Current Students
Matthew Visomirski, (B.S. Physics & Mathematics, In Progress)
Project: Characterization of Zero-Sum Replicator Dynamics
Abstract: Using a computer aided system, we are attempting to determine the relationship between the combinatorial properties of interaction graphs describing the ecological relationship of species and the resulting stability properties of fixed points in the corresponding replicator dynamics. This work is with Josh Paik (see below).
Darby Gluscevich-Kepner, (B.S. Statistics, In Progress)
Project: Nonlinear Dynamics in Political Twitter Data
Abstract: We are attempting to quantity the (quasi)-periodicity that occurs in the twitter (X) streams associated to intentional influencers as opposed to accidental influencers. For frequent posters who do not exhibit quasi-periodic behavior, we hope to identify the signature of chaotic behavior.
Past Students
Akshat Harlalka, (B.S. Computer Science, Spring 2024)
Project: Stability of Dining Clubs in the Kolkata Paise Problem with and without Cheating
Abstract: We introduce the idea of a dining club to the Kolkata Paise Restaurant Problem. In this problem, N agents choose (randomly) among N restaurants, but if multiple agents choose the same restaurant, only one will eat. Agents in the dining club will coordinate their restaurant choice to avoid choice collision and increase their probability of eating. We model the problem of deciding whether to join the dining club as an evolutionary game and show that the strategy of joining the dining club is evolutionarily stable. We then introduce an optimized member tax to those individuals in the dining club, which is used to provide a safety net for those group members who don’t eat because of collision with a non-dining club member. When non-dining club members are allowed to cheat and share communal food within the dining club, we show that a new unstable fixed point emerges in the dynamics. A bifurcation analysis is performed in this case. To conclude our theoretical study, we then introduce evolutionary dynamics for the cheater population and study these dynamics. Numerical experiments illustrate the behaviour of the system with more than one dining club and show several potential areas for future research.
ArXiv Link, Paper Link
Josh Paik, (Ph.D. Mathematics, In Progress)
Project: Completely Integrable Replicator Dynamics Associated to Competitive Networks
Abstract: The replicator equations are a family of ODEs that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold integrable. We show this by explicitly providing conserved quantities and a Poisson structure. As a corollary, we classify all tournament replicators up to dimension 6 and most of dimension 7. As an application, we show that Fig. 1 of “A competitive network theory of species diversity” by Allesina and Levine (PNAS 2011), produces quasiperiodic dynamics.
ArXiv Link, Paper Link
Gabriel Nicolosi, (Ph.D. Operations Research)
Project: Approximation of optimal control surfaces for 2×2 skew-symmetric evolutionary game dynamics
Abstract: In this paper we study the problem of approximating the general solution to an optimal control problem whose dynamics arise from a 2×2 skew-symmetric evolutionary game with arbitrary initial condition. Our approach uses a Fourier approximation method and generalizes prior work in the use of orthogonal function approximation for optimal control. At the same time we cast the fitting problem in the context of a non-standard feedforward neural network and derive the back-propagation operator in this context. An example of the efficacy of this approach is provided and generalizations are discussed.
ArXiv Link, Paper Link, ArXiv Link 2 (Appeared in 2023 IISE Conference), ArXiv Link 3
Hannah Gampe, (B.S. Mathematics, In Progress)
Project: Dynamics of a binary option market with exogenous information and price sensitivity (DARPA Research Project)
Abstract: In this paper, we derive and analyze a continuous binary option market with exogenous information. The resulting non-linear system has a discontinuous right hand side, which can be analyzed using zero-dimensional Filippov surfaces. Under general assumptions on purchasing rules, we show that when exogenous information is constant in the binary asset market, the price always converges. We then investigate market prices in the case of changing information, showing empirically that price sensitivity has a strong effect on price lag vs. information. We conclude with open questions on general M-ary option markets.
ArXiv Link, Paper Link
Connor Olson, (Ph.D. Mathematics, In Progress)
Project: Winning Mediated Thermodynamic Strategy Evolution on a Lattice (Summer Research Project)
Abstract: We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution, which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale, which defines the random fluctuations. Players with higher bank values are, thus, less likely to change strategy than players with a lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or drifting boundaries. We show the effect of a temperature increase on the underlying system and identify surprising properties of this model through numerical simulations.
