In this paper, we develop a distributionally robust optimization model for the design of rail transit tactical planning strategies and disruption tolerance enhancement under downtime uncertainty. First, a novel performance function evaluating the rail transit disruption tolerance is proposed. Specifically, the performance function maximizes the worst-case expected downtime that can be tolerated by rail transit networks over a family of probability distributions of random disruption events given a threshold commuter outflow. This tolerance function is then applied to an optimization problem for the planning design of platform downtime protection and bus-bridging services given budget constraints. In particular, our implementation of platform downtime protection strategy relaxes standard assumptions of robust protection made in network fortification and interdiction literature. The resulting optimization problem can be regarded as a special variation of a two-stage distributionally robust optimization model. In order to achieve computational tractability, optimality conditions of the model are identified. This allows us to obtain a linear mixed-integer reformulation that can be solved efficiently by solvers like CPLEX. Finally, we show some insightful results based on the core part of Singapore Mass Rapid Transit Network.

In this paper, we consider the optimal meeting scheduling problem in a commercial building over a fixed period of time, with the objectives of minimizing the cost of energy consumption by the air-conditioning system and possibly achieving more balanced power distribution. By considering a set of realistic factors, including the eligible time slots of attendees and energy consumption characteristics of meeting rooms, this problem is formulated as a constrained mixed-integer linear program, which then can be solved by an optimization solver, e.g., CPLEX. However, because the computation complexity increases dramatically with the problem size, a fast heuristic algorithm is proposed. The numerical simulations verify that the heuristic algorithm produces a near-optimal result.