Search

In this paper, we study the problem of network discovery and influence propagation, and propose an integrated approach for the analysis of lead-lag synchronization in multiple choices. Network models for the processes by which decisions propagate through social interaction have been studied before, but only a few consider unknown structures of interacting agents. In fact, while individual choices are typically observed, inferring individual influences – who influences who – from sequences of dynamic choices requires strong modeling assumptions on the cross-section dependencies of the observed panels. We propose a class of parametric models which extends the vector autoregression to the case of pairwise influences between individual choices over multiple items and supports the analysis of influence propagation. After uncovering a collection of theoretical properties (conditional moments, parameter sensitivity, identifiability and estimation), we provide an economic application to music broadcasting, where a set of songs are diffused over radio stations; we infer station-to-station influences based on the proposed methodology and assess the propagation effect of initial launching stations to maximize songs diffusion. Both on the theoretical and empirical sides, the proposed approach connects fields which are traditionally treated as separated areas: the problem of network discovery and the one of influence propagation. [ABSTRACT FROM AUTHOR]

Flash sales retailers organize online campaigns where products are sold for a short period of time at a deep discount. The demand in these events is very uncertain, but clickstream data can potentially help retailers with detailed information about the shopping process, thereby allowing them to manage such risks. For this purpose, we build a predictive model for shoppers' sequential decisions about visiting a campaign, obtaining product information and placing a purchase, which we validate using a large data set from a leading flash sales firm. The proposed hierarchical approach mirrors the different stages of the shopping funnel and allows for a direct decomposition of its main sources of variation, from customers arrival to products purchase. We identify life‐cycle dynamics and heterogeneity across campaigns and products as the main sources of variation: these allow us to provide the best predictions from a statistical standpoint, which outperform machine learning alternatives in out‐of‐sample accuracy. Our model thus enables flash sales retailers to learn about the performance of new products in a few hours and to update prices so as to better match supply and demand forecast and improve profits. We simulate our forecasting and optimization procedures on several campaigns including thousands of products and show that our model can successfully separate popular and unpopular products and lift revenues significantly. [ABSTRACT FROM AUTHOR]

One of the most efficient interior-point methods for some classes of block-angular structured problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. In this work we show that the choice of a good preconditioner depends on geometrical properties of the constraint structure. In particular, the principal angles between the subspaces generated by the diagonal blocks and the linking constraints can be used to estimate ex ante the efficiency of the preconditioner. Numerical validation is provided with some generated optimization problems. An application to the solution of multicommodity network flow problems with nodal capacities and equal flows of up to 64 million variables and up to 7.9 million constraints is also presented. These computational results also show that predictor-corrector directions combined with iterative system solves can be a competitive option for large instances. [ABSTRACT FROM AUTHOR]

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances. [ABSTRACT FROM AUTHOR]