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The description of the kinetics of the ammonia synthesis reaction has been deepened by means of a new model building technique. A number of kinetic models are offered as an alternative to these already proposed.

Particle models for hadron interactions are discussed. The various strong interaction phenomena are considered, and those features of the data which need to be incorporated in a model for it to be successful are discussed. 12 references. (JFP)

Practical, useful marketing models are a function of the skill and ingenuity applied during their development. A good deal of creative art, within a framework of systematic, scientific procedure, goes into the building of new marketing models. In practice a marketing organization may do well to gain experience with off-the-shelf models and to proceed to specific, tailor-made projects gradually as experience and skills grow. guidelines for over-all programs and specific procedures in model building are provided and illustrated with examples.

Econometric analysis is concerned with the quantitative relationships between economic variables and it can provide an important input into the decision making process of managers. Typically econometrics differs from other apsects of management science in that it considers problems primarily, though not exclusively, from a background of economics rather than of other disciplines and behaviour is usually dealt with at higher levels of data aggregation than the individual firm. This paper considers some applications of typical econometrics to the general area of managerial decision making, where primarily the techniques have a role to play in assisting the general process of data analysis. Initially discussion is pointed towards the use of the analysis for predictive purposes and the contrast with time series methods. Subsequently examples are presented where the objective is to obtain a better understanding of individual economic relationships that aim to be important inputs into the decision making process, for example cost and revenue analysis. Finally, an example is given of how these ideas contribute more generally to the activity of model building for the firm as a whole both for the purpose of forecasting and policy simulation.

A recent survey by Social Systems, Inc., indicates that since 1970 over 1000 corporations in the United States and Canada have begun developing and using corporate simulation models. However, the percentage of corporations that have experience with corporate models remains relatively small. Why aren't more corporations using these models today? Why are the corporate model users restricted to the larger corporations? Are the primary constraints impeding the use of these models technical problems, computer hardware problems, software problems, or political problems?

Examples of seismic reflection sections are shown which illustrate that over the last decade there has been a dramatic improvement in their clarity. Partly, this has been due to continuous marginal improvement in all parts of the total seismic prospecting “system”, and it is emphasised that research in progress covers a wide range of activities including instrument design, data gathering techniques, computer processing and interpretative model building. However, the greater part of the advance has been due to sustained research into the data-processing phase. Two examples are given. One concerns the accuracy of estimating the delay of one seismic signal with respect to another by picking the peak of their cross-correlation function. It is shown that corruption of the signal by noise may introduce errors of several tens of milliseconds. Such errors must obviously be avoided when static corrections are calculated automatically. The second example emphasises the nature of the assumptions behind deconvolution and shows that the seismic wavelet implied in practical deconvolution is entirely consistent with that measured by detectors placed close to the shot. In order to counteract a possible overemphasis on the importance of data-processing research, the third and final example illustrates the advance which has been made by the invention of an acceleration-cancelling hydrophone. It is not foreseen that there will be any reduction in the rate of development of the seismic technique.

The development of the voice-frequency active filters for the D3 channel bank is described. These filters are the first single-substrate RC active filters using thin-film tantalum RC and silicon integrated-circuit technology to be produced on a large scale by Western Electric. To create complete confidence in both the design and the new technology, an extensive model building and testing program was undertaken. In addition, continuous interaction with manufacturing engineers resulted in a design that facilitated the introduction of this new technology in a large-scale manufacturing environment. Significant advances were made in reducing the complexity of tuning active filters. In fact, the tuning and testing procedure has been adapted for use with a totally automated computer-controlled test set. Furthermore, a Monte Carlo statistical simulation of the manufacturing process of the filters was developed. This model includes tolerances of the manufactured components, test set errors in measuring gain and component values, resistor adjustment accuracies, and temperature and aging behavior of the components. This computer program has been an invaluable tool in determining the requirements for tuning, testing, and optimizing the final design for minimum manufacturing cost.