ArXiv Link, Paper Link
Nishanth Nakshatri, (M.S. Computer Science, 2021)
Project: Design and Analysis of a Synthetic Prediction Market using Dynamic Convex Sets
Abstract: We present a synthetic prediction market whose agent purchase logic is defined using a sigmoid transformation of a convex semi-algebraic set defined in feature space. Asset prices are determined by a logarithmic scoring market rule. Time varying asset prices affect the structure of the semi-algebraic sets leading to time-varying agent purchase rules. We show that under certain assumptions on the underlying geometry, the resulting synthetic prediction market can be used to arbitrarily closely approximate a binary function defined on a set of input data. We also provide sufficient conditions for market convergence and show that under certain instances markets can exhibit limit cycles in asset spot price. We provide an evolutionary algorithm for training agent parameters to allow a market to model the distribution of a given data set and illustrate the market approximation using two open source data sets. Results are compared to standard machine learning methods.
ArXiv Link, Paper Link
Priyadarshini Murugan, (M.S. Computer Science, 2021)
Project: Modeling Longitudinal Behavior Dynamics Among Extremist Users in Twitter Data
Abstract: We use a dynamical systems perspective to analyze a collection of 2.4 million tweets known to originate from ISIS and ISIS related users. From those users active over long period of time (i.e., 2+years), we derive sequences of behaviors and show that the top users cluster into 4 behavioral classes, which naturally describe roles within the ISIS communication structure. We then correlate these classes to the retweet network of the top users showing the relationship between dynamic behavior and retweet network centrality. We use the underlying model to formulate informed hypotheses about the role each user plays. Finally, we show that this model can be used to detect outliers, i.e. accounts that are thought to be outside the ISIS organization but seem to be playing a key communications role and have dynamic behavior consistent with ISIS members.
Paper Link
Yunong Chen, (B.S. Mathematics, 2021)
Project: Modeling Longitudinal Behavior Dynamics Among Extremist Users in Twitter Data
Abstract: The mechanism behind the emergence of cooperation in both biological and social systems is currently not understood. In particular, human behavior in the Ultimatum game is almost always irrational, preferring mutualistic sharing strategies, while chimpanzees act rationally and selfishly. However, human behavior varies with geographic and cultural differences leading to distinct behaviors. In this paper, we analyze a social imitation model that incorporates internal energy caches (e.g., food/money savings), cost of living, death, and reproduction. We show that when imitation (and death) occurs, a natural correlation between selfishness and cost of living emerges. However, in all societies that do not collapse, non-Nash sharing strategies emerge as the de facto result of imitation. We explain these results by constructing a mean-field approximation of the internal energy cache informed by time-varying distributions extracted from experimental data. Results from a meta-analysis on geographically diverse ultimatum game studies in humans, show the proposed model captures some of the qualitative aspects of the real-world data and suggests further experimentation.
ArXiv Link, Paper Link
Steven Petrone, (B.S. Honors Computer Engineering, 2020)
Project: Modeling a Hidden Dynamical System Using Energy Minimization and Kernel Density Estimates
Abstract: In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined by an underlying hidden dynamical system. Our work is inspired by earlier work on the use of KDE to detect shipping anomalies using high-density, high-quality automated information system (AIS) data as well as our own earlier work in trajectory modeling. We focus specifically on the sparse, noisy trajectory reconstruction problem in which the data are (i) sparsely sampled and (ii) subject to an imperfect observer that introduces noise. Under certain regularity assumptions, we show that the constructed estimator minimizes a specific energy function defined over the trajectory as the number of samples obtained grows.
ArXiv Link, Paper Link
Project: Nonlinear Neuron Discriminant Functions For Alternate Deep Learning Training Algorithms
Abstract: In this work we present a novel neuron discriminant function that allows for alternate training algorithms for deep learning. The new neuron type, which we call a posynomial neuron, can be combined with linear neurons to represent functions that are exponentials when inferencing new data, but are only polynomials of the network weights. We show that the properties of these net- works can be resistant to the vanishing gradient problem. We also formulate training the network as a geometric programming problem and discuss the interesting benefits this can have over training a network with gradient descent, such as data set analysis and network interpretability. We provide a C++ library that implements both posynomial and sigmoidal networks but provides flexibility for additional novel layer types. We also provide a tensor library that has applications beyond deep learning.
