Modeling 21st century project teams: docking workflow and knowledge network computational models

This paper reports on an attempt to integrate and extend two established computational organizational models\u2014SimVision\uae and Blanche\u2014to examine the co-evolution of workflow and knowledge networks in 21st century project teams. Traditionally, workflow in project teams has been modeled as sets of sequential and/or parallel activities each assigned to a responsible participant, organized in a fixed structure. In the spirit of Jay Galbraith\u2019s (1973) information processing view of organizations, exceptions\u2014situations in which participants lack the required knowledge to complete a task\u2014are referred up the hierarchy for resolution. However, recent developments in digital technologies have created the possibility to design project teams that are more flexible, self-organizing structures, in which exceptions can be resolved much more flexibly through knowledge networks that extend beyond the project or even the company boundaries. In addition to seeking resolution to exceptions up the hierarchy, members of project teams may be motivated to retrieve the necessary expertise from other knowledgeable members in the project team. Further, they may also retrieve information from non-human agents, such as knowledge repositories or databases, available to the project team. Theories, such as Transactive Memory, Public Goods, Social Exchange and Proximity may guide their choice of retrieving information from a specific project team member or database. This paper reports on a \u201cdocked\u201d computational model that can be used to generate and test hypotheses about the co-evolution of workflow and knowledge networks of these 21st century project teams in terms of their knowledge distribution and performance. The two computational models being docked are SimVision (Jin & Levitt, 1999) which has sophisticated processes to model organizations executing project-oriented workflows, and Blanche (Hyatt, Contractor, & Jones, 1997), a multiagent computational network environment, which models multitheoretical mechanisms for the retrieval and allocation of information in knowledge networks involving human and non-human agents. This paper was supported in part by a grant from the U.S. National Science Foundation for the project \u201cCo-Evolution of Knowledge Networks and 21st Century Organizational Forms (IIS- 9980109)

Markov chains, game theory, and infinite programming: Three paradigms for optimization of complex systems.

A Complex System can be defined as a natural, artificial, social, or economic entity whose model involves an inordinate, or even infinite number of variables. This thesis is an attempt to employ techniques from Markov Chains, Game Theory, and Functional Analysis to develop theory and algorithms for optimizing mathematical abstractions of Euclidean, discrete, and infinite dimensional complex systems. The first chapter focuses on Markov Chain techniques. (i) We develop a novel rigorous connection between the famous Small World phenomenon and effective Markov candidate generators for continuous optimization; (ii) We propose Adaptive Search with Amorphous Probabilities (ASAP), a unified algorithmic framework that allows for very general acceptance probabilities, adaptive tuning of parameters and guarantees convergence in probability to the optimum function value for continuous as well as stochastic optimization problems; (iii) We develop the notion of Fastest Mixing Boltzmann Chains to analytically formulate the to cool or not to cool problem for the first time. The second chapter relies on Game Theory to solve deterministic and stochastic discrete black-box optimization problems. We propose a bounded rational version of Sampled Fictitious Play (SFP). Unlike earlier work, the players in this version (i) Use samples of size one for their best response computations, (ii) Are forced to make mistakes, (iii) Have finite memory, and (iv) Are guaranteed to find optimal solutions. In the third chapter, we study two infinite dimensional complex systems: (i) Countably infinite linear programs, and (ii) Infinite horizon production planning under convex costs. We develop duality theory for countably infinite linear programs, and a characterization of their extreme points through positive variables. We develop the Shadow Simplex method that requires finite computation in each iteration and achieves value convergence. Unlike previous research in the convex production planning domain, we allow backlogging. Properties of convex network flow problems are then used to compute closed form formulas for a minimum forecast horizon.Ph.D.Applied SciencesComputer scienceOperations researchUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126158/2/3237963.pd

Abstract

In this paper, we present a simplex method for linear programs in standard form, or more precisely, linear optimization problems that have countably many non-negative variables and countably many equality constraints. Important special cases of these problems include infinite horizon deterministic dynamic programming problems and network flow problems with countably infinite nodes and arcs. After embedding the primal linear program and its dual in appropriate topological dual spaces, we develop an algebraic characterization of extreme points in terms of the basic, i.e., strictly positive variables. Although such a characterization is hard to accomplish in the most general case, we show that it can be successfully developed when the infimum of the values of basic variables of an extreme point is strictly positive. An important case where this infimum condition is met is when the components of an extreme point are integers. We illustrate how this algebraic characterization can be used to develop important extensions of some well-known results in the finite variable, finite constraint case. We characterize degeneracy and discuss challenges involved in resolving it. We show that our simplex method maintains primal feasibility and complementary slackness in every iteration and achieves dual feasibility in the limit.

Abstract

In this paper, we present a novel Markov Chain Monte Carlo framework for solving global optimization problems in the continuous domain. At each iterate, our algorithm uses a globally reaching Markov kernel to generate a candidate point in the feasible region. This candidate point is then accepted according to a possibly non-reversible acceptance probability. We derive sufficient conditions on the acceptance probability that guarantee convergence in probability to the globally optimum function value for a continuous objective function defined on a compact feasible region. We show that well known algorithms such as simulated annealing are special cases of this approach. We then extend this result to the case where the acceptance probability is allowed to be stochastic. This situation may arise when we are optimizing the expected value of a stochastic performance measure by using random function value estimates to compute acceptance probabilities. We illustrate how our analysis can be used to derive sufficient conditions for convergence of simulated annealing when applied to problems with noisy objective functions.

Sampled Fictitious Play for Black-Box Stochastic Sequential Decision Problems

In this paper, we propose an algorithm based on Sampled Fictitious Play for solving finitehorizon stochastic sequential decision problems. Our method models the decision problem as a game of identical interest between multiple players, who use the history of their past plays to improve the estimate of optimal reward in the initial state. We show that this method is able to find an optimal policy almost surely, and provide preliminary numerical results.