A program called XpY was written for the PDP-10/LDS-1 at the Princeton University Computer Graphics Laboratory, for generating and displaying models of dinucleoside phosphates. The molecule GpC, a member of this class and a fragment of the nucleic acid RNA, was subjected to X-ray diffraction analysis. The paper describes the importance of model building in X-ray analysis, and shows step by step how XpY was used to deduce the atomic coordinates of GpC from the experimental data. The program documentation is also included as an Appendix. A subjective critique of graphics is made in the Conclusions section.

The procedure of maximum‐entropy spectral analysis (MESA), used in the processing of time series data, also applies to wavenumber (bearing) analysis of signals received from a spatially distributed linear array of sensors. The method is precisely the use of autoregressive spectral analysis in the space dimension rather than in time. There are also close links to the predictive deconvolution method used in geophysical work, and to the process of constructing noise‐whitening filters in communication theory, as well as to least‐squares model building. In this note, we review the maximum‐entropy procedure pointing out all these links. The specific algorithm appropriate to a uniformly spaced line array of sensors is given, as well as one possible algorithm for use in the case of nonuniform sensor spacing.

A conceptual approach for analyzing social/external informational forces is developed for use in examining specific environment issues. A taxonomy is formulated to guide identification and study of the: (1) levels of socio-environmental systems; (2) specific flows between and within the relevant subsystems; and (3) the processes that operate within and between the subsystem. An approach to examining environmental systems is presented based on purpose of analysis, relevant goal structure, and model building focus. An illustrative model is developed and applied to unit-pricing at the retail level. Finally, the implications of attempting to analyze macro-social information flows are considered.

The nature of the art of applied mathematics is reviewed and three contemporary challenges are considered. These are the extended fields of mathematical application, the extension of applicable mathematics, and the problems associated with model building in the new fields. It is noted, however, that two aspects remain invariant: the difficulty of immaturity when making applications relevant and the essential problem‐solving theme of applied mathematics.

Recent decades have witnessed an exponential growth in the size and complexity of planning and transportation models. Associated with these model building activities has been the desire to accurately forecast demand, which in turn, involved complex predictions of population, income, land use, and a variety of variables, all of which affect future use of engineered facilities. The degree of attempted sophistication of these modeling activities has frequently been at odds with the accuracy or reliability of the given data or with the final use of the results. Less sophisticated procedures that are transparent (intuitively obvious) to a wide range of community participants are needed, and they must be based upon an understanding of how accurate we need to be.

This paper draws on the literature in management science, information systems and organization development along with practical experience to propose a process of building models that will be implemented. The steps are: (1) formulation of priors, (2) entry, (3) problem finding, (4) specification of model development criteria, (5) model building, (6) estimation and fitting, (7) tracking, and (8) continuing use. After describing the state of the art of model implementation, each step is discussed. It is hoped that this exposition will encourage comments and lead towards the specification of a methodology for model building that will make real the promise of management science.

Social scientists are continually confronted with the problem of formulating models which describe how individuals make choices among alternative courses of action with uncertain consequences. Economists have developed a class of models which seem to deal particularly well with problems of this type. These models employ the ``expected utility theorem'' of von Neumann and Morgenstern and, for reasons brought out in the paper, are generally qualitative in nature. Since the approach to modeling human behavior adopted by non-economists is generally very different from that of economists, in this paper we present a rather detailed example of the role of the expected utility theorem in qualitative model building. Specifically, we model an arsonist's decision as to the amount of time to allocate to arson and related activities and examine the responsiveness of this time allocation to changes in various policy parameters. Both the activity modeled and the method of presentation are intended to provide an introduction to the scope and power of the expected utility theorem in modeling situations of ``choice under uncertainty.''

Applications of system identification techniques to chemical, metallurgical, paper and pulp, cement and glass industries are surveyed. It is demonstrated that identification is a useful tool to determine process dynamics. This is true, particularly for processes which are difficult to model from basic physical laws only, such as blast furnaces, paper machines and cement kilns. Valuable knowledge is provided for design of regulators, as well as for design of new processes or redesign of the actual processes. Problems that play an important role in identification of real processes are discussed from a practical point of view. Experiment design, structure determination, parameter estimation, model verification and data handling are treated. The main conclusion is that interactive programs are very efficient for the handling of all the phases of model building due to its iterative nature.