Thesis Link
Justin Semonsen, (Ph.D., Rutgers University, Department of Mathematics, 2020)
Project: Opinion Dynamics in the Presence of Increasing Agreement Pressure
Abstract: In this paper, we study a model of agent consensus in a social network in the presence increasing inter-agent influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a weighted sum of internal and external behavioral pressures. We assume a weighted average update rule consistent with the classic DeGroot model and prove conditions under which a connected group of agents converge to a fixed opinion distribution, and under which conditions the group reaches consensus. We show that the update rule converges to gradient descent and explain its transient and asymptotic convergence properties. Through simulation, we study the rate of convergence on a scale-free network.
ArXiv Paper, Paper Link
Ryan Bailey, Undergraduate Operations Research, (B.S./Bowman Scholar, United States Naval Academy, 2016)
Project: On the Evolution Dynamics of Fair Strategies in the Ultimatum Game
Abstract: We construct a model of reproduction and strategic imitation in an arbitrary network of players who interact through the Ultimatum Game. In the Ultimatum Game, two people are chosen, one is the offeror and the other is the responder. The offeror is given an amount of money and offers some fraction of the money to the responder. The responder can either accept or reject the offer. If accepted, the responder gets the offered money and the offeror gets the remaining money. If rejected, neither player gets any money. We assume a society of agents have initial offer and fairness rates that change based on the success of the agent compared to other agents in the society. We also assume that all agents experience the same cost of living in the society and all agents pass on to their “children” the same proportion of their current wealth. We show that the level of wealth of each agent in a society like this is almost entirely a function of their expenses. In addition, we show that for society cost of living rates less than 0.5, both offer and fairness rates converge. Finally, we show that with cost of living rates greater than 0.5, the society engages in strategic bifurcation where two dominant strategies are used.
Joe Fitzgerald, Undergraduate Cybersciences, (B.S., United States Naval Academy, 2016)
Project: Pareto Optimal Distributed Opportunistic Sensing
Abstract: We extend prior results on a single decision maker opportunistic sensing problem to a distributed, multidecision maker setting. The original formulation of the problem considers how to opportunistically use “in-flight” sensors to maximize target coverage. In that paper, the authors show that this problem is NP-hard with a strong polynomial heuristic for a single decision maker. This paper extends this by considering a distributed decision making scenario in which multiple independent parties attempt to simultaneously engage in opportunistic sensor assignment while managing interassignment conflict. Specifically, we develop an algorithm that: 1) produces a Pareto optimal opportunistic sensor allocation; 2) requires fewer bits of communicated information than a completely centralized deconfliction approach; and 3) runs in distributed polynomial time once the individual decision makers identify their preferred (optimal) sensor allocations. We validate these claims using appropriate simulations.
Paper Link
Riley Mummah, Undergraduate Mathematics (ARL Honors Student, B.S./M.S. 2016)
Project: Swarm Control through Evolutionary Game Mechanisms
Abstract: We derive finite and infinite population spatial replicator dynamics as the fluid limit of a cellular automaton. The infinite population spatial replicator is identical to the model used by Vickers and justifies the addition of a diffusion on the replicator. The finite population form is novel and contains an intriguing nonlinear term that projects the species gradient onto the population gradient, resulting in behavior distinct from the infinite population case. We illustrate our findings with the rock-paper-scissors game and also show that the cellular automaton model can be used to understand qualitative solutions of the non-linear partial differential equations, especially with complex boundary conditions or non-differentiable starting conditions. One dimensional travelling wave solutions are derived.
ArXiv Link, Paper Link
Jim Fan, M.A. Mathematics (Ph.D., Supply Chain and Logistics, 2015)
Project: Quality Control Problem for Products in a Digital Distribution Ecosystem
Abstract: We use a control framework to analyze the profit maximization problem of digital vendors that capture market share by focusing effort on post-launch product maintenance effort. Effort influences user perception of the product and drives the revenue stream via user adoption. We show necessary and sufficient conditions for optimality, and that perceived quality declines over a product’s life cycle. This corresponds with Lehman’s 7th law of software evolution. Last, we illustrate control paths under possible market conditions, assuming linearized functions.
