arXiv subjects

Andrés Fielbaum

Publications and source records attributed to Andrés Fielbaum.

3 recordsLinked to original sources

arXiv2026

The Increasing Gap Dynamics in a General Spatial Matching Model

We study a representation of a problem that appears in numerous transport systems: $N$ servers distributed over a given space (e.g., cars on an urban network), receive random requests from arriving users who get assigned to the closest server, after which this server is replaced by a new one at a random location. We show that this creates a negative feedback loop, which we call \textit{Increasing Gap Dynamics} (IGD): when a server is assigned a spatial gap forms, which is more likely to attract new users that further widen the gap. The simplest version of our model is a one-dimensional circle, for which we derive analytical results showing that the system converges to an inefficient equilibrium, worse than both balanced and fully random distributions of servers. We prove that an optimal assignment policy always matches the user to one of its two neighbouring servers so that long gaps tend to widen. Hence, the IGD persists even when assigning optimally rather than greedily. In two dimensions, the appearance of the IGD is illustrated through simulations on a square region. Finally, simulations of a proper ride-hailing system using real data from Manhattan confirms that the IGD arises and that it is responsible for the appearance of the well-known Wild Goose Chase.

math.OC↗

arXiv2024

Idle wage as a tool to regulate the relationship between ride-hailing platforms and drivers

Ride-hailing platforms typically classify drivers as either employees or independent contractors. These classifications tend to emphasize either wage certainty or flexibility, but rarely both. We study an alternative or complementary approach: the \textit{Idle wage,} which provides with a fixed payment drivers even when they are connected without passengers on board. We adapt a well-known economic model of the supply-demand equilibrium in ride-hailing platforms and analyse how the optimal welfare and profit change with the introduction of an idle wage when drivers are risk-averse. We show that in a single-period setting, risk aversion implies that it is optimal to pay the drivers only through an idle wage. However, if the pool of available drivers is large, even a small idle wage could attract too many drivers, rendering the system unprofitable. When the demand fluctuates throughout multiple periods, we show that if the idle wage has to be constant, then it is optimal to combine the idle wage with the traditional payment via trips, so that surge pricing influences the number of drivers connected. This illustrates a relevant trade-off: Risk-aversion favours using the idle wage to attract drivers; however, if the platform is not allowed to fully adjust the idle wage over time, there may be periods in which the idle wage cannot resolve the mismatch between supply and demand. We propose a partially flexible constraint that still makes the idle wage-only solution viable. It allows the idle wage to adapt per period, as long as it fulfills a total minimum wage requirement. Numerical simulations suggest that the idle wage policy, if properly implemented, could be beneficial for the system as a whole.

math.OC↗

arXiv2019

A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems

Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on knapsack-cover inequalities achieves an integrality gap of 2. These inequalities have been exploited in more general environments, many of which admit primal-dual approximation algorithms. Inspired by problems from power and transport systems, we introduce a new general setting in which items can be taken fractionally to cover a given demand. The cost incurred by an item is given by an arbitrary non-decreasing function of the chosen fraction. We generalize the knapsack-cover inequalities to this setting an use them to obtain a $(2+\varepsilon)$-approximate primal-dual algorithm. Our procedure has a natural interpretation as a bucket-filling algorithm, which effectively balances the difficulties given by having different slopes in the cost functions: when some superior portion of an item presents a low slope, it helps to increase the priority with which the inferior portions may be taken. We also present a rounding algorithm with an approximation guarantee of 2. We generalize our algorithm to the Unsplittable Flow-Cover problem on a line, also for the setting where items can be taken fractionally. For this problem we obtain a $(4+\varepsilon)$-approximation algorithm in polynomial time, almost matching the $4$-approximation known for the classical setting.

cs.DS↗