Optimizing the distribution of perishable emergency materials in the aftermath of sudden disasters holds significant theoretical and practical value. This paper begins by defining the freshness of perishable emergency materials and develops a continuous piecewise function to describe the changes in quality and quantity of these materials at different time stages. Additionally, it considers distinct delivery requirements for each demand point regarding the same perishable emergency materials. Under the minimum freshness constraint, a vehicle distribution optimization model is established for perishable emergency materials, considering multiple distribution centers and multiple vehicles. Depending on whether the distribution center has an adequate number of vehicles, the solution can be classified into three scenarios. In the case of insufficient total emergency supplies but sufficient vehicles, an accurate algorithm is designed to address the model. Alternatively, when both the total emergency supplies and vehicles are insufficient, an approximate algorithm is developed to solve the model. Finally, when the total quantity of perishable emergency materials is inadequate, and some vehicles are sufficient while others are not, the problem is transformed into one of the first two situations to find a solution. To validate the accuracy of the model and the effectiveness of the algorithm, an analysis is conducted using the flood-stricken area in Shouguang, Shandong as a case study.

Today, distributing high quality perishable foods is one of the challenging issues in food industry. This paper introduces a deterministic vehicle routing problem model with multiple middle depots and proposes the freshness of perishable foods as a new concept to obtain optimal delivery routes. For the proposed mathematical model, profit maximization of delivering the product, minimization of the transportation costs and vehicle traveling time, and maximum level of delivered product perishability (loss of freshness) are considered. GAMS software is implemented to show the authority of the model. Furthermore, genetic algorithm (GA) has been developed to solve the model for large size instances. Several problems are tested in order to compare the exact and the GA solutions.