The distribution of emergency perishable materials after a disaster, such as an earthquake, is an essential part of emergency resource dispatching. However, the traditional single-period distribution model can hardly solve this problem because of incomplete demand information for emergency perishable materials in affected sites. Therefore, for such problems we firstly construct a multi-period vehicle path distribution optimization model with the dual objectives of minimizing the cost penalty of distribution delay and the total corruption during delivery, and minimizing the total amount of demand that is not met, by applying the interval boundary and most likely value weighting method to make uncertain demand clear. Then, we formulate the differential evolutionary whale optimization algorithm (DE-WOA) combing the differential evolutionary algorithm with the whale algorithm to solve the constructed model, which is an up-and-coming algorithm for solving this type of problem. Finally, to validate the feasibility and practicality of the proposed model and the novel algorithm, a comparison between the proposed model and the standard whale optimization algorithm is performed on a numerical instance. The result indicates the proposed model converges faster and the overall optimization effect is improved by 23%, which further verifies that the improved whale optimization algorithm has better performance.

In this study, an effective travel cost (ETC) traffic equilibrium model is proposed for multi-modal networks with uncertain demands. The multi-modal networks are transformed into supernetworks and travel demands are assumed to be closed intervals. Passenger flows and travel costs are also formulated as closed intervals to capture the effects of uncertain demands. The ETC concept is introduced and regarded as a choice criterion to develop an equilibrium model which captures travellers’ travel mode and route choice behavior under interval travel costs. The model is formulated as a variational inequality problem, and the method of successive average algorithm is adapted to interval mathematics to obtain the results in the form of interval variables. Illustrative examples are also presented to demonstrate the model’s characteristics and its differences from the traditional equilibrium model, in which the expected travel cost is regarded as the choice criterion.

The distribution of emergency perishable materials is crucial for rescue operations in disaster-stricken areas. However, the freshness of these materials changes over time, affecting the quantity of materials that can be distributed to demand points at different stages. To address this issue, this paper proposes a novel approach. Firstly, a piecewise function is constructed to describe the impact of freshness on the quality and quantity of emergency perishable materials at different time stages. Secondly, the paper establishes a vehicle distribution optimization model with the goal of maximizing the sum of the freshness of all emergency perishable materials delivered to different disaster-affected locations, taking into account the different minimum freshness constraints for the same kind of materials in different locations. Thirdly, an approximate algorithm is designed to solve the model, with the time complexity and the upper and lower bounds of the approximate ratio analyzed. Finally, an example analysis is conducted to demonstrate the validity of the proposed model and algorithm.

Post-disaster emergency perishable material distribution is an essential part of emergency relief, which is of great significance to reducing disaster losses and casualties and improving rescue efficiency. However, in actual rescue, the demand information of disaster sites is often complex to determine, and the demand for emergency perishable materials needs to be clarified. Therefore, the single-cycle distribution makes it difficult to meet the demand for emergency perishable materials at disaster sites. To effectively improve the efficiency of emergency relief, this paper constructs a distribution optimization model with a multi-cycle vehicle path and the dual objectives of minimizing the distribution delay penalty and corruption cost and minimizing the unsatisfied demand. Initially, the fuzzy demand is addressed through the application of triangular fuzzy numbers and the most probable value weighting method. Following this, a two-stage optimization algorithm is devised by integrating the K-means++ algorithm with an enhanced Differential Evolutionary Whale Optimization Algorithm (DE-WOA). This algorithm operates by first clustering the affected points and subsequently solving the multi-objective model, thereby providing a robust methodology and strategic recommendations for the distribution of perishable materials across diverse scenarios. Our study reveals that the multi-objective model developed in this paper exhibits remarkable operability and practicality in the distribution of post-disaster emergency perishable materials, as evidenced by the verification via numerical examples. Through a comparison with the single-stage whale optimization algorithm, it is evident that the enhanced two-stage differential evolutionary whale optimization algorithm not only demonstrates a substantially faster convergence rate and a superior solution quality but also proves to be more suitably adapted to the proposed model. Significantly, the overall optimization performance has been augmented by 33%, thereby providing further substantiation of the efficacy of the designed improved algorithm.