Paper Link , Thesis Link
Project: Control problems with vanishing Lie Bracket arising from complete odd circulant evolutionary games
Abstract: We study an optimal control problem arising from a generalization of rock-paper-scissors in which the number of strategies may be selected from any positive odd number greater than 1 and in which the payoff to the winner is controlled by a control variable γ. Using the replicator dynamics as the equations of motion, we show that a quasi-linearization of the problem admits a special optimal control form in which explicit dynamics for the controller can be identified. We show that all optimal controls must satisfy a specific second order differential equation parameterized by the number of strategies in the game. We show that as the number of strategies increases, a limiting case admits a closed form for the open-loop optimal control. In performing our analysis we show necessary conditions on an optimal control problem that allow this analytic approach to function.
ArXiv, Paper Link
Elisabeth Paulson , Undergraduate/Graduate Mathematics (Honors IUG Program, B.S/M.A., 2015)
Project: Deriving an optimally deceptive policy in two-player iterated games
Abstract: We formulate the problem of determining an optimally deceptive strategy in a repeated game framework. We assume that two players are engaged in repeated play. During an initial time period, Player 1 may deceptively train his opponent to expect a specific strategy. The opponent computes a best response. The best response is computed on an optimally deceptive strategy that maximizes the first player’s long-run payoff during actual game play. Player 1 must take into consideration not only his real payoff but also the cost of deception. We formulate the deception problem as a nonlinear optimization problem and show how a genetic algorithm can be used to compute an optimally deceptive play. In particular, we show how the cost of deception can lead to strategies that blend a target strategy (policy) and an optimally deceptive one.
Paper Link
Project: Minimum Probabilistic Finite State Learning Problem on Finite Data Sets: Complexity, Solution and Approximations
Abstract: In this paper, we study the problem of determining a minimum state probabilistic finite state machine capable of generating statistically identical symbol sequences to samples provided. This problem is qualitatively similar to the classical Hidden Markov Model problem and has been studied from a practical point of view in several works beginning with the work presented in: Shalizi, C.R., Shalizi, K.L., Crutchfield, J.P. (2002) An algorithm for pattern discovery in time series. Technical Report 02-10-060, Santa Fe Institute. http://arxiv.org/abs/cs.LG/0210025. We show that the underlying problem is NP-hard and thus all existing polynomial time algorithms must be approximations on finite data sets. Using our NP-hardness proof, we show how to construct a provably correct algorithm for constructing a minimum state probabilistic finite state machine given data and empirically study its running time.
Paper Link, Thesis Link
Project: Optimal Process Control of Symbolic Transfer Functions
Abstract: Transfer function modeling is a standard technique in classical Linear Time Invariant and Statistical Process Control. The work of Box and Jenkins was seminal in developing methods for identifying parameters associated with classical $(r,s,k)$ transfer functions.
Computing systems are often fundamentally discrete and feedback control in these situations may require discrete event systems for modeling control structures and process flow. In these situations, a discrete transfer function in the form of an accurate hidden Markov model of input/output relations can be used to derive optimally responding controllers.
In this paper, we extend work begun by the authors in identifying symbolic transfer functions for discrete event dynamic systems (Griffin et al. Determining A Purely Symbolic Transfer Function from Symbol Streams: Theory and Algorithms. In \textit{Proc. 2008 American Control Conference}, pgs. 1166-1171, Seattle, WA, June 11-13, 2008). We assume an underlying input/output system that is purely symbolic and stochastic. We show how to use algorithms for estimating a symbolic transfer function and then use a Markov Decision Processes representation to find an optimal symbolic control function for the symbolic system.
Paper Link
Project: Better Timing of Cyber-Conflict
Abstract: We construct a model of cyber-weapon deployment and attempt to determine an optimal deployment time for cyberweapons using this model. We compare and contrast our approach to that in Axelrod and Iliev (R. Axelrod and R. Iliev. Timing of cyber conflict. Proceedings of the National Academy of Science, (1322638111), 2013.), showing that our model accurately captures four real-world scenarios and has fewer quantities that are difficult to measure than the aforementioned approach. Under simplifying assumptions, we prove rules of thumb for determining when and wether a cyber-weapon should be deployed.
