Organizations and Complexity: Searching for the Edge of Chaos

Traditional organizational theory advocates increased differentiation and horizontal integration for organizations in unstable environments or with uncertain technologies. This paper seeks to develop a better understanding of the relationship of group structure and the level of interdependency between individuals on group performance under various task complexities. Complexity theory in general, and NK models in particular, are introduced as theoretical frameworks that offer an explanation for group performance. Simulation models are developed, based on the communication network research of Bavelas (1948) and Leavitt (1952), to explore the effects of decentralization and interdependence. The simulation model developed here shows general consistency with previous human subject experiments. However, contrary to predictions, not all decentralized group structures perform well when undertaking complex task assignments. Structures that are highly connected (actors communicating with all others) perform much worse than those with a lower level of connection. Further experiments varying both the number of actors and the degree of interdependence between them find evidence of the edge of chaos. This research advances our understanding of organizations beyond earlier models by suggesting that there is an optimal range of interconnectedness between actors or tasks that explains the variation in performance. An intriguing result is that this optimal level of interdependence is fairly low, regardless of the size of the group.     

Selecting the best choice in the full information group interview problem

We consider the problem of selecting the single best choice when several groups of choices are presented sequentially for evaluation. In the so-called group interview problem, we assume that the values of choices are random observations from a known distribution function and derive the optimal search strategy that maximizes the probability of selecting the best among all choices. Under the optimal search strategy derived by means of a dynamic programming technique, a decision maker simply selects the best choice in the group under consideration if its value is higher than the pre-specified decision value for that group. We also consider the optimal ordering strategy for the case where the decision maker is permitted to rearrange the sequence of groups for evaluation. We show that the optimal search and ordering strategies can be applied to many sequential decision problems such as the store location problem.     

The Tangled Nature Model for organizational ecology

The Tangled Nature Model—a biologically inspired model of evolutionary ecology—is described, simulated, and analyzed to show its applicability in organization science and organizational ecology. It serves as a conceptual framework for understanding the dynamics in populations of organizations. A salient dynamical feature of this model is the spontaneous generation of a symbiotic group of core organizations. This core, consisting of several dominating species, introduces a mesoscopic level between that of the individual and the whole system. Despite prolonged periods of stability, this core is disrupted at random by parasitic interactions causing sudden core rearrangements. The size distribution of the core organizations is log-normal as predicted by theory and supported by empirical findings. As a simple application of the model, we study the adaptation of organizations to changes in resource availability in terms of population size, population diversity, and ecological efficiency. We find evidence that a temporary reduction in resources forces a consolidation resulting in a sustained increase in overall efficiency, suggesting that such reductions can be applied strategically to drive incremental improvements.     

NETEST: Estimating a Terrorist Network's Structure—Graduate Student Best Paper Award, CASOS 2002 Conference

Since the events of September 11, 2001, the United States has found itself engaged in an unconventional and asymmetric form of warfare against elusive terrorist organizations. Defense and investigative organizations require innovative solutions that will assist them in determining the membership and structure of these organizations. Data on covert organizations are often in the form of disparate and incomplete inferences of memberships and connections between members. NETEST is a tool that combines multi-agent technology with hierarchical Bayesian inference models and biased net models to produce accurate posterior representations of a network. Bayesian inference models produce representations of a network's structure and informant accuracy by combining prior network and accuracy data with informant perceptions of a network. Biased net theory examines and captures the biases that may exist in a specific network or set of networks. Using NETEST, an investigator has the power to estimate a network's size, determine its membership and structure, determine areas of the network where data is missing, perform cost/benefit analysis of additional information, assess group level capabilities embedded in the network, and pose what if scenarios to destabilize a network and predict its evolution over time.     

