We consider variations of the classical jeep problems:the optimal logistics for a caravan of jeeps which travel together in the desert.The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination.Based on the dynamic program principle,the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained.Some related results such as the efficiency of the abandoned jeeps,and the advantages of more jeeps in the caravan are also presented.
A generalized Bak-Sneppen model (BS model) of biological evolution with interaction strength θ is introduced in d-dimensional space, where the 'nearest neighbors' are chosen among the 2d neighbors of the extremal site, with the probabilities related to the sizes of the fitnesses. Simulations of one- and two-dimensional models are given. For given θ > 0, the model can self-organize to a critical state, and the critical threshold fc(θ) decreases as θ increases. The exact gap equation depending on θ is presented, which reduces to the gap equation of BS model as θ tends to infinity. An exact equation for the critical exponent γ(θ) is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model.
