Régimen de Modificaciones

The availability of data and the complexity of the systems make shared vehicle systems an attractive application for operations research. Though this is recog- nized by the many papers published over the last five years (cf. Sections 2 and

9.1), the impact on practice seems limited. In fact, a study by de Chardon et al. [2016] found that in the space of bike-sharing, operators did not use optimization to support their decision-making. Even worse, the study states that

[..] New York City is the sole operator we know using custom soft- ware forecasting station demand and trip flows [..].

Many of the contributions in Part I overcome this limitation, as they have had impact on the bike-sharing systems operated by Motivate International (incl. New York City, Boston, San Francisco, and others). We summarize these industry implementations at the end of Part I, in Chapter 8.

On availability of data. Most of the data we relied on is publicly available. The demand-rates used to compute the inventory model in Part I are based on historic ridership-data and a live-feed of the number of bikes at each station.2 _The

observed real impact in Section 6.4 also rely on the latter. The data underlying the pilots conducted for overnight rebalancing (cf. Section 6.2) as well as the data underlying the Bike Angels analysis (cf. Section 5) are proprietary to NYCBS.

Part I

Inventory Models in Bike-Sharing

Systems

CHAPTER 2

RELATED WORK

”We’re meant to keep doing better. We’re meant to keep discussing and debating and we’re meant to read books by great historical schol- ars and then talk about them” — J. Breckenridge

Over the past decade bike-sharing has become a prominent research topic within areas such as data mining, machine learning, and optimization. In this chapter, we provide an extensive literature review of this research area. We begin by summarizing the literature on routing for rebalancing, then discuss existing work on forecasting in bike-sharing systems, and finally describe related work on the design of bike-sharing systems.

2.1

Routing

Much of the research on bike-sharing systems has focused on optimizing the routes of rebalancing trucks employed by system operators. A particularly influential paper in this context is Raviv and Kolka [2013] who define a user dissatisfaction function to measure the number of out-of-stock events at an individual station as a function of the number of bikes at the station. Different ways of computing this cost function have been suggested by Schuijbroek et al. [2017], O’Mahony et al. [2016], and Parikh and Ukkusuri [2014]. Subsequent work by Raviv et al. [2013] defined a routing problem based on the user dissatisfaction function: at first, a time bound is given in which trucks can be routed to move bikes within the system; thereafter, no more decisions are made, and the objective

is given by the expected number of out-of-stock events, given the configuration of bikes resulting from the trucks’ rebalancing. Such routing problems, and attempts to solve them to optimality for larger and larger instances, were further investigated by Forma et al. [2015], Ho and Szeto [2014], and Szeto et al. [2016], among others. Parts of our work in Section 6 are very much related to those papers. Similarly, a line of work, starting with Rainer-Harbach et al. [2013] and followed by Raidl et al. [2013] and Kloim ¨ullner et al. [2014] investigated greedy strategies for the rebalancing problem, though they considered a slight variation (i.e., a fluid version) of the user dissatisfaction function. The work by Kloim ¨ullner et al. [2014] stands out in that regard in that it also applies to the dynamic case, in which unsatisfied demand also occurs during the rebalancing process. An orthogonal approach to rebalancing has been taken by Shu et al. [2013], O’Mahony et al. [2016], and Jian and Henderson [2015]; all of these papers aim to find the optimal configuration of bikes at the beginning of some period. Shu et al. [2013] assume complete knowledge of the future and solve a flow problem; O’Mahony et al. [2016] employs the user dissatisfaction function; Jian and Henderson [2015] use a simulation-optimization based approach to capture network effects. In these three versions, limited means for rebalancing (and thus, the routing aspect of the problem) are disregarded since the focus is solely on the optimal allocation of bikes. Contardo et al. [2012], Vogel et al. [2014], and Nair et al. [2013] are similar to Shu et al. [2013] in that they solve particular flow problems rather than routing problems. Nair et al. [2013] aims to obtain certain service levels with at least some probability. Vogel et al. [2014] presents an NP-hard flow model that also takes into consideration a rebalancing cost. All of these assume that not only the rate of rentals and returns at each station is known, but also the routing probability of each customer, i.e., the probability

of a customer at a given station having a particular destination. An approach similar to that of Jian and Henderson [2015] was pursued by Datner et al. [2017], in which they also account for the cost of longer travel times due to out-of-stock events rather than minimizing only the number of out-of-stock events.

A disjoint line of work has focused on minimizing the length of the route of a single capacitated truck, or the combined length of routes for a fleet of such trucks, that needs to visit nodes with given demand and supply. The paper by Benchimol et al. [2011] is an early example of such work. They give an approximation algorithm, a hardness result, and a polynomial-time algorithm for instances, wherein the underlying graph is a tree. The same problem has been studied by Chemla et al. [2013] and Dell’Amico et al. [2014] from a mixed- integer programming perspective. Further works in the same spirit have been pursued by Erdo ˘gan et al. [2014], Erdo ˘gan et al. [2015], and Bulh ˜oes et al. [2018]. Interestingly, Di Gaspero et al. [2013], in a sense, combines the approaches of maximizing impact and minimizing travel time: given fixed targets for each station, the authors aim to minimize a weighted combination of travel time and absolute value distance (summed over all stations) between the targeted bike allocation and the one resulting from rebalancing.

Some recent papers have taken different approaches based on robust optimiza- tion. Ghosh et al. [2016] studies a repositioning appraoch based on an iterative two-player game, in which the environment generates a demand scenario out of feasible demand scenarios; they apply this approach to small systems with 20 stations. They also develop a simulation model, which Lowalekar et al. [2017] uses to demonstrate the benefit of multi-stage stochastic optimization. Ghosh et al. [2017] makes explicit the distinction between routing and repositioning with

the former being about minimizing travel time and the latter being about finding the best obtainable allocation.

In contrast to the work outlined on rebalancing with trucks, O’Mahony and Shmoys [2015] also investigates the use of trailers in bikesharing systems; later work by Freund et al. [2016] (cf. Section 6) also considers so-called corrals.