An overview of modeling in the energy field and its role in the formulation of national energy policy is presented. The nature of the modeling task and the various steps that it encompasses are described. The methodological alternatives available to the energy system planner in the conceptualization, development, and use of models are presented. Alternative policy instruments in the various supply and demand sectors are examined and their use in policy analysis is discussed. Finally, recent experience in the modeling field is drawn upon to exemplify the interactive nature of model building and point out some areas of immediate challenge that hold promise for the future.

Bennett R. J. (1974) Process identification for time series modelling in urban and regional planning, Reg. Studies 8, 157–174. Present dynamic urban and regional models are shown to be largely a priori in their specifications. In developing an a posteriori approach to model building two criteria are defined: operationality and parsimony of the resulting model. One particular family of processes that satisfy these criteria are the family of autoregressiv-moving average and transfer function processes. The identification of a set of time series for North-West England in the time domain, the frequency domain, and by iterative estimation is shown to lead to models of the processes by this family which are operational and parsimonious. It is suggested that the techniques used in this identification can be made the basis of an inferential methodology for model building which leads naturally to statistical forecasts and policy.

Along with rapidly growing knowledge in the area of organizational behavior, there is a growing interest in formulating organization theories in more precise and predictive models than verbal theor...

Two urban planners recommend the fostering of local settlement systems, defined as interconnected groups of places with a total population of at least 200,000 around one or more central cities that are linked with suburban places by journeys to work and cultural or shopping trips at the rate of at least 10 trips a year per capita. Such systems are differentiated from urban agglomerations, a narrower concept restricted to the central urbanized portion of local settlement systems. The development of local settlement systems is recommended on two grounds: (1) to make central-city services available to a larger share of the population, and (2) to provide more diversified employment opportunities through the construction of industrial satellite towns. Two types of systems are distinguished: Type I requires further development to provide a fuller set of services and broader employment opportunities; Type II, already fully developed, requires the regulation of central city growth and the provision of spe...

The author discusses the possibility for generalization of the geometrical structure analysis for both solids and liquids. The analysis of structures can be reduced to the geometrical problem of classifying the neighbourhoods of individual points and to the way these neighbourhoods can be related to each other. For the purpose of structure analysis and model building the geometrical point of view seems to be quite applicable.

The dynamic factor technology, has received increased attention as a major variable in industrial management. Yet, its role is as yet to be more clearly defined.1 An increasing number of articles a...

It appears to be generally agreed that there ought to be a close integration of economic theory and the building of econometric models, together with the auxiliary activities of data collection and processing. If this is to be so, then every econometric model must be a special purpose model or at best a model designed for a limited range of related uses. A model is, by definition, an image of reality that is simplified according to certain criteria of what is important and what is not. Its construction necessarily reflects the main preoccupations of its builders, the relations and measures they think relevant to the problems they face, and even their particular versions of economic theory. This leaves the door wide open for differences in emphasis, in priorities, and even in fundamental interpretations of economic phenomena. In short, a model appropriate for, say, Quebec, will necessarily differ considerably from models constructed for the federal government or its agencies and from models set up by large corporations for their own use. And it is not just a matter of fitting different parameters into the same logical structure; the logical structures themselves will differ.Secondly, if true integration of model building with economic theory is to be attained, and if a solid observational basis is to be secured, we must work very close to the micro-economic level. This means that models must be disaggregated, since our most solid theoretical results are in micro-economics.

It is argued that current attempts to model human learning behavior commonly fail on one of two counts: either the model assumptions are artificially restricted so as to permit the application of mathematical techniques in deriving their consequences, or else the required complex assumptions are imbedded in computer programs whose technical details obscure the theoretical content of the model. The first failing is characteristic of so-called mathematical models of learning, while the second is characteristic of computer simulation models. An approach to model building which avoids both these failings is presented under the title of a black-box theory of learning. This method permits the statement of assumptions of any desired complexity in a language which clearly exhibits their theoretical content.