Finding maximum subgraphs with relatively large vertex connectivity

We consider a clique relaxation model based on the concept of relative vertex connectivity. It extends the classical definition of a k-vertex-connected subgraph by requiring that the minimum number of vertices whose removal results in a disconnected (or a trivial) graph is proportional to the size of this subgraph, rather than fixed at k. Consequently, we further generalize the proposed approach to require vertex-connectivity of a subgraph to be some function f of its size. We discuss connections of the proposed models with other clique relaxation ideas from the literature and demonstrate that our generalized framework, referred to as f-vertex-connectivity, encompasses other known vertex-connectivity-based models, such as s-bundle and k-block. We study related computational complexity issues and show that finding maximum subgraphs with relatively large vertex connectivity is NP-hard. An interesting special case that extends the R-robust 2-club model recently introduced in the literature, is also considered. In terms of solution techniques, we first develop general linear mixed integer programming (MIP) formulations. Then we describe an effective exact algorithm that iteratively solves a series of simpler MIPs, along with some enhancements, in order to obtain an optimal solution for the original problem. Finally, we perform computational experiments on several classes of random and real-life networks to demonstrate performance of the developed solution approaches and illustrate some properties of the proposed clique relaxation models.     

Optimal bidding in auctions of mixed populations of bidders

A mixed population of bidders consists of two asymmetric groups. Members of the first group are game-theoretic players, who maximize their expected profit and incorrectly believe that their opponents act similarly. The second group of bidders adopts an irrational strategy: they either choose their bids randomly following a given probability distribution, in a “naïve” form of bidding, or follow a decision-theoretic approach, maximizing their expected profit under the assumption that all other bids are random. In a sealed bid private-value procurement auction we examine the optimal strategy of a new player, who has perfect knowledge of the structure of the mixed bidder population and enters the auction. The optimal bid of the new bidder is derived when the cost and mark-up follow a uniform distribution in [0, 1]. The effect of the relative size of the group of game-theoretic bidders and the population size on the optimal bid price is established.     

Setting expediting repair policy in a multi-echelon repairable-item inventory system with limited repair capacity

Inventory systems with limited repair capacity are affected by congestion externalities, caused by use of a shared service. There is incompatibility between individual and system optimisation in considering congestion externalities. Three models are described that investigate the congestion effect in a multi-echelon inventory system which has two modes of repair, each with a limited repair capacity. An expanding repair policy employed by the bases in order to choose which repair mode to use is described and compared with different expediting policies related to congestion externalities. The expanding repair policy that considers congestion externalities was found to lead to better system performance measurement than an expanding policy with no congestion. The results of the numerical experiment indicate that the model that ignores congestion externalities—that is, the model that measures each base as an individual—leads to poorer performance measurement for every expediting repair policy, and particularly for the optimal expediting repair policy.     

An Optimal Design Problem in Wave Propagation

We consider an optimal design problem in wave propagation proposed in Sigmund and Jensen (Roy. Soc. Lond. Philos. Trans. Ser. A 361:1001–1019, 2003) in the one-dimensional situation: Given two materials at our disposal with different elastic Young modulus and different density, the problem consists of finding the best distributions of the two initial materials in a rod in order to minimize the vibration energy in the structure under periodic loading of driving frequency Ω. We comment on relaxation and optimality conditions, and perform numerical simulations of the optimal configurations. We prove also the existence of classical solutions in certain cases.     

Intra-organizational Networks and Performance: A Review

Intra-organizational network research had its first heyday during the empirical revolution in social sciences before World War II when it discovered the informal group within the formal organization. These studies comment on the classic sociological idea of bureaucracy being the optimal organization. Later relational interest within organizational studies gave way to comparative studies on the quantifiable formal features of organizations. There has been a resurgence in intra-organizational networks studies recently as the conviction grows that they are critical to organizational and individual performance. Along with methodological improvements, the theoretical emphasis has shifted from networks as a constraining force to a conceptualization that sees them as providing opportunities and finally, as social capital. Because of this shift it has become necessary not only to explain the differences between networks but also their outcomes, that is, their performance. It also implies that internal and external networks should no longer be treated separately.Research on differences between intra-organizational networks centers on the influence of the formal organization, organizational demography, technology and environment. Studies on outcomes deal with diffusion and adaptation of innovation; the utilization of human capital; recruitment, absenteeism and turnover; work stress and job satisfaction; equity; power; information efficiency; collective decision making; mobilization for and outcomes of conflicts; social control; profit and survival of firms and individual performance.Of all the difficulties that are associated with intra-organizational network research, problems of access to organizations and incomparability of research findings seem to be the most serious. Nevertheless, future research should concentrate on mechanisms that make networks productive, while taking into account the difficulties of measuring performance within organizations, such as the performance paradox and the halo-effect.     

