An interactive decision support system for the bank courier routing problem

In this paper, we present an interactive decision support system for collecting and processing financial transit material for the Southeast Bank N.A. The underlying model is a bicriteria shortest path problem. The system provides a feasible solution in a matter of minutes, which provides the decision maker with an opportunity to perform “what if” analysis. The system can be extended to other vehicle routing problems with inventory components.     

Trajectories of lattice particles using the new approach to no integrability

We study two systems which lead to a lattice when an integration path is specified in “aesthetic field theory”. One of these cases involves nonsoliton type particles (magnitudes of maxima and minima oscillate in time). The other system is made up of soliton type particles. The two systems are intrinsically three-dimensional. We speak of the third dimension as “time”. In one of our solutions, the particles move on straight line trajectories, insofar as our numerical work indicates. In the other solution, the soliton type particles undergo what appears to be simple harmonic motion in both the x- and y-directions (loop motion). We then study these two systems using the new approach to integrability which involves a superposition principle and is characterized by a unique change function at each point. We still find multi maxima and minima. The systems are not as symmetric as the lattice. The soliton characteristic is preserved by the new method. We investigated the motion of lattice particles. We found evidence of maxima (minima) regions coalescing so that the location of the maxima (minima) became difficult to follow. The concept of location of particles may not even have a well-defined meaning here. We find examples of soliton particles appearing and disappearing. We conclude that the manner of integration in a no integrability theory can transform a system with well-defined trajectories into a system where particles can no longer be followed in time.     

A neural fuzzy control system with structure and parameter learning

A general connectionist model, called neural fuzzy control network (NFCN), is proposed for the realization of a fuzzy logic control system. The proposed NFCN is a feedforward multilayered network which integrates the basic elements and functions of a traditional fuzzy logic controller into a connectionist structure which has distributed learning abilities. The NFCN can be constructed from supervised training examples by machine learning techniques, and the connectionist structure can be trained to develop fuzzy logic rules and find membership functions. Associated with the NFCN is a two-phase hybrid learning algorithm which utilizes unsupervised learning schemes for structure learning and the backpropagation learning scheme for parameter learning. By combining both unsupervised and supervised learning schemes, the learning speed converges much faster than the original backpropagation algorithm. The two-phase hybrid learning algorithm requires exact supervised training data for learning. In some real-time applications, exact training data may be expensive or even impossible to obtain. To solve this problem, a reinforcement neural fuzzy control network (RNFCN) is further proposed. The RNFCN is constructed by integrating two NFCNs, one functioning as a fuzzy predictor and the other as a fuzzy controller. By combining a proposed on-line supervised structure-parameter learning technique, the temporal difference prediction method, and the stochastic exploratory algorithm, a reinforcement learning algorithm is proposed, which can construct a RNFCN automatically and dynamically through a reward-penalty signal (i.e., “good” or “bad” signal). Two examples are presented to illustrate the performance and applicability of the proposed models and learning algorithms.     

On behavior of two-dimensional non-plane parallel turbulent flows of inviscid gas

The time behavior of two-dimensional flows of inviscid gas in which the velocity component normal to the plane of independent variables and the vorticity components parallel to this plane are different from zero, is investigated. Equations of such flows form two different subsystems. The first subsystem describes a plane parallel (“primary”) flow without the third velocity component, and is independent of the second subsystem consisting of a single equation for the third velocity component and determining the “secondary” flow. The flows are analyzed with sufficient detail without using numerical integration which carries with it unavoidable errors, and without linearization, both of which are employed to a lesser or greater degree in the study of the evolution of vortical structures (see /1–6/).     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

Implicit algorithms for solving the Cauchy problem for the equations of the dynamics of mechanical systems

It is shown that in the numerical solution of the Cauchy problem for systems of second-order ordinary differential equations, when solved for the highest-order derivative, it is possible to construct simple and economical implicit computational algorithms for step-by-step integration without using laborious iterative procedures based on processes of the Newton-Raphson iterative type. The initial problem must first be transformed to a new argument — the length of its integral curve. Such a transformation is carried out using an equation relating the initial parameter of the problem to the length of the integral curve. The linear acceleration method is used as an example to demonstrate the procedure of constructing an implicit algorithm using simple iterations for the numerical solution of the transformed Cauchy problem. Propositions concerning the computational properties of the iterative process are formulated and proved. Explicit estimates are given for an integration stepsize that guarantees the convergence of the simple iterations. The efficacy of the proposed procedure is demonstrated by the numerical solution of three problems. A comparative analysis is carried out of the numerical solutions obtained with and without parametrization of the initial problems in these three settings. As a qualitative test the problem of the celestial mechanics of the “Pleiades” is considered. The second example is devoted to modelling the non-linear dynamics of an elastic flexible rod fixed at one end as a cantilever and coiled in its initial (static) state into a ring by a bending moment. The third example demonstrates the numerical solution of the problem of the “unfolding” of a mechanical system consisting of three flexible rods with given control input.     

