On the information about individual utilities used in social choice

This paper investigates the consequences of the requirement tha a social choice method should convey as much information as possible about the individuals' values. It is first shown that if interpersonal comparisons of utilities are excluded, then the only information about individual values that can be used in the context of social choice is ordinal information. It is then argued that Arrow's independence condition demands that only a part of the information about the individual preferences be used in the social choice. Finally, it is shown that the requirement of maximal information gives strong support to Smith's (1973) ‘separability’ condition. In combination with Smith's result this shows that the choice methods that convey the most information about individual preferences are the ‘generalized point systems’ (also called ‘scoring functions’ or ‘ranking systems’).     

The Single-Period Inventory Problem with Triangular Demand Distribution

A simple method is presented for determining ‘closed-form’ solutions for an optimum (s, S) ordering policy for the single-period inventory problem with a set-up cost of ordering and the uncertain total demand over the period represented by a triangular probability density function. The distribution reflecting the decision maker's degree of belief that all values of total demand outside of two (possibly ‘soft’) limits are barely credible and all values within the limits have uniform increasing probability density towards a (possibly ‘soft’) modal value. The importance of the closed form solutions obtained is that they remove the need for enumeration over alternative values of s in determining the optimum (s, S) ordering policy, also they can be encoded in an algorithm simple to implement and they allow easy sensitivity analysis of the results to perturbations in the estimates of the problem parameters. A numerical example is presented to illustrate the essential features of the method.     

A unified theory for coherent systems in reliability II. A unified viewpoint on multinary coherent systems through monotone coherence and relevance

Binary coherent system theory has played an important part in reliability. Its extension to (‘degradable’ or ‘multistate’ or) multinary systems has recently been considered in various papers, through various definitions. This paper studies the most general model for multinary systems, proposes a unified viewpoint on multinary coherent systems and gives unified arguments to apply and to investigate further the binary and multinary cases. In a more detailed way, the ‘helpful bridge’ lately proposed by Block and Savits¹ between the binary and multinary cases is completed and multinary systems then can be studied in terms of monotone binary coherent systems, introduced in a companion paper.² Through various results, multinary systems are examined in terms of structure functions and of life functions; fundamental relations for their analysis are obtained with their set characterizations; the main axis that can be retained among the numerous types of coherence is emphasized, in a unified way, through relevance; reliability models are examined through performance processes, life lengths and performance functions; and Birnbaum's factors of importance are thoroughly extended to the multinary case. Fundamental results proposed in previous studies are thus completed with a shorter unified approach.     

On the Nature of OR — Entering the Fray

In 1980 a seminar of operational researchers and practitioners from a variety of different countries concluded that there was a remarkable consensus about the way that the process of operational research and systems analysis should be understood and practised. Since then the development of new methods has continued apace, stimulated by interaction with the social sciences and paradigms other than natural science. This paper enters the debate, started in this journal, about the nature of OR's status as science or technology. It recognizes the historic claims of science on OR, but it suggests that for ‘private’ consumption, technology will prove more fruitful, and for ‘public’ consumption practitioners will increasingly adopt the label ‘consultant’. Ackoff's original six-step method of OR is updated to reflect current OR practice. The process suggested acknowledges the importance of context, socio-political factors and the growing role of facilitation.     

From Optimizing to Learning: A Development of Systems Thinking for the 1990s

In any subject concerned with rational intervention in human affairs, theory must lead to practice; but practice is the source of theory: neither theory nor practice is prime. We can examine this ‘groundless’ relation by asking what intellectual framework F is applied in what methodology M to what area of application A? If we do this for O.R., systems analysis, systems engineering etc., we see that F and M have changed dramatically between the 1950s and the 1980s, yielding the ‘hard’ and ‘soft’ traditions of systems thinking. The ‘hard’ tradition, based on goal seeking, is examined in the work of Simon and contrasted with the ‘soft’ tradition, based on learning, as exemplified in the work of Vickers and the development of soft systems methodology. The two are complementary, but the relation between them is that the ‘hard’ is a special case of ‘soft’ systems thinking. This analysis makes sense of the recent history of management science and helps to prepare us for the 1990s.     

The metalogic of economic predictions,calculations and propositions

Indeterminacy is a matter of concern in the analysis of ideal forms and this paper shows that Gödel incompleteness and undecidability directly pertain to the analysis of theoretical economic systems - specifically, that certain solution concepts such as ‘predictions of characteristics of policy outcomes guided by a social welfare function’, ‘the existence of equilibrium’, ‘the existence of welfare optima’ are subject to Gödel undecidability. This consideration brings into question the convention of a finite decision unit or economic actor, and the paper considers more-appropriate (metatheoretic) assumption structures and the implications of specifying richer information structures in microeconomics and choice theory.     

