A Weighted Network Modeling Approach for Analyzing Product Competition

2021 ◽  
Author(s):  
Yaxin Cui ◽  
Faez Ahmed ◽  
Zhenghui Sha ◽  
Lijun Wang ◽  
Yan Fu ◽  
...  
Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Yaxin Cui ◽  
Faez Ahmed ◽  
Zhenghui Sha ◽  
Lijun Wang ◽  
Yan Fu ◽  
...  

Statistical network models have been used to study the competition among different products and how product attributes influence customer decisions. However, in existing research using network-based approaches, product competition has been viewed as binary (i.e., whether a relationship exists or not), while in reality, the competition strength may vary among products. In this paper, we model the strength of the product competition by employing a statistical network model, with an emphasis on how product attributes affect which products are considered together and which products are ultimately purchased by customers. We first demonstrate how customers’ considerations and choices can be aggregated as weighted networks. Then, we propose a weighted network modeling approach by extending the valued exponential random graph model to investigate the effects of product features and network structures on product competition relations. The approach that consists of model construction, interpretation, and validation is presented in a step-by-step procedure. Our findings suggest that the weighted network model outperforms commonly used binary network baselines in predicting product competition as well as market share. Also, traditionally when using binary network models to study product competitions and depending on the cutoff values chosen to binarize a network, the resulting estimated customer preferences can be inconsistent. Such inconsistency in interpreting customer preferences is a downside of binary network models but can be well addressed by the proposed weighted network model. Lastly, this paper is the first attempt to study customers’ purchase preferences (i.e., aggregated choice decisions) and car competition (i.e., customers’ co-consideration decisions) together using weighted directed networks.


2021 ◽  
Author(s):  
Wenyue Sun ◽  
Sathish Sankaran

Abstract Reservoir management routinely requires assimilating historical data and predicting field performance against multiple production strategies before implementing them in the field. However, traditional numerical methods are often cumbersome to characterize, build and calibrate at a timescale that can be used reliably for such short-term decision cycles such as production forecasting, IOR optimization and production rate control. Simpler analytical models make assumptions and lack the rigor needed to adequately model these systems. Pure data-driven methods may lack physical insights or have limited range of applicability. Model fidelity, speed, interpretability, suitability to automate and ease-of-use are some key modeling traits that are desired for reservoir management purposes. In this work, we propose to use a reservoir graph-network modeling approach (RGNet), based on the concept of diffusive time of flight, to forecast well performance using routinely measured field measurements (e.g. bottomhole pressure and rates). We propose a novel, model order reduction method based on discretized time of flight for multiple wells with interference. It simplifies the 3D reservoir flow problem into a flow network representation that can be solved as a 2D simulation model with any general-purpose reservoir simulator. Parameters in RGNet model cover well productivity index, grid pore volume and transmissibility, which are estimated through a history-matching process. After history matching, multiple posterior RGNet models are generated to quantify subsurface uncertainties. The RGNet modeling approach allows various fluid-flow physics to be modeled within the grids and boundary conditions, and is applicable to a range of conventional and unconventional reservoirs with different flow mechanisms. We applied the proposed approach on a field case reservoir models for multiple wells with interference. By virtue of the reduced complexity, the modeling methodology is highly scalable and still retains physical interpretability. The calibration method produces parsimonious models and provides uncertainty estimates in history matching parameters with range of outcomes. In addition, the RGNet models are much faster to simulate, over 1000x speed up, compared with full-physics models. We then used RGNet models for well-control and flood optimization and achieved significant improvement over field net-present-values. Parameterization of the proposed reservoir graph-network modeling approach provides a unique and sustainable way to reduce model complexity needed for reservoir management purposes. The method is rooted in physical principles and provides an explainable dynamic reservoir model that can be effectively used to understand reservoir behavior and optimize performance. The lightweight model lends itself naturally to fast computation that are required for scenario analysis and optimization.


Author(s):  
Yaxin Cui ◽  
Faez Ahmed ◽  
Zhenghui Sha ◽  
Lijun Wang ◽  
Yan Fu ◽  
...  

Abstract Statistical network models allow us to study the co-evolution between the products and the social aspects of a market system, by modeling these components and their interactions as graphs. In this paper, we study competition between different car models using network theory, with a focus on how product attributes (like fuel economy and price) affect which cars are considered together and which cars are finally bought by customers. Unlike past work, where most systems have been studied with the assumption that relationships between competitors are binary (i.e., whether a relationship exists or not), we allow relationships to take strengths (i.e., how strong a relationship is). Specifically, we use valued Exponential Random Graph Models and show that our approach provides a significant improvement over the baselines in predicting product co-considerations as well as in the validation of market share. This is also the first attempt to study aggregated purchase preference and car competition using valued directed networks.


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