problem and reduced the original problem to it. We shall refine the convoy idea of Phipps and subsequently view a more general jeep problem, which we solve for jeep convoys as well as for a single jeep. In the last section we solve Maddex' jeep problem.