Product Variety Strategies for Vertically Differentiated Products in Two Stage Production, Preprint, ASU, 2013 [abstract] [pdf]

Setting production capacities for production agents making selfish routing decisions, Preprint, Jacobs University 2016 [abstract] [pdf]

Kinetic models and intrinsic timescales: Simulation comparison for a 2nd order queueing model, Preprint, ASU 2016 [abstract] [pdf]

Simultaneous Workload Allocation and Capacity Dimensioning for Distributed Production Control, Procedia CIRP(2016) pp. 460-465, doi: 10.1016/j.procir.2015.12.117 [abstract] [pdf]

A kinetic model for an agent based market simulation, Networks and Heterogeneous Media, Volume 10, Number 3, September 2015, pp 527- 542, doi:10.3934/nhm.2015.10.527 [abstract] [pdf]

Integrating release and dispatch policies in production models, Networks and Heterogeneous Media, Volume 10, Number 3, September 2015, pp 511- 526, doi:10.3934/nhm.2015.10.511 [abstract] [pdf]

Feedback control for priority rules in re-entrant semiconductor manufacturing, Applied Mathematical Modelling 39 (2015) 4655 - 4664, http://dx.doi.org/10.1016/j.apm.2015.03.061 [abstract] [pdf]

Simplification of DES models of M/M/1 tandem queues by approximating WIP-dependent inter-departure times, SIMULATION published online 28 August 2014 DOI: 10.1177/0037549714546665 [abstract] [pdf]

A Population-Growth Model for Multiple Generations of Technology Products, Manufacturing & Service Operations Management 15(3), pp. 343 - 360, © 2013 INFORMS [abstract] [pdf]

Modeling production planning and transient clearing functions, Logist. Res. DOI 10.1007/s12159-012-0087-8 (2012). [abstract] [pdf]

The production planning problem: Clearing functions, variable leads times, delay equations and partial differential equations in: Decision Policies for Production Networks, D. Armbruster, K.G. Kempf (eds), p. 289 - 303, Springer Verlag (2012). [abstract] [pdf]

Continuous Dynamic Models, Clearing Functions, and Discrete-Event Simulation in Aggregate Production Planning in: New Directions in Informatics, Optimization, Logistics, and Production , TutORials in Operations Research ONLINE, Pitu Mirchandani, Tutorials Chair and Volume Editor J. Cole Smith, Series ed., 103126 (2012). [abstract] [pdf]

A scalar conservation law with discontinuous flux for supply chains with finite buffers, SIAM J. Appl. Math. {\bf 71 (4), p 1070 - 1087 (2011). [abstract] [pdf]

Control of continuum models of production systems, IEEE Trans. Automatic Control {\bf 55} (11), p 2511 - 2526 (2010). [abstract] [pdf]

A Hyperbolic Relaxation Model for Product Flow in Complex Production Networks, Discrete and continuous dynamical systems Supplement 2009, pp. 790 - 799 [abstract] [pdf]

Controlling a re-entrant manufacturing line via the push-pull point, International Journal of Production Research, 46 (16), 4521 - 4536 (2008) [abstract] [pdf]

Kinetic and fluid model hierarchies for supply chains supporting policy attributes, Bulletin of the Inst. Math., Academica Sinica 2:433-460, 2007. [abstract] [pdf]

Bucket Brigades with Worker Learning, European Journal of Operational Research, 176, 264- 274 (2007) [ abstract] [pdf]

Multiscale analysis of re- entrant production lines: An equation-free approach, Physica A, 363(1), 1-13, 2006 [abstract] [pdf]

A Model for the Dynamics of large Queuing Networks and Supply Chains, SIAM J. Applied Mathematics 66(3) pp. 896-920. 2006 [abstract] [pdf]

Bucket Brigades when Worker Speeds do not Dominate Each Other Uniformly, European Journal of Operational Research, 172,(1), 213-229, 2006 [ abstract] [pdf]

A continuum model for a re-entrant factory, Operations research 54(5), 933-950, 2006 [abstract] [pdf]

Thermalized kinetic and fluid models for re-entrant supply chains, SIAM J. on Multiscale modeling and Simulation, 3(4), pp 782 - 800, (2005) [abstract] [pdf]

Kinetic and fluid model hierarchies for supply chains SIAM Multiscale Model. Simul. 2(1), pp 43-61 2004 [abstract] [pdf]

Control and Synchronization in Switched Arrival Systems, Chaos 13 (1), 128-137 (2003) [abstract] [pdf]

Periodic orbits in a class of re-entrant manufacturing systems, Mathematics of Operations Research 25(4), p. 708 - 725, 2000 [abstract] [pdf]

Social Optima of Need-Based Transfers, Preprint, ASU 2016 [abstract] [pdf]

Elastic and inelastic collisions of swarms, Physica D, 12/2016, http://dx.doi.org/10.1016/j.physd.2016.11.008 [abstract] [pdf]

Swarming in bounded domains, Physica D, 12/2016, http://dx.doi.org/10.1016/j.physd.2016.11.009 [abstract] [pdf]

Towards the Optimal Balance of Centralized and Decentralized Control in Complex Production Systems, Preprint, Jacobs University 2016 [abstract] [pdf]

Setting production capacities for production agents making selfish routing decisions, Preprint, Jacobs University 2016 [abstract] [pdf]

