Multiple Jeeps Problem With Container Restriction

Jeep problem is a mathematical model relates to logistics in extreme situa-tion,which has wide application in problems like exploration and aircraft prob-lems and interests many researchers.The optimal distance and driving strategy of multiple jeeps problem are known.This paper considers multiple jeeps problem with container restriction by extending the multiple jeeps problem to jeeps with multiple load.This paper extends the multiple jeeps problem to jeeps with multiple load at first and gives its optimal solution.The way to prove the optimality of the solution is to show that this solution is an upper bound of all feasible solution,and that this solution can be realized by a driving strategy,which means that this solution is the optimal one.The dual problem of multiple jeeps problem with multiple load is also discussed in this paper.It is shown that maximizing the travel distance and minimizing the consumed fuel are equivalent.Since it is complicated in the proof of the feasibility and optimality of a driving strategy,giving the optimal solution of multiple jeeps problem with con-tainer restriction directly is difficult.This paper takes another way to approach the problem.The optimal solution of problem without restriction must be the optimal solution of problem with restriction if it is feasible under restriction,since the optimal solution under restriction will not exceed it without restriction.This paper shows that with restriction,the part of travel that nearest to the destina-tion can reach the optimal solution of problem without restriction by an existing driving strategy,and the part of travel that relatively near to the destination can also reach it by Strategy C that introduced by this paper.For other parts of the travel,this paper proposed a driving strategy called Strategy H to help them reach the optimal solution of problem without restriction.In this paper,the necessary and sufficient condition to ensure the feasibility of Strategy H is obtained.The maximal feasible distance of Strategy H is also given in this paper.When dealingl with the effect that container restriction has on drivingl strat-egy,this paper gives a necessary and sufficient condition that container restriction affects a driving strategy.The Strategy H for multiple jeeps problem proposed in this paper is flexible,which offers more options when solving applied problems These conclusions about multiple jeeps problem are the basis of later works,and offer gist for the constructing of strategies in many practical problems.