Paper Link
Project: Cooperation can emerge in prisoner’s dilemma from a multi-species predator prey replicator dynamic
Abstract:In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner’s dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk–Dove where both species can converge to stable (asymmetric) mixed strategies.
Paper Link
Seth Henry, Undergraduate Mathematics (B.S. Honors in Mathematics, 2014)
Project: Random Variable Toolbox
Abstract: In this paper, numerical methods for the solution of a reliability modeling problem are presented by finding the steady state solution of a Markov chain. The reliability modeling problem analyzed is that of a large system made up of two smaller systems each with a varying number of subsystems. The focus of this study is on the optimal choice and formulation of algorithms for the steady-state solution of the generator matrix for the Markov chain associated with the given reliability modeling problem. In this context, iterative linear equation solution algorithms were compared. The Conjugate-Gradient method was determined to have the quickest convergence with the Gauss-Seidel method following close behind for the relevant model structures. Current work associated with this project analyzes the convergence of the Successive Over-Relaxation method. This work is part of a larger program for simulating, processing, and analyzing stochastic processes associated with simulation of naval systems.
Paper Link
Emily Battaglia, Undergraduate Mathematics/Economics (B.S. Honors in Mathematics, 2014)
Project: Two Mathematical Models of Inequality in Economics
Abstract: The issues surrounding income inequality are a topic that has garnered a lot of attention in recent years. Since the mid-1980s, the United States has become the most unequal of the advanced industrial countries, with income inequality growing at a pace that has not been seen since the Great Depression. With increasing income inequality, the potential benefits and harms become more widely debated. Robert Reich, former United States Secretary of Labor under President Bill Clinton, argues that income inequality impedes the buying power of the middle class while simultaneously allowing the upper class to store more of its wealth, rather than spend it. This thesis studies Reich’s claim that income inequality is a fundamental detriment to growth. Income inequality is primarily studied in this thesis through two different lenses: a macro Solow model and a micro agent-based model. Once the theoretical foundation of each model is formulated, the models are used to run simulations to qualitatively examine income inequality. Our results from the Solow model show that in the presence of income inequality, the per capita capital of the wealthiest continues to rise, while the per capita capital of the middle class remains stagnant and the per capita capital of the lower class decreases. The agent-based model shows that the savings of the poor and middle classes are stagnant with inequality, while the savings of the rich continues to rise.
Thesis Link
Brian Cai, Undergraduate Mathematics (B.S. Honors in Mathematics, 2014)
Project: An Optimal Control Problem Arising from an Evolutionary Game
Abstract: We execute an integrative study of evolutionary game theory and optimal control. We first study the basics of evolutionary game theory and introduce the model that we would like to study based on the game of Rock-Paper-Scissors. We then move on to an introduction of optimal control and identify the requirements that need to be fulfilled in order for a solution to become optimal. Finally, we explore different methods of modeling the Rock-Paper-Scissors game as an optimal control problem and try to find an optimal control that minimizes the cost of the game. Various linearization schemes are attempted and the results are discussed.
Thesis Link
Michael Thein, Graduate Industrial Engineering (M.S., 2014)
Project: An In Depth Analysis of Sudoku with Focus in Integer and Constraint Programming
Abstract: We analyze sudoku in detail. We study sudoku as it pertains to computational complexity, graph coloring, and various programming methods that can be used to solve sudoku. We construct integer and constraint programs to solve sudoku problems. We conduct empirical experiments using these programs. Our results exhibit constant solve times for our integer program and varied solve times for our constraint program depending on difficulty. For easier sudokus, constraint programming performs significantly faster,but as difficulty increases, our integer program exhibited faster solve times. Additionally, we applied a heuristic. When combined with a heuristic, the constraint program solve times were significantly improved. The solve times were drastically better than those of our integer program for easy, medium, and hard difficulty, and were only slightly worse for evil difficulty. We tested to see how solve times reduced when more information is provided to our constraint solver. We observe an exponential decay function in solve times as more cells were filled in. Finally, we present future research that we wish to conduct.
