Optimization Models for Pickup-And-Delivery Problems with Reconfigurable Capacities

When a transportation service accommodates both people and goods, operators sometimes opt for vehicles that can be dynamically reconfigured for different demands. Motivated by air service in remote communities in Canada’s north, we define a pickup-and-delivery problem in which aircraft can add or remove seats during a multi-stop trip to accommodate varying demands. Given the demand for people and cargo as well as a seat inventory at each location, the problem consists in finding a tour that picks up and delivers all demand while potentially reconfiguring the vehicle capacity at each location by adding or removing seats. We develop a total of six models using three different approaches: constraint programming, mixed integer programming, and domain-independent dynamic programming. Our numerical experiments indicate that domain-independent dynamic programming is able to substantially outperform the other technologies on both solution quality and run-time on a set of randomly generated instances spanning the size of real problems in northern Canada.