Simultaneous Workload Allocation and Capacity Dimensioning for Distributed Production Control, Procedia CIRP(2016) pp. 460-465, doi: 10.1016/j.procir.2015.12.117 [abstract] [pdf]

An agent-based modeling optimization approach for understanding behavior of engineered complex adaptive systems, Socio-Economic Planning Sciences (2016), http://dx.doi.org/10.1016/j.seps.2016.04.003 [abstract] [pdf]

An agent model for the high end gamers market, Advances in Complex Systems Vol. 16 (2013) 1350028 (33 pages), doi = {10.1142/S0219525913500288} [abstract] [pdf]

Node Survival in Networks under Correlated Attacks, PLoS ONE 10(5): e0125467. doi:10.1371/journal. pone.0125467 [abstract] [pdf]

Need-based transfers on a network: a model of risk-pooling in ecologically volatile environments, Evolution & Human Behavior, 36, 4, pp. 265 - 273, (2015) [abstract] [pdf]

Basketball Teams as Strategic Networks PLoS ONE 7(11) (2012): e47445. doi:10.1371/journal.pone.0047445 [abstract] [pdf]

Localized Solutions in Parametrically Driven Pattern Formation , Phys. Rev. E 68, 016213 (2003) [abstract] [pdf]

Dynamics of polar reversals in spherical dynamos, Proceedings of the Royal Society A, London, 459, 577-596 (2003). [ abstract] [pdf]

Three level signal transduction cascades lead to reliably timed switches, Journal of Theoretical Biology 361 (2014) 69 - 80, [abstract] [pdf]

Basketball Teams as Strategic Networks PLoS ONE 7(11) (2012): e47445. doi:10.1371/journal.pone.0047445 [abstract] [pdf]

Design of Robust Distribution Networks Run by Third Party Logistics Service Providers, Advances in Complex Systems, 15 (5) (2012) 1150024 [abstract] [pdf]

Structural Properties of third-party logistics networks, in: Proceedings of the 2nd International Conference on Dynamics in Logistics (LDIC 2009), Ed. H.-J. Kreowski et al, Bremen, 2010. [abstract] [doc]

Information and material flows in complex networks, short survey, Physica A 363(1), Pages xi-xvi, 2006 [abstract] [pdf]

Autonomous Control of Production Networks using a Pheromone Approach, Physica A, 363(1), 104-114, 2006 [abstract] [pdf]

Does synchronization of networks of chaotic maps lead to control?, Chaos 15 014101, 2005 [abstract] [pdf]

Noisy Heteroclinic networks, Chaos 13 (1), 71-79 (2003) [ abstract] [pdf]

Perturbed on-off intermittency, Phys. Rev. E. 64 016220-1 - 9, (2001) [ abstract] [pdf]

Noise and O(1) Amplitude Effects on Heteroclinic Cycles, Chaos, 9(2) p.499-506, (1999) [abstract] [pdf]

Analyzing the dynamics of cellular flames [abstract]

Symmetry and the Karhunen Loéve analysis [abstract]

Three level signal transduction cascades lead to reliably timed switches, Journal of Theoretical Biology 361 (2014) 69 - 80, [abstract] [pdf]

Time dependent Michaelis-Menten Equations for Open Enzyme Networks, n Engineering of Chemical Complexity II, eds. A.S. Mikhailov and G. Ertl World Scientific, Singapore, 2014 [abstract] [pdf]

Evolution of uncontrolled proliferation and the angiogenic switch in cancer, Mathematical Biosciences and Engineering 9(4), 843- 876, (2012). [abstract] [pdf]

Noise and seasonal effects on the dynamics of plant-herbivore models with monotonic plant growth functions, International Journal of Biomathematics, 4(3), p 255 - 274, (2011) [abstract] [pdf]

Dispersal effects on a discrete two- patch model for plant-insect interactions, Journal of Theoretical Biology 268, 84-97 (2011). [abstract] [pdf]

Dynamic simulations of single molecule enzyme networks, J. Phys. Chem. B, 2009, 113 (16), 5537-5544 [abstract] [pdf]

Dynamics of a plant- herbivore model. Journal of Biological Dynamics, 2(2), 89-101, 2008 [abstract] [pdf]

On the stability of queueing networks and fluid models, preprint 2010 [abstract] [pdf]

Biologically inspired mutual synchronization of manufacturing machines, preprint 2010 [abstract] [pdf]

Need based transfers (NBTs) are actions to compensate losses after disasters. They are based on shared values and reflect the understanding of the random nature of disasters. To study them, agent based simulations are performed whereby individuals that fall below a threshold (e.g. welfare threshold) will receive help from a single individual who is rich enough to help within a network of connections. An NBT policy acts as risk pooling and its rules have a comprehensive impact on a whole community and its economy: It is found that for short time horizons, optimizing the survival rate of a community is similar to a cutting-stock optimization problem, leading to a policy that closely matches need and giving ability between a recipient and a donor. However, in the long-term this policy leads to the growth of a highly vulnerable subgroup of the population and thus ultimately to low survival rates. It is shown that, on such a long time horizon, a policy that asks the richest potential donor leads to a log-normal wealth distribution that becomes optimal for the survival rate. When individuals make decisions how to build up an insurance network, it is shown that an optimal network has low variance in the node degrees leading to equal sharing of the risk and benefit of such an NBT insurance relationship. Finally, a quasi-equilibrium simulation model is derived that allows for the study of time-dependent and slowly evolving NBT-economies and policies. Keywords: Risk pooling, wealth distributions, agent based simulations, mutual help networks

