Jing Liang, Zhuowen Li, Peiwei Zhang
Abstract: Schools deliver lunch for students, especially students who cannot shortly leave campus, as an urgent response to restaurants and business lockdowns during COVID-19. Unlike traditional traveling problems, we consider the special circumstance that school is the only supplier during the COVID-19 period and ethically help students. In this report, we discuss and answer: (1) the data and assumption we used for University of Michigan during the COVID-19; (2) the model and the constraints we concerned for the lunch delivery problem during the COVID-19; (3) the numerical results and the shortest paths.
Xiaoyi Qu, Yansheng Xiong, Chengdong Zhang
Abstract: We study a vehicle routing problem with time window intervals (VRPTW) as schools deliver lunches to students who study from home during a lockdown due to a pandemic. We first consider a Mixed Integer Linear Programming (MILP) formulation for the VRPTW. Computational results on the MILP shows that the proposed MILP indicates correlation exists between the minimum number of vehicles required and the width of time window intervals desired when regional data is utilized. Additionally, in-depth analysis on the running times of the solver with various objective functions reveals that for similar results, succinct objective functions require much less solver runtime. Thus, we recommend succinct objective functions when running time is limited in specific problems. Lastly, we provide readers with a multi-period MILP model to better simulate the real-world situations, aiming to provide more realistic results.
Mark Bobrovnikov
Abstract: The problem I pursue to solve seeks to minimize the overall student waiting time for their lunch, which is the difference between the preferred eating time of the student and the delivery time of their lunch. The optimal solution will have the lowest total waiting time, which will indicate that the average student will not have to wait too long for their lunch to arrive. The solution will be presented as a table of student IDs, indicating the path that each vehicle will need to take to achieve the lowest waiting times.