To realize the benefits of network connectivity in transfer-based transit networks, it is critical to minimize transfer disutility for passengers by synchronizing timetables of intersecting routes. Nonetheless, in real-world practice, transit agencies commonly build timetables without accounting adequately for stochastic operations and with slight or no consideration of synchronization among intersecting routes at transfer nodes. Given the significance of transfers for many transit users, it is imperative to develop seamlessly synchronized timetables that account for the stochastic nature of transit operations. In this research, we investigate the stochastic transfer synchronization problem, which seeks to synchronize the timetables of different routes in a transit network to reduce transfer waiting times, delay times, and unnecessary in-vehicle times. We present a sophisticated two-stage stochastic mixed-integer programming model that takes into account variability in passenger walking times between bus stops, bus running times, dwell times, and demand uncertainty. Our model incorporates new features related to dwell time determination by considering passenger arrival patterns at bus stops which have been neglected in the literature on transfer synchronization and timetabling. We solve a sample average approximation of our model using a problem-based scenario reduction approach, and the progressive hedging algorithm. As a proof of concept, our computational experiments on two single transfer nodes in the City of Toronto, with a mixture of low- and high-frequency routes, demonstrate the potential advantages of the proposed model. Our findings highlight the necessity and value of incorporating stochasticity in transfer-based timetabling models.

Radical cuts in emissions typically involves the integration of multiple energy carriers in the energy system, putting additional strain on energy system modelling tools and practitioners. The modelling framework JuMP developed for mathematical optimization in Julia offers great speed and flexibility in combining multiple modules/packages.

EnergyModelsX is a framework for energy systems modelling that is designed to be easy to extend, e.g. with more detailed technology descriptions for certain analyses. PiecewiseAffineApprox is a package to simplify finding good linear approximations from e.g. more detailed dynamical simulation models which may be used to define MILP formulations from non-linear models.

We illustrate how EnergyModelsX and PiecewiseAffineApprox can be used together on a use case from the Arctic. The first use case in the ZEESA project concerns reducing emissions at Isfjord Radio at Svalbard, a remote location in the Arctic. The energy system there includes existing renewable energy from solar, and potentially generation from wind turbines. The model includes use of surplus heat from existing diesel generators or potentially hydrogen technologies such as electrolysers and fuel cells. To improve the quality of the results, the standard EnergyModelsX model will be extended with more detailed description of e.g. electrolyser efficiency operating at different loads and more detailed description of available heat at given operating temperatures.

Integrating electric vehicle (EV) and robot-based parcel delivery alongside pick-up points, known as parcel lockers (PL), could benefit from the EV's efficiency, the robot's maneuverability, and the PL's flexibility. Parcels are loaded onto EVs, equipped with robots at the central depot. These vehicles then distribute parcels directly to customers (EV-based home-delivery service) or PLs for customer collection (self-collection service). Additionally, EVs may make stops at designated points, typically parking sites, to deploy robots that deliver packages to nearby customers (robot-based home-delivery service). Afterward, the robots return to the same EV to retrieve another package or recharge their batteries, employing the "dispatch-wait-collect" tactic. Due to its theoretical complexities, this multi-modal delivery system has yet to be addressed in the literature. The introduced parcel delivery approach is called the Electric Vehicle Routing Problem with Robots, Parcel Lockers, and Time Windows (EVRP-RPLTW). It minimizes the EV route and usage costs, the route cost of robots, and the utilization cost of PLs while satisfying the EVs and robots' cargo load and battery capacities, the PL's accommodation capacity and coverage range, and customers’ (hard) time window constraints. A novel mixed-integer linear programming (MIP) model is proposed for EVRP-RPLTW to study and analyze the optimal solution of the problem under various scenarios. Several valid inequalities are proposed to strengthen the MIP model, and the sensitivity of the problem's parameters is analyzed. The computational results show the superiority of the introduced approach over the EVRP-TW, and some managerial insights are also presented.

Bicycle sharing systems (BSS) are vital to urban transportation networks, presenting complex optimization challenges. One such challenge is managing service levels for large-scale BSS, where the aim is to strategically redistribute bicycles across stations to anticipate fluctuating demand for origin-destination trips. While numerous studies tackle this issue, none, to our knowledge, have effectively handled real-life-sized BSS comprising thousands of stations, tens of thousands of bicycles, and hundreds of thousands of daily trips.
We propose a two-step approach. First, we determine next morning service requirements by formulating and solving stochastic programs to compute the bicycle quantities at each station. Second, we design vehicle routes to satisfy as many of these bicycle quantities as possible.
Computational experiments utilize data from major BSS in Boston, Montréal, New York, and Washington D.C. Our results demonstrate efficient problem-solving with solutions closely approaching optimality. Additionally, we offer managerial insights into bicycle and station usage within BSS, facilitating better operational strategies.