Kinetic models of stochastic production flows can be expanded into deterministic moment equations and thus approximated with appropriate closures. A second order model for the product density and the product speed has previously been proposed. A systematic analysis comparing simulations of the partial differential equations (PDE) with discrete event simulations (DES) is performed. Specifically, factory production is modeled as an M/M/1 queue where the arrival process is a non-homogeneous Poisson process. Three fundamental scenarios for such a time dependent influx are studied: An instant step up/step down of the arrival rate, an exponential step up/step down and periodic variation of the average arrival rate. It is shown that the second order model in general yields significant improvements over the first order model. Adding diffusion into the PDE further improves the agreement in particular for queues with low utilization. The analysis also points to fundamental open issues regarding kinetic models of time dependent agent based simulations. Memory effects and the possibility of resonance in deterministic models are caused by intrinsic timescales of the PDE that are not present in the original stochastic processes. 2010 Mathematics Subject Classification. 60K35, 90B30, 93A30. Key words and phrases. Kinetic models, Production systems, Simulations, 2nd order models, transients.

Scattering interactions of swarms in potentials that are generated by an attraction–repulsion model are studied. In free space, swarms in this model form a well-defined steady state describing the translation of a stable formation of the particles whose shape depends on the interaction potential. Thus, the collision between a swarm and a boundary or between two swarms can be treated as (quasi)-particle scattering. Such scattering experiments result in internal excitations of the swarm or in bound states, respectively. In addition, varying a parameter linked to the relative importance of damping and potential forces drives transitions between elastic and inelastic scattering of the particles. By tracking the swarm’s center of mass, a refraction rule is derived via simulations relating the incoming and outgoing directions of a swarm hitting the wall. Iterating the map derived from the refraction law allows us to predict and understand the dynamics and bifurcations of swarms in square boxes and in channels Keywords: Swarm models; Swarm scattering; Swarm reflection; Attraction - repulsion model

The Vicsek model is a prototype for the emergence of collective motion. In free space, it is characterized by a swarm of particles all moving in the same direction. Since this dynamic does not include attraction among particles, the swarm, while aligning in velocity space, has no spatial coherence. Adding specular reflection at the boundaries generates global spatial coherence of the swarms while maintaining its velocity alignment. We investigate numerically how the geometry of the domain influences the Vicsek model using three type of geometry: a channel, a disk and a rectangle. Varying the parameters of the Vicsek model (e.g. noise levels and influence horizons), we discuss the mechanisms that generate spatial coherence and show how they create new dynamical solutions of the swarming motions in these geometries. Several observables are introduced to characterize the simulated patterns (e.g. mass profile, center of mass, connectivity of the swarm). Keywords: Swarm models; Agent simulations; Dynamics of swarms

Traditionally, the capacity dimensioning step within the manufacturing system design process takes a known and fixed distribution of production flow across path alternatives to derive capacity demand based on a desired target utilization level. Setting target levels for machine utilization provides limits on throughput-times and allows to provide capacity buyers against changes in the production mix. In this contribution, we transfer this rationale into the world of Industry 4.0, where Cyber-Physical Systems can make autonomous and selfish routing decisions. Under this new framework, non-cooperative agents make decisions based on the capacity allocation and the decisions of all other agents, thus creating a feedback between flow and capacity distribution that makes existing methods for capacity dimensioning inapplicable. We use methods and insight from algorithmic game theory and operations research to investigate the capacity dimensioning process in this context. We proof properties of the throughput-time optimal allocation of production capacity under fixed target utilization for important queue classes. Our findings not only provide a quantitative, easy to operationalize tool for production system designers, but explore a trade-off between cost and flexibility that arises naturally in this regime. Keywords: Capacity Dimensioning; Cyber-Physical Systems; Industry 4.0; Algorithmic Game Theory

Across disciplines, the devolution of control authority is perceived as a promising response to increasing complexity. It is an expression of a new, complexity-driven understanding of systems in many fields of science. In production control, new concepts like the (Industrial) Internet-of-Things, Smart Factories, etc. seek to apply intelligent agents to provide a “bottom-up” control of manufacturing systems. Here, as in other disciplines, fundamental questions about the role and mechanisms of leaders and leadership in such distributed system are yet unanswered. Using a minimal model and drawing inspiration from complex leadership theory, we investigate the long hold tenet about the existence of an optimal combination of local autonomy and central control. We provide further insight into the mechanisms of coordination in complex systems by investigating the evolution of solution patterns and the flow of information in the network. By applying a forward model, we translate our statements about the coordination process can be translated into actual system performance. We compare our findings with propositions from literature, both on organization science and on production control literature. While using production control as motivation and key field of application, our paper is beneficial to researchers in many disciplines exploring the “control vs. autonomy” duality. Keywords: coordination, simulation, networking systems, interdisciplinary, organization, control

Capacity dimensioning in production systems is an important task within strategic and tactical production planning which impacts system cost and performance. Traditionally capacity demand at each work system is determined from standard operating processes and estimated production flow rates, accounting for a desired level of utilization or required throughput times. However, for distributed production control the flows across multiple possible production paths are not known a priori. In this contribution, we use methods from algorithmic game-theory and trac-modeling to predict the flows, and hence capacity demand, across work systems based on the available production paths and desired output rates, assuming non-cooperative agents with global information. We propose an iterative algorithm that converges simultaneously to a feasible capacity distribution and a flow distribution over multiple paths that follows Wardrop’s first principle. We demonstrate our method on models of real-world production networks. Keywords: Agent Based Manufacturing Control, Capacity Dimensioning, Resource Requirements Problem, Algorithmic Game Theory

Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis–Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades. Keywords: MAP-kinase network, Michaelis–Menten equations, Time-dependent ODEs

The reduction of mass-action equations for substrate-enzyme re- actions with time dependent inflows to Michaelis-Menten equations is stud- ied. A mathematically rigorous singular perturbation scheme is used. Time dependent Michaelis-Menten equations are derived as the O(1) approxima- tion in the perturbation expansion based on the same small parameter that leads to a valid expansion for closed systems. This justifies the practice to use the Michaelis-Menton approximation in time dependent systems and supports its use in networked systems. Error propagation of the approximation scheme in complex reaction networks is discussed. Error bounds are developed that suggest small errors for finite and fast signal propagation in cascading systems analogous to signal transduction cascades. Error bounds in the general case remain an open problem.

The objective of this study is to present a formal agent-based modeling (ABM) platform that enables managers to predict and partially control patterns of behaviors in certain engineered complex adaptive systems (ECASs). The approach integrates social networks, social science, complex systems, and diffusion theory into a consumer-based optimization and agent-based modeling (ABM) platform. Demonstrated on the U.S. electricity markets, ABM is integrated with normative and subjective decision behavior recommended by the U.S. Department of Energy (DOE) and Federal Energy Regulatory Commission (FERC). Furthermore, the modeling and solution methodology address shortcomings in previous ABM and Transactive Energy (TE) approaches and advances our ability to model and understand ECAS be- haviors through computational intelligence. The mathematical approach is a non-convex consumer- based optimization model that is integrated with an ABM in a game environment. Keywords: Agent-based modeling and simulation, Complex adaptive systems, Non-linear complexity, US electricity markets, Demand response, Transactive energy

Understanding the driving forces in the markets of their products is a basic necessity for any business. Quantitative models are either aggregated over large market segments or restricted to utility models of an individual’s buying decision. While the aggregate models acknowledge that customer interactions are important they do not model them and hence have no way to adjust their model to changing business environments. This paper bridges the gap between individual decisions and the overall market behavior using agent based simulations to model the sales of computer chips in the high-end gamers market. The simulation environment is dynamic and models the succession of 19 products introduced over a 40 month time horizon which includes the recession of 2008 - 2010. Simulated sales are compared to actual sales data and are used to adjust the parametrization of the agents and their environment. We found that only two agent parameters are sufficient to obtain a very reasonable fit between simulations and data: The amount of money available for the gaming hobby and a parameter related to the gaming success of the high-end gamers. Keywords: Market modeling; semiconductor market; multiple sales generations.

We study the product variety and pricing decisions in a supply chain that includes two competing producers who plan to work with middle-tier companies. End customers are characterized by the amount of money they are willing to pay for different quality levels. Products reach the end customers via assembly companies positioned in the middle-tier between the producers and the end customers. We analyze the influence of the assembly companies on the market equilibrium. We consider a multi-leader Stackelberg game between the producers and assembly companies, and compare different supply chain configurations: direct-shipping with no middle-tier, monopoly with a single assembly company, and duopoly with two assembly companies. We find that in the Nash equilibrium producers and assembly companies should choose to differentiate their product offering. The presence of the middle-tier assembly companies can reduce the intensity of competition in the supply chain and increase the revenue for the producer of the low-end product whereas the producer of the high-end product prefers either the direct shipping or a duopoly with product differentiation depending on the quality levels of the products. We show that product differentiation is not always the equilibrium strategy for the assembly companies. Key words : Product variety, Vertical differentiation, Game theory, Supply chain.

Need-based transfers are a widespread form of human cooperation across cultures that enhance survival in mar- ginal environments. Examples include central place food sharing among foragers and stock friendships among pastoralists. Previous models have demonstrated that such systems lead to higher rates of herd survival under volatile ecological conditions, such as those experienced by the Maasai of East Africa. The Maasai use a need- based transfer system called osotua that leads to risk pooling. Here we implement osotua-style asking and giving rules on a network in order to understand which network features promote herd survival. We find that (1) great- er network size increases herd survival when individuals selectively ask their wealthiest partner for livestock but not when they ask a partner at random, (2) greater network connectedness improves herd survival regardless of whether individuals ask their wealthiest partner or ask a partner at random, (3) greater network heterogeneity leads to higher herd survival with selective asking of wealthy partners and decreases herd survival for random asking. In general, selective asking of wealthy partners is associated with higher rates of herd survival. We also examined the features of survival networks in order to understand the characteristics of the networks that result from 50 simulated years of osotua-style sharing under ecologically volatile conditions and the elimination of individuals who do not stay above sustainability threshold. These results will help inform further fieldwork on the need-based transfer systems and increase our understanding of features of sharing networks that enable risk pooling. Simple decentralized sharing rules can be highly effective for pooling risk, suggesting that complex cultural institutions may not be necessary for expansion into ecologically marginal environments. Keywords: Risk pooling, Sharing, Cooperation, Social insurance

We study the interplay between correlations, dynamics, and networks for repeated attacks on a socio-economic network. As a model system we consider an insurance scheme against disasters that randomly hit nodes, where a node in need receives support from its network neighbors. The model is motivated by gift giving among the Maasai called Osotua. Survival of nodes under different disaster scenarios (uncorrelated, spatially, temporally and spatio-temporally correlated) and for different network architectures are studied with agent- based numerical simulations. We find that the survival rate of a node depends dramatically on the type of correlation of the disasters: Spatially and spatio-temporally correlated disasters increase the survival rate; purely temporally correlated disasters decrease it. The type of correlation also leads to strong inequality among the surviving nodes. We introduce the concept of disaster masking to explain some of the results of our simulations. We also analyze the subsets of the networks that were activated to provide support after fifty years of random disasters. They show qualitative differences for the different disaster scenarios measured by path length, degree, clustering coefficient, and number of cycles.

