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After the earthquake, it is important to ensure the emergency supplies are provided in time. However, not only the timeliness, but also the fairness from different perspectives should be considered. Therefore, we use a multilevel location-routing problem (LPR) to study the fairness of distribution for emergency supplies after earthquake. By comprehensively considering the time window constraints, the partial road damage and dynamic recovery in emergency logistics network, the stochastic driving time of the vehicle, and the mixed load of a variety of emergency materials, we have developed a multiobjective model for the LRP in postearthquake multimodal and fair delivery of multivariety emergency supplies with a limited period. The goal of this model is to minimize the total time in delivering emergency supplies and to minimize the maximum waiting time for emergency supplies to reach demand points. A hybrid heuristic algorithm is designed to solve the model. The example shows that this algorithm has a high efficiency and can effectively realize the supply of emergency supplies after the earthquake within the specified period. This method might be particularly suitable for the emergency rescue scenarios where the victims of the earthquake are vulnerable to mood swings and the emergency supplies need to be fairly distributed.

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Structure radio beams with diverse radiation patterns exhibit huge potentials in many applications. In this paper, we propose a plane spiral orbital angular momentum (PS-OAM) based structure radio beam construction scheme, in which several PS-OAM waves are superposed together to acquire the anticipated radiation pattern and phase distribution in azimuthal domain. Firstly, some typical shapes of the radiation patterns are demonstrated. Then, the properties of this kind of structure radio beam, for example diversity, periodicity, vorticity and directional gain are analysed in detail from mathematical analysis and simulation verification. Finally, a proof of principle experiment is carried out at 10 GHz using a multi PS-OAM antenna to further testify the feasibility of the structure radio beam construction. The interesting properties provided by structure radio beams would offer promising solutions to radar imaging, smart antenna, massive multiple input multiple output (MIMO) and spatial modulation multiple input multiple output (SM-MIMO). INDEX TERMS Structure radio beam, radiation pattern, orbital angular momentum, diversity, vorticity. I. INTRODUCTION