Gerardo Berbeglia

Bio: Gerardo Berbeglia is an academic researcher from Melbourne Business School. The author has contributed to research in topics: Discrete choice & Monopoly. The author has an hindex of 14, co-authored 62 publications receiving 1676 citations. Previous affiliations of Gerardo Berbeglia include HEC Montréal & University of Melbourne.

Static pickup and delivery problems: a classification scheme and survey

Abstract: Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a three-field classification scheme for these problems. It surveys the methods used for solving them.

A Hybrid Tabu Search and Constraint Programming Algorithm for the Dynamic Dial-a-Ride Problem

Abstract: This paper introduces a hybrid algorithm for the dynamic dial-a-ride problem in which service requests arrive in real time. The hybrid algorithm combines an exact constraint programming algorithm and a tabu search heuristic. An important component of the tabu search heuristic consists of three scheduling procedures that are executed sequentially. Experiments show that the constraint programming algorithm is sometimes able to accept or reject incoming requests, and that the hybrid method outperforms each of the two algorithms when they are executed alone.

A Comparative Empirical Study of Discrete Choice Models in Retail Operations

Abstract: Demand estimation is a fundamental task in retail operations and revenue management, providing the necessary input data for inventory control, assortment and price optimization models. The task is particularly difficult in operational contexts when product availability varies over time and customers may substitute. In addition to the classical multinomial logit (MNL) model and its variants (e.g., nested logit, mixed MNL), new demand models have been proposed (e.g., the Markov chain model) and others have been revisited (e.g., the rank-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column generation, EM algorithms). In this paper, we conduct a systematic, empirical study of different demand models and estimation algorithms, spanning both maximum likelihood and least squares criteria. Through an exhaustive set of numerical experiments on synthetic and real data, we provide comparative statistics of the quality of the different choice models and estimation methods, and characterize operational environments suitable for different model/estimation implementations.

Assortment optimization under a multinomial logit model with position bias and social influence

Abstract: Motivated by applications in retail, online advertising, and cultural markets, this paper studies the problem of finding an optimal assortment and positioning of products subject to a capacity constraint in a setting where consumers preferences can be modeled as a discrete choice under a multinomial logit model that captures the intrinsic product appeal, position biases, and social influence. For the static problem, we prove that the optimal assortment and positioning can be found in polynomial time. This is despite the fact that adding a product to the assortment may increase the probability of selecting the no-choice option, a phenomenon not observed in almost all models studied in the literature. We then consider the dynamics of such a market, where consumers are influenced by the aggregate past purchases. In this dynamic setting, we provide a small example to show that the natural and often used policy known as popularity ranking, that ranks products in decreasing order of the number of purchases, can reduce the expected profit as times goes by. We then prove that a greedy policy that applies the static optimal assortment and positioning at each period, always benefits from the popularity signal and outperforms any policy where consumers cannot observe the number of past purchases (in expectation).

Proceedings of the National Academy of Sciences

Abstract: where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment

Abstract: Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, and anytime. These services present enormous potential for positive societal impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride-sharing. Recently, a large-scale study highlighted some of the benefits of car pooling but was limited to static routes with two riders per vehicle (optimally) or three (with heuristics). We present a more general mathematical model for real-time high-capacity ride-sharing that (i) scales to large numbers of passengers and trips and (ii) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it through a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. We quantify experimentally the tradeoff between fleet size, capacity, waiting time, travel delay, and operational costs for low- to medium-capacity vehicles, such as taxis and van shuttles. The algorithm is validated with ∼3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride-sharing with rider capacity of up to 10 simultaneous passengers per vehicle. The algorithm applies to fleets of autonomous vehicles and also incorporates rebalancing of idling vehicles to areas of high demand. This framework is general and can be used for many real-time multivehicle, multitask assignment problems.