A kinetic model for a specific agent based simulation to generate the sales curves of successive generations of high-end computer chips is developed. The resulting continuum market model consists of transport equations in two variables, representing the availability of money and the desire to buy a new chip. In lieu of typical collision terms in the kinetic equations that discontinuously change the attributes of an agent, discontinuous changes are initiated via boundary conditions between sets of partial differential equations. A scaling analysis of the transport equations determines the different time scales that constitute the market forces, characterizing different sales scenarios. It is argued that the resulting model can be adjusted to generic markets of multi-generational technology products where the innovation time scale is an important driver of the market. Keywords: Kinetic theory, agent based simulations, market models, multi- generational technology products.

Aggregate production planning for highly re–entrant production processes is typically generated by finding optimal release rates based on clear- ing function models. For production processes with very long cycle times, like in semiconductor production, dispatch policies are used to cover short term fluctuations. We extend the concept of a clearing function to allow control over both, the release rates and priority allocations in re-entrant production. This approach is used to improve the production planning problem using combined release and the allocation dispatch policy. The control parameter for priority allocation, called the push-pull point (PPP), separates the beginning of the factory which employs a push policy from the end of the factory, which uses a pull policy. The extended clearing function model describes the output of the factory as a function of the work in progress (wip) and the position of the PPP. The model’s qualitative behavior is analyzed. Numerical optimization results are compared to production planning based only on releases. It is found that controlling the PPP significantly reduces the average wip in the system and hence leads to much shorter cycle times. Keywords: Production planning, dispatch control, partial differential equations, re-entrant production.

Typical semiconductor production is re-entrant and hence requires priority decisions when parts compete for production capacity at the same machine. A standard way to run such a factory is to start to plan and to finish according to demand. Often this results in a push policy where early production steps have priority over later production steps at the beginning of the production line and a pull policy where later steps have priority at the end of the production line. The point where the policies switch is called the push–pull-point (PPP). We develop a control scheme based on moving the PPP in a continuum model of the production flow. We show that this control scheme significantly reduces the mismatch between demand and production output. The success of the control scheme as a function of the frequency of control action is analyzed and optimal times between control actions are determined. Keywords: Re-entrant production, Feedback control, Partial differential equations, Dispatch policy control

This paper presents two algorithms to analytically approximate work in process (WIP)-dependent inter-departure times for tandem queues composed of a series of M/M/1 systems. The first algorithm is used for homogeneous tandem queues, the second for such with bottlenecks. Both algorithms are based on the possible combinations of distributing the WIP on the queues. For each combination the time to the next departure is estimated. A weighted average of all estimated times of each WIP level is calculated to get the expected mean inter-departure time. The generated inter- departure times are used in a simple model of the tandem queue. The inter-departure times, the average WIP and aver- age cycle time of the tandem queue and the simple model are compared in several tandem queue parameterizations. Results show only a small error between the simple model and the tandem queue, rendering this approach applicable in many applications. Keywords: discrete event simulation, simplification, WIP-dependent inter-departure times

In this paper, we consider the demand for multiple successive generations of products and develop a population growth model that allows demand transitions across multiple product generations, and takes into consideration the effect of competition. We propose an iterative descent method for obtaining the parameter estimates and the covariance matrix, and show that the method is theoretically sound and overcomes the difficulty that the units-in-use population of each product is not observable. We test the model on both simulated sales data and Intel’s high-end desktop processor sales data. We use two alternative specifications for product strength in this market – performance, and performance/price ratio. The former demonstrates better fit and forecast accuracy, likely due to the low price-sensitivity of this high-end market. In addition, the parameter estimate suggests that, for the innovators in the diffusion of product adoption, brand switchings are more strongly influenced by product strength than within-brand product upgrades in this market. Our results indicate that compared to the Bass model, the Norton-Bass model, as well as the Jun-Park choice-based diffusion model, our approach is a better fit for strategic forecasting which occurs many months or years before the actual product launch. Keywords: Product Transitions, Forecasting, Multiple-generation Demand Model, Diffusion

Keywords: Supply chains, conservation laws, asymptotics.

We present a model hierarchy for queuing networks and supply chains, analogous to the hierarchy leading from the many body problem to the equations of gas dynamics. Various possible mean field models for the interaction of individual parts in the chain are presented. For the case of linearly ordered queues the mean filed models and fluid approximations are verified numerically.

Standard stochastic models for supply chains predict the throughput time (TPT) of a part from a statistical distribution, which is dependent on the Work in Progress (WIP) at the time the part enters the system. So, they try to predict a transient response from data which are sampled in a quasi steady state situation. For re- entrant supply chains this prediction is based on insufficient information, since subsequent arrivals can dramatically change the TPT. This paper extends these standard models, by introducing the concept of a stochastic phase velocity which dynamically updates the TPT estimate. This leads to the concepts of temperature and diffusion in the corresponding kinetic and fluid models for supply chains.

