DECISION SCIENCES AND INFORMATION MANAGEMENT

Speaker: Daniel Garcia Rasines (Imperial College London, UK) Title: Randomized selective inference In contemporary statistical applications, selection of the formal inferential problem is typically done after some level of interaction with the data. Usually, an initial exploratory analysis is used to identify interesting aspects of the population under study, and then the same dataset is used to learn about them. Such “data snooping” invalidates classical inferential procedures. Many approaches have been proposed to ensure inferential validity in these settings. In this talk, I will present an alternative to data splitting based on randomization which allows for higher selection and inferential power. I will describe the theoretical and empirical advantages of this method and discuss some related problems of current interest.

Title: The Dial-a-Ride Problem with Limited Pickups per Trip The Dial-a-Ride Problem (DARP) is an optimization problem that involves determining optimal routes and schedules for several vehicles to pick up and deliver items at minimum cost. Motivated by real-world carpooling and crowdshipping scenarios, we introduce an additional constraint imposing a maximum number L on the number of pickups per trip. This results in two new variants of the DARP, namely the Multi-vehicle Dial-a-Ride Problem with Limited Pickups per Trip (DARP-LPT) and the Dial-a-Ride Problem with Limited Pickups per Trip (DARP-LPT). In MDARP-LPT, vehicles have unique origins and destinations, while in DARP-LPT, all vehicles share a single fixed depot. We apply a unified fragment-based method to address both problems, where a fragment is a partial path. Specifically, we extend two formulations from Rist and Forbes (2021): the Fragment Flow Formulation (FFF) and the Fragment Assignment Formulation (FAF). Our polyhedral analysis establishes FFF's superiority over FAF, a conclusion further validated by computational experiments. Furthermore, our results show that FFF and FAF significantly outperform traditional arc-based formulations in terms of solution quality and time. Regarding the inputs of fragment-based formulations, Alyasiry et al. (2019) propose the full fragment set SFF with longer partial paths, while Rist and Forbes (2021) introduce the restricted fragment set SRF with shorter partial paths. We contribute two new fragment sets: the path-enumerated full fragment set SPFF, generated by enumerating paths and decomposing them into full fragments, and the mixed fragment set SMF, which decomposes a portion of SFF into restricted fragments while preserving the rest. Subsequently, we assess the computational performance of different fragment sets using the formulation FFF. The results show that in MDARP-LPT with a lower value of $L$, SPFF outperforms SFF, and SFF performs better than SRF. Additionally, for DARP-LPT, SMF surpasses both SRF and SFF in computational performance when instances have more flexible time windows and a higher value of L. In meeting room or online via Teams (Meeting ID: 332 688 469 52 Passcode: JZ9nSB)

Fairness through randomization: an operations research perspective