Role of Interaction in Enhancing the Epistemic Utility of 3D Mathematical Visualizations

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally accepted that making these visualizations interactive can improve their utility, it is still not clear what role interaction plays in such activities. Interacting with MVs can be viewed as performing low-level epistemic actions on them. In this paper, an epistemic action signifies an external action that modifies a given MV in a way that renders learners’ mental processing of the visualization easier, faster, and more reliable. Several, combined epistemic actions then, when performed together, support broader, higher-level epistemic activities. The purpose of this paper is to examine the role that interaction plays in supporting learners to perform epistemic activities, specifically spatial reasoning involving 3D MVs. In particular, this research investigates how the provision of multiple interactions affects the utility of 3D MVs and what the usage patterns of these interactions are. To this end, an empirical study requiring learners to perform spatial reasoning tasks with 3D lattice structures was conducted. The study compared one experimental group with two control groups. The experimental group worked with a visualization tool which provided participants with multiple ways of interacting with the 3D lattices. One control group worked with a second version of the visualization tool which only provided one interaction. Another control group worked with 3D physical models of the visualized lattices. The results of the study indicate that providing learners with multiple interactions can significantly affect and improve performance of spatial reasoning with 3D MVs. Among other findings and conclusions, this research suggests that one of the central roles of interaction is allowing learners to perform low-level epistemic actions on MVs in order to carry out higher-level cognitive and epistemic activities. The results of this study have implications for how other 3D mathematical visualization tools should be designed.     

Real options in strategic investment games between two asymmetric firms

This paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strategic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strategic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader’s and follower’s optimal investment thresholds. In a duopoly market with negative externalities, a firm may reduce loss of real options value by selecting appropriate pre-emptive entry. When one firm has a dominant advantage over its competitor, both the dominant firm and dominated firm enter at their respective leader’s and follower’s optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead.     

On the parametric uncertainty quantification of the Rothermel's rate of spread model

Parametric uncertainty quantification of the Rothermel's fire spread model is presented using the Polynomial Chaos expansion method under a Non-Intrusive Spectral Projection (NISP) approach. Several Rothermel's model input parameters have been considered random with an associated prescribed probability density function. Two different vegetation fire scenarios are considered and NISP method results and performance are compared with four other stochastic methodologies: Sensitivity Derivative Enhance Sampling; two Monte Carlo techniques; and Global Sensitivity Analysis. The stochastic analysis includes a sensitivity analysis study to quantify the direct influence of each random parameter on the solution. The NISP approach achieved performance three orders of magnitude faster than the traditional Monte Carlo method. The NISP capability to perform uncertainty quantification associated with fast convergence makes it well suited to be applied for stochastic prediction of fire spread.     

A note on the Poisson boundary of lamplighter random walks

The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups Γ endowed with a “rich” boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich (Ann. Math. 152:659–692, 2000). A geometrical method for constructing the strip as a subset of the lamplighter group ${\mathbb {Z}_{2}\wr \Gamma}$ starting with a “smaller” strip in the group Γ is developed. Then, this method is applied to several classes of base groups Γ: groups with infinitely many ends, hyperbolic groups in the sense of Gromov, and Euclidean lattices. We show that under suitable hypothesis the Poisson boundary for a class of random walks on lamplighter groups is the space of infinite limit configurations.     