Thesis Link
Ryan Tatko, Undergraduate Economics (B.S., 2013)
Project: Game Theoretic Formation of a Centrality Based Network
Abstract: We model the formation of networks as a game where players aspire to maximize their own centrality by increasing the number of other players to which they are path-wise connected, while simultaneously incurring a cost for each added adjacent edge. We simulate the interactions between players using an algorithm that factors in rational strategic behavior based on a common objective function. The resulting networks exhibit pairwise stability, from which we derive necessary stable conditions for specific graph topologies. We then expand the model to simulate non-trivial games with large numbers of players. We show that using conditions necessary for the stability of star topologies we can induce the formation of hub players that positively impact the total welfare of the network.
ArXiv Link, Paper Link
David Zach, Graduate Mathematics (M.A., 2013)
Project: Exploration of an m-player Voting Game on Discrete and Continuous Spaces
Abstract: We wish to model election politics as a game in which the candidates are the players and the objective of the game is to garner a plurality of the vote. The voters are distributed across some space, and the candidates must position themselves on this same space to appeal to as many voters as possible. The candidates are free to move about and revise their positions in their best interest to win the election. In this particular game, we are not taking into account the candidates’ own beliefs, but rather only the optimal placement of their opinions based on an existing voter distribution.
Paper Link
Christopher Cluskey, Undergraduate Computer Science and Engineering (Honors in Mathematics, 2013)
Project: Exploration of an m-player Voting Game on Discrete and Continuous Spaces
Abstract: We provide an introduction to Hidden Markov Models (HMM) followed by a description of the Causal State Splitting and Recon- struction Algorithm, a variation on a HMM construction method. We then describe how to write the CSSR Algorithm as a linear integer program and demonstrate a simple example.
Thesis Link
Shaun Lichter, Graduate Mathematics/Operations Research (M.A. [Math], 2011, Ph.D. [OR] 2013)
Project: A Game Theoretic Approach to Network Formation
Abstract: As an alternative view to the graph formation models in the statistical physics community, we introduce graph formation models using network formation through selfish competition as an approach to modeling graphs with particular topologies. We introduce a model with nonlinear payoffs that results in a pairwise stable graph with an arbitrary degree sequence. Further, we introduce a model with link bias that also shows how networks with arbitrary degree sequences may be formed as a result of selfish competition where agents have a preference for linking with one player over another. For each of these models, we present an optimization model for calculating the price of anarchy, which measures the price of decentralized link decisions by players vs centralized link decisions. We introduced coercion into the model, by considering general network constraints that may be enforced by a player that is in the game. This model also enables the modeler to analyze the effect of removing a player from the game. We further investigate a specific application of our results to collaborative oligopolies. We extend the results of Goyal and Joshi (S. Goyal and S. Joshi. Networks of collaboration in oligopoly. Games and Economic behavior, 43(1):57-85, 2003), who first considered the problem of collaboration networks of oligopolies and showed that under certain linear assumptions network collaboration produced a stable complete graph through selfish competition. We show with nonlinear cost functions and player payoff alteration that stable collaboration graphs with an arbitrary degree sequence can result. We then show conditions under which these results can be applied to spatial collaborative oligopolies.
ArXiv Link 1, ArXiv Link 2, ArXiv Link 3, ArXiv Link 4 Paper Link 1, Paper Link 2, Thesis Link
Wilmarie Rios, Graduate Industrial Engineering (M.S., 2011)
Project: Multiple sourcing for department of defense supply chains
Abstract: Tactical operations and theater distribution in military supply chains play an important role in the success of a mission. Responsive and efficient delivery of supplies is essential to maintain equipment readiness, especially in combat operations. High uncertainty in demand and supply has a direct impact in readiness levels during combat military operations. Readiness levels are sensitive to sources of disruption, primarily from shortages, but also natural disasters, weather conditions, failure of communication and information systems, political instability, and terrorist attacks. This thesis measures uncertainty in a military supply chain from the brigade unit’s perspective using exponentially distributed lead times, and investigates multiple sourcing as a strategy to improve readiness by reducing the expected supply lead time while increasing the order yield or percentage of order successfully received by brigade units. Multiple sourcing can potentially increase readiness by 70% – 90% and increasing order yield by 15%-21%. This work also proposes a process which contains past data to model supply lead times and determine the number of depots that supply a brigade unit along with the quantity of supplies to order while keeping the net order cost low. The solutions are presented using a Value Path Approach.
Thesis Link