Multicriteria order acceptance decision support in over-demanded job shops: A neural network approach

Order acceptance is an important issue in job shop production systems where demand exceeds capacity. In this paper, a neural network approach is developed for order acceptance decision support in job shops with machine and manpower capacity constraints. First, the order acceptance decision problem is formulated as a sequential multiple criteria decision problem. Then a neural network based preference model for order prioritization is described. The neural network based preference model is trained using preferential data derived from pairwise comparisons of a number of representative orders. An order acceptance decision rule based on the preference model is proposed. Finally, a numerical example is discussed to illustrate the use of the proposed neural network approach. The proposed neural network approach is shown to be a viable method for multicriteria order acceptance decision support in over-demanded job shops.     

Integration of particle swarm optimization-based fuzzy neural network and artificial neural network for supplier selection

This study is intended to develop an intelligent supplier decision support system which is able to consider both the quantitative and qualitative factors. It is composed of (1) the collection of quantitative data such as profit and productivity, (2) a particle swarm optimization (PSO)-based fuzzy neural network (FNN) to derive the rules for qualitative data, and (3) a decision integration model for integrating both the quantitative data and fuzzy knowledge decision to achieve the optimal decision. The results show that the decision support system developed in this study make more precise and favorable judgments in selecting suppliers after taking into account both qualitative and quantitative factors.     

On an observer-related unequivalence between spatial dimensions of a generic Cremonian universe

Given a generic Cremonian space-time, its three spatial dimensions are shown to exhibit an intriguing, “two-plus-one” partition with respect to standard observers. Such observers are found to form three distinct, disjoint groups based on which one out of the three dimensions stands away from the other two. These two subject-related properties have, to our knowledge, no analogue in any of the existing physical theories of space-time; yet, in one of them, the so-called Cantorian model, a closer inspection may reveal some traits of such a “space split-up.”     

Component commonality via hierarchical orthogonal arrays and detailing economic decision matrices

Component commonality (CC) implies products using many common parts, desensitized to the range of product applications (noise), and meeting the functionality objectives of the product line. This paper lists a nine-step methodology for developing CC and applies it to a problem. These steps utilize the major concepts of analytical modeling, economic decision matrices (EDM), quality loss functions (QLS) for variates and weighted utilities, stochastic models, finite element (FE) simulations for concurrent engineering, and statistical design of experiments (DOE) for uncertainty in either application, statistics or managerial decisions. The details of the first six steps were illustrated in a previous paper by application to a problem involving a slider link subjected to an extreme range of “noise” (various inertia/pressure loadings). Six candidate designs of steel, aluminum and titanium were generated using an analytical model and a sensitivity study. The DOE utilized Taguchi's orthogonal arrays. These designs were ranked using cost, weight, and factors of safety with respect to yielding. A refining EDM with a three-part robustness criteria selected two candidates (best was steel, followed by aluminum) considering inner noise in the managerial decisions. In the current paper, the last three steps of the nine-step methodology are applied to these two candidates in order to obtain the “optimal” part for CC. The FE stress results are used with a modified Goodman fatigue criteria, and a stochastic model is developed based upon beta (strength) and three-parameter Weibull (stress) distributions. The model is then used in a detailing EDM to determine the stochastic reliability associated with a QLS defined with respect to fatigue reliability. A “fine-tuned” aluminum candidate is shown to meet a priori reliability requirements and have low-quality losses. However, both original candidates exhibited some high-quality losses, even though such losses were acceptable in the preceding refining EDM. The authors demonstrate that this loss of quality can be prevented if a fatigue criteria is used in both the refining and detailing EDM stages of the design process and, “warranty failures” are based on stochastic rather than deterministic definitions of maximum environmental conditions.     

A quantum mechanical approach to a fuzzy theory

Recently, we proposed a general measurement theory for classical and quantum systems (i.e., “objective fuzzy measurement theory”). In this paper, we propose “subjective fuzzy measurement theory”, which is characterized as the statistical method of the objective fuzzy measurement theory. Our proposal of course has a lot of advantages. For example, we can directly see “membership functions” (= “fuzzy sets”) in this theory. Therefore, we can propose the objective and the subjective methods of membership functions. As one of the consequences, we assert the objective (i.e., individualistic) aspect of Zadeh's theory. Also, as a quantum application, we clarify Heisenberg's uncertainty relation.     

A simple decision model of counterproliferation

We develop a simple decision model of counterproliferation involving a status quo “incumbent” and a nuclear “entrant”. The problem is examined as a one-stage interaction in two phases: nuclear development and deployment. We examine the conditions that will influence the decision to move pre-emptively against a proliferator's nuclear program. Particular attention is given to the role of uncertainty in determining the expected costs of action at different points in the entrant's weapon's development and deployment cycle. The model permits us to determine the optimal time to act given varying levels of information concerning entrant behavior. In conclusion, we examine the tradeoffs between the expected costs of action and the costs of intelligence.     

