Applicable systems thinking

Systems is a broad topic. Almost any subject area can claim an interest in systems and much has been written about it. Most of the literature concentrates upon philosophical issues and debates about the subject, relatively little upon the usefulness and the practice of systems ideas. This review focusses upon systems practice, recognises and distinguishes between systemic and systematic and considers traditional OR methods, Systems Analysis and Systems Engineering in contrast to the works of Beer, Ackoff and Checkland. All three claim that they have achieved considerable successes in applying their ideas in consulting roles. There is some overlap between their approaches, but each has a distinct style and methodology.     

Cellular dynamics: How individual decisions lead to global urban change

Models of micro-macro dynamics based on the bifurcation paradigm have helped gain some deep insights into the behavior of certain kinds of complex systems, including urban systems. Here an alternative kind of model will be presented, the scope and qualitative behavior of which appears to be similar to that of the models of the bifurcation type, although it is arguably more general, not being restricted to real-valued functions. This alternative framework is derived from discrete modeling theory and generalizes the notion of ‘cellular automata’. In the application outlined here, the large-scale evolution of urban residential densities is represented as the result of a large number of interdependent investment decisions made by individual developers. The exact relation of this model with a bifurcation model of the same process remains an interesting theoretical question.     

Invariant measures for systems of Kolmogorov equations

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these measures are absolutely continuous with respect to the Lebesgue measure and study some of their main properties. Finally, we show that they characterize the asymptotic behaviour of the semigroup at infinity.     

Optimization methods in multilevel systems: A methodological survey

Hierarchical features are characteristics of many systems in the real world. The task of coordinating such systems is a highly complex one. Various coordination principles have been proposed in literature, of which the Interaction Prediction Principle and the Internation Balance Principle are the most commonly used. In this paper, optimization methods for multilevel systems based on these two principles are reviewed. Linear dynamic systems with quadratic performance criteria are singled out for special attention in view of their potentiality for applications in the empirical context. A brief overview is also presented of certain applications of multilevel systems to practical problems.     

Finding all solutions to polynomial systems and other systems of equations

In a previous paper, the authors suggested a procedure for obtaining all solutions to certain systems ofn equations inn complex variables. The idea was to start with a trivial system of equations to which all solutions were easily known. The trivial system was then perturbed into the given system. During the perturbation process, one followed the solution paths from each of the trivial solutions into the solutions of the given system. All solutions to the given system were thereby obtained.This paper utilizes a different approach that eliminates the requirement of the previous paper for a leading dominating term in each equation. We add a dominating term artificially and then fade it. Also we rely on mathematically more fundamental concepts from differential topology. These advancements permit the calculation of all solutions to arbitrary polynomials and to various other systems ofn equations inn complex variables. In addition, information on the number of solutions can be obtained without calculation.Work supported in part by NSF Grant No. MCS77-15509 and ARO Grant No. DAAG-29-78-G-0160.Work supported in part by ARO Grant No. DAAG-29-78-G-0160     

Some results on systems of quasi-variational inclusion problems and systems of generalized quasi-variational inclusion problems

In this paper, we study systems of quasi-variational inclusion problem and systems of quasi-variational disclusion problem. From the existence theorems of solution for these two types of problems, we study various types of systems of quasi-variational inclusion problems, systems of quasi-equilibrium problems, systems of quasi-KKM theorem, abstract economics and system of KKM theorem. We also show their equivalent relations. We study further existence theorems of solution for generalized quasi-variational inclusion problem. Our results are different from any existence result in the literature.     

Mental representations of important real-life decisions

Two studies investigated how decision makers characterize alternatives in important real-life decisions, which they themselves had made (to leave a partner, to choose an education and to choose a home). First, the participants indicated a very high degree of involvement in the decisions studied and about half of the participants gave maximum involvement ratings for the partner decision. Second, the results showed that concepts that are essential in most decision theories, such as, consequence, probability and value were important characteristics of the decisions. Third, emotion, positive and negative affect were also important characteristics. Fourth, value and emotion were uncorrelated. Fifth, the patterns of characteristics of decisions made in the past did not differ markedly from the characteristics given to future decisions. Principal component analyses were performed on the ratings of applicability of the different characteristics across participants for each decision situation. Three factors were extracted. There was one factor for positive affect/emotions and another factor for negative affect/emotions verified in oblique solutions. Thus, different scales are needed to represent emotion/affect components (and not bipolar scales) in real-life important decisions. The third factor represented the way in which a decision was represented (moving pictures dialogue etc.). An analysis restricted to the participants who rated 100% involvement showed an additional fourth factor with “what others would think”, “similar situations”, “values” and “money” as the most prominent characteristics. This points to the importance of controlling for participant involvement in studies of human decision making to enable generalizations to real-life decisions.     