Inadvertent leaks: exploration via agent-based dynamic network simulation

A significant volume of information leaks in organizations are inadvertent, a form of information spillage. Because the leakage of information is driven by the complex interaction of technology, social, and behavioral factors, we use a hybrid agent-based and dynamic network model, Construct, to simulate the flow of sensitive information in knowledge-driven organizations. Because interaction patterns often change when an organization is under stress, we simulate stress to the organization with effect-based (reliability and integrity) crisis scenarios. Using a virtual experiment, we vary the crisis scenarios, organization’s structure, IT connections, and pressure to separate personnel based on security ratings. Our experiment suggests that the organization’s structure, IT connections, separation pressure, and typical performance all influence how much an organization suffers from inadvertent leakage. In evaluating how organizations respond to crisis, organizations with stove-piped IT tend to clamp down on leakage in response to the crisis, while organizations with Mesh IT tend to have more leakage. Integrity crises tend to decrease leakage; while reliability crises tend to increase leakage in organizations, especially those with Mesh-based IT.     

On the Distribution of the Number of Fixed Vectors for the Finite Classical Groups

Motivated by analogous results for the symmetric group and compact Lie groups, we study the distribution of the number of fixed vectors of a random element of a finite classical group. We determine the limiting moments of these distributions, and find exactly how large the rank of the group has to be in order for the moment to stabilize to its limiting value. The proofs require a subtle use of some q-series identities. We also point out connections with orthogonal polynomials.     

AN INDICATOR FOR ECOSYSTEM EXTERNALITIES IN FISHING

Ecosystem externalities arise when one use of an ecosystem affects its other uses through the production functions of the ecosystem. We use simulations with a size‐spectrum ecosystem model to investigate the ecosystem externality created by fishing of multiple species. The model is based upon general ecological principles and is calibrated to the North Sea. Two fleets are considered: a “forage fish” fleet targeting species that mature at small sizes and a “large fish” fleet targeting large piscivorous species. Based on the marginal analysis of the present value of the rent, we develop a benefit indicator that explicitly divides the consequences of fishing into internal and external benefits. This analysis demonstrates that the forage fish fleet has a notable economic impact on the large fish fleet, but the reverse is not true. The impact can be either negative or positive, which entails that for optimal economic exploitation, the forage fishery has to be adjusted according to the large fish fishery. With the present large fish fishery in the North Sea, the two fisheries are well adjusted; however, the present combined exploitation level is too high to achieve optimal economic rents.     

A note on the Poisson boundary of lamplighter random walks

The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups Γ endowed with a “rich” boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich (Ann. Math. 152:659–692, 2000). A geometrical method for constructing the strip as a subset of the lamplighter group \mathbb Z₂\wr G{\mathbb {Z}_{2}\wr \Gamma} starting with a “smaller” strip in the group Γ is developed. Then, this method is applied to several classes of base groups Γ: groups with infinitely many ends, hyperbolic groups in the sense of Gromov, and Euclidean lattices. We show that under suitable hypothesis the Poisson boundary for a class of random walks on lamplighter groups is the space of infinite limit configurations.     

Multiscale decision-making: Bridging organizational scales in systems with distributed decision-makers

Decision-making in organizations is complex due to interdependencies among decision-makers (agents) within and across organizational hierarchies. We propose a multiscale decision-making model that captures and analyzes multiscale agent interactions in large, distributed decision-making systems. In general, multiscale systems exhibit phenomena that are coupled through various temporal, spatial and organizational scales. Our model focuses on the organizational scale and provides analytic, closed-form solutions which enable agents across all organizational scales to select a best course of action. By setting an optimal intensity level for agent interactions, an organizational designer can align the choices of self-interested agents with the overall goals of the organization. Moreover, our results demonstrate when local and aggregate information exchange is sufficient for system-wide optimal decision-making. We motivate the model and illustrate its capabilities using a manufacturing enterprise example.     

DEA-based hypothesis tests for comparing two groups of decision making units

In this paper, we develop five statistical tests to compare the efficiencies of different groups of DMUs. We consider a data generating process (DGP) that models the deviation of the output from the best practice frontier as the sum of two components, a one-sided inefficiency term and a two-sided random noise term. We use simulation to evaluate the performance of the five tests against the Banker tests (Banker, 1993) that were designed for DGPs containing a single one-sided error term. It is found that while the Banker tests are very effective when efficiency dominates noise, the tests developed in this paper perform better than the Banker tests when noise levels are significant.