Rolls-Royce aero engines are used by 200 airlines, 300 corporate customers and 77 armed forces. To date 34 000 aeroplane engines have been built and, in the time that it has taken you to read this far, 10 aircraft propelled by Rolls-Royce engines have taken off.The business is located in Scotland, England and Ireland and in England stretches from Bristol to North Yorkshire with the main head office at Derby.

Little information is available which allows comparison between the results of wind-tunnel studies on model buildings with full-scale effects experienced in the natural wind. What information there is often shows marked discrepancies in the wind-tunnel data. Very much more information is required concerning the influences experienced by full-scale buildings. The considerable complexities of instrumentation experienced in obtaining measurements on full sized buildings, together with the high inherent costs, have had limiting influences on the volume of experimental work undertaken. Results are given in this report of a study, carried out in the field, of wind effects on a half full-size single storey model building. The profiles in the natural wind over the site were measured and the pressure effects experienced by the model were recorded. Many interesting features were discovered in the results, which require careful consideration, and the investigation yielded valuable data which were used in a comparison with the results of a subsequent wind-tunnel study on small scale model buildings, the results of which will be published later.

This article presents the findings of a survey conducted among British companies to discover to what extent marketing models are being used in practice. In two previous articles we discussed the problems of model building in marketing, examined several recent developments, argued that there was a need to measure the current status of marketing model building in Britain, and made a partial assessment of the state‐of‐the‐art by reviewing some of the most significant literature. The purpose of this paper is to present the findings of a survey we conducted among British companies to discover to what extent marketing models are being used in practice. We also present the conclusions we have drawn from the project.

The paper is concerned with some methodological and technical aspects of regional analysis and model building and focuses on a specific application with Italian data at provincial level. The frame of reference of the discussion is national territorial planning and the definition of spatial policies of urbanization and regional development. Regional analysis is seen in relation to planning decision making, data availability, socio-economic determinants and spatial analysis. These relationships are stated in a specific way which suggests methodological approaches for a comprehensive and systematic monitoring of the state of the region.

The subject of statistical sales forecasting has recently been brought to prominence as a major area of management decision-making by the growth of a substantive literature and the establishment of several research groups to investigate the building of forecasting models. Whilst a lot of attention has been focused on the relatively newer disciplines of technological forecasting and multiple-equation model building of macro-economic systems, statistical sales forecasting methods have also been subject to considerable development and a number of radically new techniques have emerged. The authors believe that it is timely to review the current ‘state of the art’ of sales forecasting methodology. This study examines a wide range of models in use although it is not intended as a comprehensive guide.

A class of time series models suitable for representing discrete univariate time series is introduced. These models are capable of representing both stationary and nonstationary series and can be easily generalized to allow for seasonality and to accommodate a leading indicator. In addition a model building strategy is discussed and the problem of forecasting is considered. Finally, the methodology is illustrated with several examples.

The steel industry is one of the first industries where operational research was successfully applied. The objective of the present paper is to summarize such applications high-lighting benefits and difficulties involved in the studios and in their subsequent implementation. The paper is divided into three sections. The first section contains a brief survey of the reported ease studies in literature pertaining to the application of O.R. techniques and methodology in production problems in the stool industry. The second section deals with a few case studies which illustrate the model building procedures and their usefulness in real life. The final section of the paper is devoted to a discussion of the potential areas where O.K. techniques and. methodology can be fruitfully applied in modeling production processes for control purposes.

A statistical approach to model a papermaking process and to control paper basis weight is presented. The process behavior is described by a mathematical model which takes into consideration both the input-output dynamics and disturbances coming into the system. The model building procedure was based on a three-step approach of identification, estimation and diagnostic checking. The disturbance model is accounted for by a discrete time series model, whereas the dynamic model is a discrete transfer function model. The simplicity of the modeling process lies in the fact that only the input-outpul data are necessary without recourse to a complicated analysis of the physical system itself. An optimal control equation was arrived at whereby the basis weight of the paper was to be controlled at a specified target value. Confirmation runs were conducted to check the effectiveness of the control equation.