Symmetrization of diagonalizable complex differential systems

Let L be a first order system where D₀=∂/∂x₀, Dj=∂/∂xj, y is a real vector parameter, I is the idendity 3×3 matrix and aj(y) is a 3×3 matrix-valued complex smooth function.Let L(y,ξ) be the symbol of L(y,D). We assume: ∀y, the real reduced dimension of L in y is 5 and L(y,ξ) is symmetrizable: ∃T(y) such that: T−1(y)L(y,ξ)T(y) is hermitian ∀ξ. We assume the nonexistence of some double characteristics depending on the reduced form of the system. Then: L(y,ξ) is smoothly symmetrizable ? ∃T(y) smooth (same smoothness as the coefficients) such that: T−1(y)L(y,ξ)T(y) is hermitian ∀ξ.     

Consistency of finite systems of convex inequalities

We give necessary and sufficient conditions for the existence of a convex functionu which satisfies a finite list of inequalities of the typeu(a)<u(b) oru(a)≤u(b), wherea, b are finite dimensional vectors.     

The dynamics of price, quality and productivity improvement decisions

Although quality has received significant attention during the last decades and its economic benefits are beyond any doubt, lots of questions have remained unanswered as to how much, when, and in what to invest to maintain sustainable competitive advantage. A model is introduced here to guide a firm in addressing these questions. The firm produces a single product and operates in a market where monopolistic competition is effective. Demand for the product in the industry depends on both price and performance quality. Increasing productivity knowledge decreases unit production cost, but demand for the company’s product decreases over time, as competitors will be able to offer products with similar performance. Productivity and quality knowledge can be developed through induced and autonomous learning in order to strengthen company position. The paper provides an optimal control formulation of the problem and develops necessary conditions for optimality and characterizes the dynamics of optimal price, quality and investment decisions.     

Toward a classification of complex systems

The purpose of this paper is to suggest process-based organizing principles as a foundation for an objective classification of complex systems that arise as dissipative structures. It is characteristics of a dissipative structure that one process may generate many different states. Conversely, similar states may occur in systems with different processes. A classification of systems that is based upon system state (morphology) is bound to complicated by these properties. In fact, rather than being representable as a simple tree, such a classification becomes a highly interconnected network, thus negating much of its usefulness as a clarifying tool. Because of the non-uniqueness of system state in evolutionary systems, a classification based upon process should be less ambiguous and thus more useful.     

Asymptotic and total stability for generalized dynamical systems

The existence of solutions to a class of nonlinear problems depending on a parameter is proved using the Gaierkin method The principal difficulty is that when the parameter crosses a critical value the bound edness of the approximate solutions is no longer obvious. Applications are indicated.     

The design of colliery information and control systems

The paper is concerned with describing an investigation of information usage in the control of colliery operations. The premise of the work is that to make the most of new information retrieval technology currently being installed in collieries research in needed to provide compatible advances in methods of information usage. The approach adopted was to construct a continuous simulation model using system dynamics capable of providing a laboratory assessment of alternative managerial control policies based on alternative sources and levels of aggregation of information.The model developed represents a typical colliery situation composed of three working coal-faces and incorporating planning, production, development and manpower sectors. The face sectors transform coal reserves to mined coal output, under manpower constraints and geological shocks, and these are all interlinked by means of allocation policies for manpower and machine shifts.A range of policies for the exercise of control through these allocations are considered subject to a range of shocks. It is concluded that, although there are difficulties in designing single policies which are universally best, there are clear advantages associated with fully integrated colliery policies based on information inputs from all aspects of the operations.     

Quality and pricing decisions in production/inventory systems

In this article, we consider the impact of finite production capacity on the optimal quality and pricing decisions of a make-to-stock manufacturer. Products are differentiated along a quality index; depending on the price and quality levels of the products offered, customers decide to either buy a given product, or not to buy at all. We show that, assuming fixed exogenous lead times and normally distributed product demands, the optimal solution has a simple structure (this is referred to as the load-independent system). Using numerical experiments, we show that with limited production capacity (which implies load-dependent lead times) the manufacturer may have an incentive to limit the quality offered to customers, and to decrease market coverage, especially in settings where higher product quality leads to higher congestion in production. Our findings reveal that the simple solution assuming load-independent lead times is suboptimal, resulting in a profit loss; yet, this profit loss can be mitigated by constraining the system utilization when deciding on quality and price levels. Our results highlight the importance of the relationship between marketing decisions and load-dependent production lead times.     