Parallel iteration across the steps of high-order Runge-Kutta methods for nonstiff initial value problems

For the parallel integration of nonstiff initial value problems (IVPs), three main approaches can be distinguished: approaches based on “parallelism across the problem”, on “parallelism across the method” and on “parallelism across the steps”. The first type of parallelism does not require special integration methods and can be exploited within any available IVP solver. The method-parallelism approach received much attention, particularly within the class of explicit Runge-Kutta methods originating from fixed point iteration of implicit Runge-Kutta methods of Gaussian type. The construction and implementation on a parallel machine of such methods is extremely simple. Since the computational work per processor is modest with respect to the number of data to be exchanged between the various processors, this type of parallelism is most suitable for shared memory systems. The required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor 2. The third type of parallelism (step-parallelism) can be achieved in any IVP solver based on predictor-corrector iteration and requires the processors to communicate after each full iteration. If the iterations have sufficient computational volume, then the step-parallel approach may be suitable for implementation on distributed memory systems. Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The dynamic step-parallel iteration process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to achieve speed-up factors up to 15.     

Systems of first-order chemical reactions

We consider the classical model in chemical kinetics of a system of n species in which each species is converted to every other species by a first-order reaction. Solutions to the initial-value problem are given in matrix form and the properties of the n × n matrix K representing the system are analysed. For arbitrary (i.e. non-negative) values of the first-order rate constants, zero is an eigenvalue, and the other eigenvalues are complex with negative real parts. Thus, in this case the system generally oscillates to equilibrium. However, if the principle of microscopic reversibility is applied, and if each species is converted directly to every other species, then the system cannot oscillate but must converge “exponentially” to equilibrium. We discuss when K is diagonalizable, and we calculate a bound for the eigenvalues of K. Special forms of K, corresponding to special systems of reactions, are also examined; these include reactions in the configuration of a “chain”, a “cycle”, a “node” and reactions comprising combinations of these. We find again that if the principle of microscopic reversibility is rigorously applied then oscillations cannot take place, but that if this principle is not applied then oscillations may take place. The system of rate equations considered can be used to model various chemical, physical and biological phenomena.     

A comparison of the monomial method and the S-system method for solving systems of algebraic equations

Two numerical methods for solving systems of equations have recently been proposed: a method based on monomial approximations (the “monomial method”) and a technique based on S-system methodology (the “S-system method”). The two methods have been shown to be fundamentally identical, that is, they are both equivalent to Newton's method operating on a transformed version of the system of equations. Yet, when applied specifically to algebraic systems of equations, they have significant computational differences that may impact the relative computational efficiency of the two methods. These computational differences are described. A combinatorial strategy for locating many, and sometimes all, solutions to a system of nonlinear equations has also been suggested previously. This paper further investigates the effectiveness of this strategy when applied to either of the two methods.     

Experiences with Using Expert Systems in O.R.

Increased awareness of expert systems technology, and the availability of relevant software, has tempted many O.R. groups to investigate the expert systems approach. This paper considers the strategies open to O.R. groups interested in employing expert systems, reviews some of the relevant software, and discusses what those O.R. groups who have already investigated the use of expert systems methods are actually doing.Some of the authors' experience of developing expert systems is discussed. The development of an expert system that helps bankers analyse company accounts is presented. The use of expert system methods as vehicles for decision analysis, and the possibilities for producing systems that act as O.R. consultants are also discussed.     

Stability of linear almost-Hamiltonian periodic systems

A linear Hamiltonian system with periodic coefficients is subject to a small “dissipative” perturbation that makes it asymptotically stable. The conditions under which the perturbation remains dissipative for all Hamiltonian systems sufficiently close to the original one are discussed.     

SIMULEX — a multiattribute DSS to solve rescheduling problems

Knowledge-based systems (KBS) can help to make simulation available to a large group of users. We want to exemplify this by describing a decision support system (DSS) for short term rescheduling in manufacturing called SIMULEX. It couples expert systems, simulation, and a multiattribute decision making (MADM) procedure to assist the production manager. After an introduction to simulation as a problem solving tool, the current problems in production control and the goals of the project are described. Then, the various components of SIMULEX are explained in some detail. Some results and a short outlook conclude the article.     

Global stabilization of a certain class of nonlinear dynamical systems using state detection

This note is concerned with the stabilization of control systems using an estimated state feedback. The global stabilization problem for a relatively broad class of nonlinear plants is discussed. Moreover, using the “input to state stability” property introduced by Sontag [1–4] and detectability condition, we show that the system can be globally asymptotically stable using a state detection.     

Fuzzy stability and synchronization of hyperchaos systems

This paper studies stability and synchronization of hyperchaos systems via a fuzzy-model-based control design methodology. First, we utilize a Takagi–Sugeno fuzzy model to represent a hyperchaos system. Second, we design fuzzy-model-based controllers for stability and synchronization of the system, based on so-called “parallel distributed compensation (PDC)”. Third, we reduce a question of stabilizing and synchronizing hyperchaos systems to linear matrix inequalities (LMI) so that convex programming techniques can solve these LMIs efficiently. Finally, the generalized Lorenz hyperchaos system is employed to illustrate the effectiveness of our designing controller.