In the event of a widespread power outage due to a disaster, telecom companies will run a backup power supply in the telecom buildings to maintain services. Since the amount of reserve power decreases with time, each building needs to replenish power from a power supply vehicle. To minimize the impact on telecommunication services during power outages, the time of power failure in telecommunication buildings must be minimized. The optimal route of the power supply vehicle is the one that ensures the shortest possible outage time at the affected buildings. Since delays must be compared per building, the problem of searching for this route is difficult to represent as a standard vehicle routing problem. Instead, this paper introduces the Bottleneck Vehicle Routing Problem, which asks for a route plan that minimizes the maximum damage caused by the outage of power. A branch-and-bound method for the single-vehicle case and a column generation method for the multiple-vehicle case are presented. These methods are shown to be effective through numerical experiments.

In this study, we consider the real-world problem of assigning students to classes, where each student has a preference list, ranking a subset of classes in order of preference. We use existing successful approaches to contribute the work of Gunma University; however, in practice, one method does not always yield the best results, and new concepts and adjustments are required to find improved results depending on real instances in the field. Thus, we propose minimax-rank constrained maximum-utility matchings and a compromise between maximum-utility matchings and fair matchings, where a matching is said to be fair if it lexicographically minimizes the number of students assigned to classes not included in their choices, that assigned to their last choices, that assigned to their penultimate choices, and so on. In addition, we compare our methods with the Boston mechanism and the deferred acceptance mechanism. We also observe the potential inefficiency of the student proposing deferred acceptance mechanism with single tie-breaking, which is a hot topic in the literature on the school choice problem.