A distributionally robust optimisation model for last mile relief network under mixed transport

The last mile relief network is the final stage of the relief chain but the most critical stage for ensuring the timely delivery of relief supplies after a disaster. Due to the suddenness of the disaster, balancing the shortages of relief supplies and the high demands of victims is a serious problem. We introduce a mixed transport way of relief supply transportation between points of distributions and demand nodes in our problem to face the manpower and resource limitations. We establish a bi-objective distributionally robust optimisation model to balance transportation time and transportation safety, where the demand, transportation time, freight and safety coefficient are assumed to be uncertain variables with partial distribution information. We also deduce the refinement robust counterparts under the ambiguous sets to prove the safe tractable approximations of chance constraints. Finally, we conduct a case study of Tonghai county earthquake to illustrate the efficiency of our proposed distributionally robust model.