Keywords: Re-entrant supply chains, Traffic flow models, Boltzmann equation, Chapman-Enskog, Fluid limits.

High-volume, multistage continuous production flow through a re-entrant factory is modeled through a conservation law for a continuous-density variable on a continuous-production line augmented by a state equation for the speed of the production along the production line. The resulting nonlinear, nonlocal hyperbolic conservation law allows fast and accurate simulations. Little’s law is built into the model. It is argued that the state equation for a re-entrant factory should be nonlinear. Comparisons of simulations of the partial differential equation (PDE) model and discrete-event simulations are presented. A general analysis of the model shows that for any nonlinear state equation there exist two steady states of production below a critical start rate: A high-volume, high-throughput time state and a low-volume, low-throughput time state. The stability of the low-volume state is proved. Output is controlled by adjusting the start rate to a changed demand rate. Two linear factories and a re-entrant factory, each one modeled by a hyperbolic conservation law, are linked to provide proof of concept for efficient supply chain simulations. Instantaneous density and flux through the supply chain as well as work in progress (WIP) and output as a function of time are presented. Extensions to include multiple product flows and preference rules for products and dispatch rules for re-entrant choices are discussed.

Subject classifications: production/scheduling: approximations; simulations: efficiency; mathematics.

A chaotic model of a production flow called the switched arrival system is extended to include switching times and maintenance. The probability distribution of the chaotic return times is calculated. Scheduling maintenance, loss of production due to switching and control of the chaotic dynamics is discussed. A coupling parameter to couple switched arrival systems serially, based on lost production, is identified. Simulations of three parallel and three serial levels were performed. Global synchronization of the switching frequencies between serial levels is achieved. An analytic model allows to predict the self balancing properties of the serial system.

A two worker bucket brigade is studied where one worker has a constant speed over the whole production line and the other is slower over the first portion and faster over the second portion of the line. We analyze the dynamics and throughput of the bucket brigade under two different assumptions: (i) workers can pass each other, and (ii) workers are blocked when an upstream worker runs into a downstream worker. We show that a slight modification of the bucket brigade will always lead to a self organizing production line. The bucket brigade either balances to a fixed point or settles into a period-two orbit. Insights for the management of the bucket brigades for the various scenarios are discussed using results on the throughput performance and self-organization. Extensions to multiple skill levels and more workers are outlined.

The dynamics and throughput of a bucket brigade production system is studied when workers' speeds increase due to learning. It is shown that, if the rules of the bucket brigade system allow a re-ordering of its workers then the bucket brigade production system is very robust and will typically rebalance to a self-organizing optimal production arrangement. As workers learn only those parts of the production line that they work on, the stationary velocity distribution for the workers of a stable bucket brigade is non-uniform over the production line. Hence, depending on the initial placement of the workers, there are many different stationary velocity distributions. It is shown that all the stationary distributions lead to the same throughput.

Queue changes associated with each step of a manufacturing system are modeled by constant vector fields (fluid model of a queueing network). Observing these vector fields at fixed events reduces them to a set of piecewise linear maps. It is proved that these maps show only periodic or eventually periodic orbits. An algorithm to determine the period of the orbits is presented. The dependence of the period on the processing rates is shown for a 3(4)-step, 2-machine problem.

The Mathieu partial differential equation is analyzed as a prototypical model for pattern formation due to parametric resonance. After averaging and scaling it is shown to be a perturbed Nonlinear Schr\"{o}dinger Equation. Adiabatic perturbation theory for solitons is applied to determine which solitons of the NLS survive the perturbation due to damping and parametric forcing. Numerical simulations compare the perturbation results to the dynamics of the Mathieu PDE. Stable and weakly unstable soliton solutions are identified. They are shown to be closely related to oscillons found in parametrically driven sand experiments.

Structurally stable heteroclinic cycles (SSHC) are proposed as the mathematical structures that are responsible for the reversals of dipolar magnetic fields in spherical dynamos. The existence of SSHCs involving dipolar magnetic fields generated by convection in a spherical shell for a nonrotating sphere is rigorously proven. The possibility of SSHCs in a rotating shell is proposed and their existence in a low dimensional model of the magnetohydrodynamic equations is numerically confirmed. The resulting magnetic time series shows a dipolar magnetic field, aligned with the rotation axis that intermittently becomes unstable, changes the polar axis, starts rotating, disappears completely and eventually reestablishes itself in its original or opposite direction, chosen randomly.

We consider networks of chaotic maps with different network topologies. In each case, they are coupled in such a way as to generate synchronized chaotic solutions. By using the methods of control of chaos we are controlling a single map into a predetermined trajectory. We analyze the reaction of the network to such a control. Specifically we show that a line of 1-d logistic maps that are unidirectionally coupled can be controlled from the first oscillator whereas a ring of diffusively coupled maps cannot be controlled for more than 5 maps. We show that rings with more elements can be controlled if every third map is controlled. The dependence of unidirectionally coupled maps on noise is studied. The noise level leads to a finite synchronization lengths for which maps can be controlled by a single location. A 2-d lattice is also studied.