Analysis of customer lifetime value and marketing expenditure decisions through a Markovian-based model

The general aim of this study is to provide a guide to the future marketing decisions of a firm, using a model to predict customer lifetime values. The proposed framework aims to eliminate the limitations and drawbacks of the majority of models encountered in the literature through a simple and industry-specific model with easily measurable and objective indicators. In addition, this model predicts the potential value of the current customers rather than measuring the current value, which has generally been used in the majority of previous studies. This study contributes to the literature by helping to make future marketing decisions via Markov decision processes for a company that offers several types of products. Another contribution is that the states for Markov decision processes are also generated using the predicted customer lifetime values where the prediction is realized by a regression-based model. Finally, a real world application of the proposed model is provided in the banking sector to show the empirical validity of the model. Therefore, we believe that the proposed framework and the developed model can guide both practitioners and researchers.     

Interaction dynamics of two reinforcement learners

The paper investigates a stochastic model where two agents (persons, companies, institutions, states, software agents or other) learn interactive behavior in a series of alternating moves. Each agent is assumed to perform “stimulus-response-consequence” learning, as studied in psychology. In the presented model, the response of one agent to the other agent's move is both the stimulus for the other agent's next move and part of the consequence for the other agent's previous move. After deriving general properties of the model, especially concerning convergence to limit cycles, we concentrate on an asymptotic case where the learning rate tends to zero (“slow learning”). In this case, the dynamics can be described by a system of deterministic differential equations. For reward structures derived from [2×2] bimatrix games, fixed points are determined, and for the special case of the prisoner's dilemma, the dynamics is analyzed in more detail on the assumptions that both agents start with the same or with different reaction probabilities.     

Heavy traffic analysis of controlled multiplexing systems

The paper develops the mathematics of the heavy traffic approach to the control and optimal control problem for multiplexing systems, where there are many mutually independent sources which feed into a single channel via a multiplexer (or of networks composed of such subsystems). Due to the widely varying bit rates over all sources, control over admission, bandwidth, etc., is needed to assure good performance. Optimal control and heavy traffic analysis has been shown to yield systems with greatly improved performance. Indeed, the heavy traffic approach covers many cases of great current interest, and provides a useful and practical approach to problems of analysis and control arising in modern high speed telecommunications. Past works on the heavy traffic approach to the multiplexing problem concentrated on the uncontrolled system or on the use of the heavy traffic limit control problem for applications, and did not provide details of the proofs. This is done in the current paper. The basic control problem for the physical system is hard, and the heavy traffic approach provides much simplification. Owing to the presence of the control, as well as to the fact that the cost function of main interest is “ergodic”, the problem cannot be fully treated with “classical” methods of heavy traffic analysis for queueing networks. A basic result is that the optimal average costs per unit time for the physical problem converge to the optimal cost per unit time for the limit stationary process as the number of sources and the time interval goes to infinity. This convergence is both in the mean and pathwise senses. Furthermore, a “nice” nearly optimal control for the limit system provides nearly optimal values for the physical system, under heavy traffic, in both a mean and pathwise sense. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the importance of behavioral operational research: The case of understanding and communicating about dynamic systems

We point out the need for Behavioral Operational Research (BOR) in advancing the practice of OR. So far, in OR behavioral phenomena have been acknowledged only in behavioral decision theory but behavioral issues are always present when supporting human problem solving by modeling. Behavioral effects can relate to the group interaction and communication when facilitating with OR models as well as to the possibility of procedural mistakes and cognitive biases. As an illustrative example we use well known system dynamics studies related to the understanding of accumulation. We show that one gets completely opposite results depending on the way the phenomenon is described and how the questions are phrased and graphs used. The results suggest that OR processes are highly sensitive to various behavioral effects. As a result, we need to pay attention to the way we communicate about models as they are being increasingly used in addressing important problems like climate change.     

On the computation of solutions of systems of interval polynomial equations

Systems of algebraic equations with interval coefficients are very common in several areas of engineering sciences. The computation of the solution of such systems is a central problem when the characterization of the variables related by such systems is desired.In this paper we characterize the solution of systems of algebraic equations with real interval coefficients. The characterization is obtained considering the approach introduced in J. Comput. Appl. Math. 136 (2001) 271.