Traditional tools and software for social network analysis are seldom scalable and/or fast. This paper provides an overview of an R package called fastnet, a tool for scaling and speeding up the simulation and analysis of large-scale social networks. fastnet uses multi-core processing and sub-graph sampling algorithms to achieve the desired scale-up and speed-up. Simple examples, usages, and comparisons of scale-up and speed-up as compared to other R packages, i.e., igraph and statnet, are presented.

This paper studies the multi-period freight consolidation problem for a third-party logistics (3PL) provider that transships multiple products from multiple suppliers to a single end customer. The shipments are first transported to select consolidation terminals where the 3PL provider aims to consolidate the inbound shipments so as to reduce costs. This imposes a complex decision problem to the 3PL provider since consolidation may require that the inbound shipments spend more time at the terminals, whereas all shipments have prespecified pickup dates and delivery deadlines. Moreover, the shipments picked up from the suppliers are indivisible, that is, a shipment cannot be split into multiple lots and assigned to separate routes. This paper presents a mixed-integer linear programming model and proposes a heuristic for solving the resulting problem. The proposed heuristic partitions the multi-period problem into multiple subproblems by splitting the planning horizon into smaller mutually exclusive units which makes the planning problem relatively insensitive to the length of the planning horizon and hence scalable. The effectiveness of the proposed heuristic is demonstrated via a real-life problem: a close-to-optimal solution for a 360-day planning problem that could not be solved using commercial solvers due to its size is obtained within two hours.

This article presents a stochastic opinion dynamics model where (a) the opinion of each agent in a network is modeled as a probability distribution as against a point object, (b) consensus is defined as the stability region of the ensuing set of stochastic difference equations, and (c) compromise solutions can be derived between agents who don't have a consensus. The model is well suited for tracking opinion dynamics over large online systems such as Twitter and Yelp where opinions need to be extracted from the user-generated text data. Theoretical conditions for the existence of consensus and the impact that stubborn agents have on opinion dynamics are also presented.

This article presents the relationship between a firm's advertisement spending and sales in a duopoly when information about the competitors' advertisement spending is unavailable. The competitive interaction between the firms has been modeled as imperfect information Cournot and Stackelberg games and the conditions for subgame perfect Bayesian Nash equilibrium are presented. The results suggest that when the firms are similar in size and advertisement effectiveness, both firms are better off sharing their advertising plans with each other. On the other hand, when one of the firms is a market leader, the follower may profit from the leader's advertisement spending and so is better off keeping the leader guessing. A practical approach to estimate the optimum advertisement budget based on the expected values of the competitors' historic advertising spending is presented as well.

This article describes how the average path length (APL) of a network is an important metric that provides insights on the interconnectivity in a network and how much time and effort would be required for search and navigation on that network. However, the estimation of APL is time-consuming as its computational complexity scales nonlinearly with the network size. In this article, the authors develop a computationally efficient random node pair sampling algorithm that enables the estimation of APL with a specified precision and confidence. The proposed sampling algorithms provide a speed-up factor ranging from 240-750 for networks with more than 100,000 nodes. The authors also find that the computational time required for estimation APL does not necessarily increase with the network size; it shows an inverted U shape instead.

This article presents a restricted maximum likelihood-based algorithm to estimate who influences whose opinions and to what degree when agents share their opinions over large online social networks such as Twitter. The proposed algorithm uses multi-core processing and distributed computing to provide a scalable solution as the optimization problems are large in scale; a network with 10,000 agents and average connectivity of 100 requires estimates of about 1 million parameters. A computational study is then used to show that the estimates are efficient and robust when the full rank conditions for the covariance matrix are met. The results also highlight the importance of the quantity of the information being shared over the social network for the inference of the influence structure.

Knowing the extent of influence an agent exerts over the other agents over online social networks such as Twitter and Facebook is important as it helps identify opinion leaders and predict how opinions are likely to evolve. However, this information regarding the extent of influence exerted by agents on each other is difficult to obtain as it is unobservable and the data available to estimate it is scarce, often incomplete, and noisy. Further, the number of unknown parameters that need to be estimated to infer the extent of influence between any given pair of agents is very large. A particle-learning-based algorithm is proposed to estimate the influence matrix that indicates the extent of influence any agent exerts on any other in a social network. Computational studies have been used to determine the efficiency, learning rates and asymptotic properties, and robustness (to missing information) of the proposed particle learning algorithms. The results indicate that the proposed algorithm shows fast convergence rates, yields efficient estimates of the influence matrix, is scalable, and is robust to incomplete information. Further, the network topology, and not just the network size, impacts the learning rate. The learning rate also slows down as the percentage of missing information increases.

This article presents a practical approach to estimate the substitution probabilities between products at a retail store by using the store's point of sale data and prospect theory based structural restrictions on the consumer choice behavior. The prospect theory-based reference dependent preference structure imposed on the consumer choice behavior (a) accounts for how consumers make their original choice as well as how they substitute, (b) eliminates the IIA and IPS assumptions that the standard utility theory based models impose on consumer choice, and (c) alleviates the need for inventory information for estimating the substitution probabilities. Simulations and empirical studies have been used to show that the estimates of the substitution probabilities are efficient and are robust to stock-out rates.

There is growing interest in developing the abilities to simulate realistic social networks and analyze data generated from existing online social networks such as Facebook and Twitter. Amongst other things, researchers and practitioners need these abilities to study how opinions and information diffuse over networks and identify the influential agents in networks. However, the sizes of the social networks that need to be simulated and the amount of user generated data that needs to be analyzed is growing at a faster rate than the computational power of most of the modern day computers. This paper presents a memory efficient network representation and computational resource allocation algorithm that yields a scale-up of about 400; thus, given a constraint on the availability of computational resources, researchers can now use the proposed algorithm to simulate and analyze networks that are more than 100 times larger than what they could simulate otherwise. The proposed network representation is conducive to multi-core processing and random node sampling. Algorithms for computationally efficient execution of three random-node-sampling-based methods to estimate network metrics such as the network diameter and average path length are also presented in the paper. These algorithms yield a speed-up of about 40 even when the researcher requires a precision of more than 98%. The scale-up and speed-up numbers are based on a detailed performance analysis of the proposed algorithms that was conducted on synthetic networks of sizes ranging from 1000 to 1,000,000 nodes. The observed scale-up and speed-up performance of the proposed algorithms has been validated against the algorithms used in igraph and statnet-two popular network data analysis software package, and these results are also presented in this paper.