A basic requirement for on-off intermittency to occur is that the system possesses an invariant subspace. We address how on-off intermittency manifests itself when a perturbation destroys the invariant subspace. In particular, we distinguish between situations where the threshold for measuring the on-off intermittency in numerical or physical experiments is much larger than or is comparable to the size of the perturbation. Our principal result is that as the perturbation parameter increases from zero, a metamorphosis in on-off intermittency occurs in the sense that scaling laws associated with physically measureable quantities change abruptly. A geometric analysis, a random-walk model, and numerical trials support the result.

The dynamics of structurally stable heteroclinic cycles connecting fixed points with one dimensional unstable manifolds under the influence of noise is analyzed. Fokker Planck equations for the evolution of the probability distribution of trajectories near heteroclinc cycles are solved. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained.

Keywords: dynamical systems, heteroclinic cycles, noise-induced dynamics, intermittency.

The influence of small noise on the dynamics of heteroclinic networks is studied, with a particular focus on noise-induced switching between cycles in the network. Three different types of switching are found, depending on the details of the underlying deterministic dynamics: random switching between the heteroclinic cycles determined by the linear dynamics near one of the saddle points, noise induced stability of a cycle, and intermittent switching between cycles. All three responses are explained by examining the size of the stable and unstable eigenvalues at the equilibria.

Keywords: dynamical systems, heteroclinic cycles, noise-induced dynamics, intermittency.

Keywords: Complex systems; Many-particle systems; Multi-agent models; Network theory; Information flows; Socio- and econo-physics; Traffic physics; Biophysics; Biologistics.

Keywords: Production networks; Autonomous control; Pheromones; Discrete-event simulation models; Fluid models.

A third party logistic provider operates a distribution network with minimal control over supply and demand. The operation is characterized by three levels: a strategic level that includes the location and sizing of warehouse, a tactical level that determines the links between customers, warehouses and producers and an operational level that determines the size of the flows through the links at any given time. An algorithm to optimize the operational level is determined for a given network structure. Starting with a fully connected network, optimal operations are determined. A reduced network is found by deleting the least used links until the operational costs increase dramatically. The topological structures of the reduced network as a function of backlog and transportation costs are determined..

We asked how team dynamics can be captured in relation to function by considering games in the first round of the NBA 2010 play-offs as networks. Defining players as nodes and ball movements as links, we analyzed the network properties of degree centrality, clustering, entropy and flow centrality across teams and positions, to characterize the game from a network perspective and to determine whether we can assess differences in team offensive strategy by their network properties. The compiled network structure across teams reflected a fundamental attribute of basketball strategy. They primarily showed a centralized ball distribution pattern with the point guard in a leadership role. However, individual play-off teams showed variation in their relative involvement of other players/positions in ball distribution, reflected quantitatively by differences in clustering and degree centrality. We also characterized two potential alternate offensive strategies by associated variation in network structure: (1) whether teams consistently moved the ball towards their shooting specialists, measured as “uphill/downhill” flux, and (2) whether they distributed the ball in a way that reduced predictability, measured as team entropy. These network metrics quantified different aspects of team strategy, with no single metric wholly predictive of success. However, in the context of the 2010 play-offs, the values of clustering (connectedness across players) and network entropy (unpredictability of ball movement) had the most consistent association with team advancement. Our analyses demonstrate the utility of network approaches in quantifying team strategy and show that testable hypotheses can be evaluated using this approach. These analyses also highlight the richness of basketball networks as a dataset for exploring the relationships between network structure and dynamics with team organization and effectiveness.

We consider a third party logistics service provider (LSP), who faces the problem of distributing different products from suppliers to consumers having no control on supply and demand. In a third party set-up, the operations of transport and storage are run as a black box for a fixed price. Thus the incentive for an LSP is to reduce its operational costs. The objective of this paper is to find an efficient network topology on a tactical level, which still satisfies the service level agreements on the operational level. We develop an optimization method, which constructs a tactical network topology based on the operational decisions resulting from a given model predictive control (MPC) policy. Experiments suggest that such a topology typically requires only a small fraction of all possible links. As expected, the found topology is sensitive to changes in supply and demand averages. Interestingly, the found topology appears to be robust to changes in second order moments of supply and demand distributions

Video data from experiments on the dynamics of two dimensional flames are analyzed. The Karhunen Loéve (KL-) analysis is used to identify the dominant spatial structures and their temporal evolution for several dynamical regimes of the flames. A data analysis procedure to extract and process the boundaries of flame cells is described. It is shown how certain spatial structures are associated with certain temporal events. The existence of small scale, high frequency, turbulent background motion in almost all regimes is revealed.

The Karhunen Loéve (K-L) analysis is widely used to
generate low dimensional dynamical systems,
which have the same low dimensional attractors as
some large scale simulations of PDEs.
If the PDE is symmetric with respect to a symmetry group `G`,
the dynamical system has to be equivariant under `G`
to capture the full phase space.
It is shown that symmetrizing the `K-L` eigenmodes
instead of symmetrizing the data leads to considerable computational savings,
if the K-L analysis is done in the snapshot method.
The feasability of the approach is demonstrated
with an analysis of Kolmogorov flow.