A brief description of various socio-ecological models and their data requirements have been presented in this paper. It is evident that there is an enormous gap between the need for the data on the “quality of life” and the actual supply of such data. It has been argued that any model building effort in the area of ecological system must wait until an adequate data base is established. However, the identification of data requirements for the construction of such models points out the characteristics of statistical information system that should be established.

Model building in physical, statistical, simulation or other form, is making an increasing contribution to the problem solving methodology in economics, industry, government, and technological development (1). More specifically, in the present context, simulation models can offer a distinctive and valuable contribution to the understanding by management of complex business systems, interactions and environment and indicate ways toward improvement, financial and otherwise (2). The advent of powerful computers in the last few years is the decisive factor which has decided the means of realizing the full potential of simulation models, hitherto unattainable because of the vast amount of data processing and calculation required. The purpose of this article is to indicate the approach to and scope of a computerized simulation model for long term production strategy decision making (3). While the model relates to the system and data of a specific production unit, manufacturing electronic components, the principles are widely applicable in any size and type of company. It is not a specifically large company technique.

As electronic systems continue to evolve into more and more complex structures, the search for better and more efficient reliability prediction techniques naturally takes on added momentum. Needed are not only systematic methods of mathematical model building that will simplify the procedures involved but also noncomplex ways of obtaining solutions to many practical problems. This paper illustrates the applicability of transition diagram in describing the state space of a complex system, repairable or nonrepairable, and shows the methodology of writing the set of first-order linear differential equations representing the system performance by inspection of the transition diagram. A discussion of some applicable properties of linear signal-flow graphs is included. Methods of solving problems by inspection techniques are clearly explained and specific examples are given to illustrate the concepts. The mean time Tm for a system to pass for the first time from its initial state to a failed state is usually a statistic of prime interest. Certain properties of Laplace transform are used to illustrate how Tm of a general complex system, repairable or nonrepairable, can be obtained by solving a set of simultaneous algebraic equations. Flow graph techniques of solution by inspection are shown to be a valuable tool in obtaining analytical solutions for Tm of many practical systems.

The paper is concerned with the empirical foundations of the natural and social sciences, namely, the formulation and testing of theories based on logically objective analyses of empirical observations. In many instances, both in the experimental and non-experimental sciences, this involves the use of logical empiricism in a stochastic context. The manner in which a scientist begins to construct a model is described, and some relevant definitions are put forward. Illustrations are drawn from several fields, and in particular economics, in which the empirical observations are analyzed as a sample realization of a stochastic process. In this fashion the concepts of stochastic economics are introduced, together with an integrated system of definitions to cover the basic assumptions, the economic theory relevant under these assumptions, and the model into which both these are incorportated. The logical, empirical and operational characteristics of economic theories are next considered, and certain basic requirements are put forward for simultaneous advancement of the generality and validity of these theories, in order to increase their explanatory power. The paper concludes with a short analysis of the practical utility of models for purposes of explanation, prediction, and decision making.

An example drawn from fleet air defense illustrates the use of a very simple device which simulates the physical situation to be analyzed in the task of constructing a mathematical model of the situation. Such a simulator is also helpful in explaining the results of the analysis to the people for whom they are intended and in estimating the errors introduced by various computational approximations. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.

Summary We argue that optimization is an ideal theme on which to build a model‐building course. We describe a particular model, the cost of adjustment model in the theory of the firm, in some detail to illustrate the richness of optimal models.

The rate of oxidation of potato chips as a function of oxygen partial pressure, extent of oxidation and equilibrium relative humidity was determined. We used the results to build mathematical models with the rate of oxidation as the dependent variable and the other three factors as independent variables. A mixed approach was used in model building which included incorporation of the knowledge of kinetics of lipid autoxidation mechanisms in food products as well as empirical relations. We developed a relatively simple model with only four constants. Statistical analysis indicates a good fit of this equation to the experimental results and suggests an experimental design allowing evaluation of the constants with less experimentation. The equation developed is useful for package simulation and optimization and storage life prediction, and we expect that the model can be applied to other food products.