The major goal of evolutionary oncology is to explain how malignant traits evolve to become cancer “hallmarks.” One such hallmark—the angiogenic switch—is difficult to explain for the same reason altruism is difficult to explain. An angiogenic clone is vulnerable to “cheater” lineages that shunt energy from angiogenesis to proliferation, allowing the cheater to outcompete cooperative phenotypes in the environment built by the cooperators. Here we show that cell- or clone-level selection is sufficient to explain the angiogenic switch, but not because of direct selection on angiogenesis factor secretion— angiogenic potential evolves only as a pleiotropic afterthought. We study a multiscale mathematical model that includes an energy management system in an evolving angiogenic tumor. The energy management model makes the counterintuitive prediction that ATP concentration in resting cells increases with increasing ATP hydrolysis, as seen in other theoretical and empirical studies. As a result, increasing ATP hydrolysis for angiogenesis can increase proliferative potential, which is the trait directly under selection. Intriguingly, this energy dynamic allows an evolutionary stable angiogenesis strategy, but this strategy is an evolutionary repeller, leading to runaway selection for extreme vascular hypo- or hyperplasia. The former case yields a tumor-on-a- tumor, or hypertumor, as predicted in other studies, and the latter case may explain vascular hyperplasia evident in certain tumor types.

We formulate a simple host-parasite type model to study the interaction of certain plants and herbivores. Our two dimensional discrete time model utilizes leaf and herbivore biomass as state variables. The parameter space consists of the growth rate of the host population and a parameter describing the damage inflicted by herbivores. We present insightful bifurcation diagrams in that parameter space. Bistability and a crisis of a strange attractor suggest two control strategies: Reducing the population of the herbivore under some threshold or increasing the growth rate of the plant leaves.

We formulate general plant-herbivore interaction models with monotone plant growth functions (rates). We study the impact of monotone plant growth functions in general plant-herbivore models on their dynamics. Our study shows that all monotone plant growth models generate a unique interior equilibrium and they are uniform persistent under certain range of parameters values. However, if the attacking rate of herbivore is too small or the quantity of plant is not enough, then herbivore goes extinct. Moreover, these models lead to noise sensitive bursting which can be identified as a dynamical mechanism for almost periodic outbreaks of the herbivore infestation. Montone and non-monotone plant growth models are contrasted with respect to bistability and crises of chaotic attractors.

Along with the growth of technologies allowing accurate visualization of biochemical reactions to the scale of individual molecules has arisen an appreciation of the role of statistical fluctuations in intracellular biochemistry. The stochastic nature of metabolism can no longer be ignored. It can be probed empirically, and theoretical studies have established its importance. Traditional methods for modeling stochastic biochemistry are derived from an elegant and physically satisfying theory developed by Gillespie. However, although Gillespie’s algorithm and its derivatives efficiently model small-scale systems, complex networks are harder to manage on easily available computer systems. Here we present a novel method of simulating stochastic biochemical networks using discrete events simulation techniques borrowed from manufacturing production systems. The method is very general and can be mapped to an arbitrarily complex network. As an illustration, we apply the technique to the glucose phosphorylation steps of the Embden-Meyerhof-Parnas pathway in E. coli. We show that a deterministic version of the discrete event simulation reproduces the behavior of an analogous deterministic differential equation model. The stochastic version of the same model predicts that catastrophic bottlenecks in the system are more likely than one would expect from deterministic theory.

Understanding the driving forces for the markets of their products is a basic necessity for any business. Quantitative models are either ag- gregated over large market segments or restricted to utility models of an individual’s buying decision. While the aggregate models acknowl- edge that customer interactions are important they do not model them and hence have no way to adjust their model to changing business en- vironments. This paper develops crucial methodology to bridge this gap between the individual decisions and the overall market behavior using agent based simulations to model the sales of computer chips in the High- End Gamers market. The simulation environment is dynamic and models the succession of 19 products introduced over a 40 month time horizon which includes the recession of 2008 - 2010. Simulated sales are compared to actual sales data and are used to adjust the parameterization of the agents and their environment. Only two agent parameters are sufficient to obtain a very reasonable fit between simulations and data: The amount of money available for the gaming hobby and a parameter related to the gaming skills of the High-End Gamers.

The stability of the Lu-Kumar queueing network is re-analyzed. It is shown that the associated fluid network is a hybrid dynamical system that has a succession of invariant subspaces leading to global stability. It is explained why large enough stochastic perturbations of the production rates lead to an unstable queuing network while smaller perturbations do not change the stability. The two reasons for the instability are the break- ing of the invariance of the subspaces and a positive Lyapunov exponent. A service rule that stabilizes the system is proposed

An aggregate continuum model for production flows and supply chains with finite buffers is proposed and analyzed. The model extends earlier partial differential equations that represent deterministic coarse grained models of stochastic production systems based on mass conservation. The finite size buffers lead to a discontinuous clearing function describing the throughput as a function of the work in progress. Following previous work on stationary distribution of WIP along the production line, the clearing function becomes dependent on the production stage and decays linearly as a function of the distance from the end of the production line. A transient experiment representing the break down of the last machine in the production line and its subsequent repair is analyzed analytically and numerically. Shock waves and rarefaction waves generated by blocking and re-opening of the production line are determined. It is shown that the time to shutdown of the complete flow line is much shorter than the time to recovery from a shutdown. The former evolves on a transportation time scale whereas the latter evolves on a much longer time scale. Comparisons with discrete event simulations of the same experiment are made.

A biologically inspired manufacturing control system for synchronous delivery of jobs at a batch machine is developed. This control system is based on a synchronization mechanism of enzymes replacing the role of product molecules with kanbans. This manufacturing control system works well, provided the variability in service times is not too high.

armbruster@asu.edu updated August 7, 2015