Beyond methodology choice: critical systems thinking as critically systemic discourse

Professional competence in applied disciplines such as OR/MS requires both technical expertise and critically reflective skills. Yet, a widespread misconception has taken hold of the OR/MS community: ‘critical’ and ‘emancipatory’ systems methodologies are opposed to ‘hard’ and ‘soft’ ones as if they were sensible alternatives. Accordingly, adequate ‘methodology choice’ is now widely considered a key condition of reflective professional practice; critical systems thinking (CST) is understood to deal mainly with this issue. The present paper argues that this conception of CST is neither theoretically sound nor conducive to reflective practice. An examination of the two major current strands of CST suggests some basic requirements of an alternative conception: (1) Reflective practice depends more on a framework of critical argumentation and discourse than on a framework of methodology choice. (2) A well-conceived discursive systems approach will give a proper place to the public sphere. (3) The much-discussed emancipatory orientation of CST inheres in the methodological requirements of discourse rather than in an arbitrary ‘commitment’ on the part of the systems practitioner. (4) Systemic boundary critique—the methodological core concept of critical systems heuristics (CSH)—allows us to translate these requirements into practical methodology. (5) Contrary to present conceptions of methodological pluralism or ‘complementarism’, boundary critique must not be subordinated to methodology choice, for it is constitutive of all critical inquiry and practice. These considerations lead to a reconstitution of CST, and to a new view of reflective professional practice in general, as critically systemic discourse.     

Process and content: two ways of using SSM

Soft systems methodology (SSM) includes several ways of gaining a rich appreciation of the problem situation addressed. ‘Analysis One’, exploration of the intervention itself, is the subject here, since it is sparsely covered in the literature. The analysis is conducted in terms of three roles: ‘client’, ‘problem solver’ and ‘problem owner’. Whoever is in the role of ‘problem solver’ is free to define a list of possible ‘problem owners’, which brings many perspectives to bear on the situation. It was realized that ‘client’ and ‘problem solver’ should themselves feature in the ‘problem owner’ list. The ‘problem’ owned by the ‘problem solver’ is that of undertaking the intervention. This led to a realization that SSM is relevant to both the content of a perceived situation (SSMc) and the process of dealing with that content (SSMp). This development is described and illustrated by work in the National Health Service. The focus of the SSM use was to define the intellectual process for a service specification project which NHS professionals would themselves carry out.     

Patterned Systems Design

The explosion in the use of on-line computer systems has resulted in very large numbers of people being exposed to these systems and has added greatly to the importance of ‘user-friendliness’.In this paper, a fresh approach, which makes ‘option’ selection easier, is described. The approach not only leads to user-friendly systems but also aids the design process, program development and testing, and system maintenance.The essence of the approach is that it leads to systems which conform to familiar patterns.     

How is cultural influence manifested in the formation of mathematics textbooks? A comparative case study of resource book series between Shanghai and England

Focusing on issues about the development of mathematics textbooks from a cultural perspective, this study examined a widely-used curriculum resource series, One Lesson One Exercise, published in China, and its adapted English series, published in the UK, to explore how cultural influence is manifested in the two series of resource books. For the study we established a conceptual framework classifying culture into six types in relation to people’s beliefs, values and ways of interacting about them, for data collection and analysis. The results indicate that there exist considerable differences between the Chinese and the English series that are related to cultural factors. It appears that, to a large extent, culture plays an essential role in the development of mathematics textbooks. Concerning the different types of culture, the results show that most adaptations between the Chinese series and the English series are related to ‘ways of behaving and customs’ and ‘artifacts, flora and fauna’, followed by ‘identities’ and ‘geography’, and the least are related to ‘organisations’ and ‘history’. Based on the study, we argue that the relevance and importance of culture to the development of mathematics textbooks must not be underestimated, and more research in this direction is needed.     

Metrics for bullwhip effect analysis

A bullwhip measurement system based on a two-criterion assessment—‘internal process efficiency’ and ‘customer service level’—is developed in this paper. The framework is designed to assess both individual (single member) and systemic (whole supply chain) performances. Data collection and calculation methods, update and monitoring mechanisms, as well as related procedures for each metric used, are detailed. A comparative analysis with a recent work by Barlas and Gunduz is performed, showing that the adoption of the proposed performance measurement system can help academics and practitioners to better understand, study and avoid the bullwhip effect. Such analysis also provides evidence on the relevance of considering when analysing the bullwhip effect in supply chains, the ‘customer importance’ aspect that is often forgotten in the published literature.     

Reduced order modeling of nonlinear time periodic systems subjected to external periodic excitations

In this work, new methodologies for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov–Floquet (L–F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and nonlinearity takes the form of quasiperiodic functions. The techniques proposed here construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system.Specifically, two methods are discussed to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’. The second novel technique proposed here extends the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on this extended invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via extended invariant manifold approach is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handling systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. It is anticipated that these order reduction techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.     

Initial Conditions and the ‘Open Systems’ Argument against Laws of Nature

This article attacks ‘open systems’ arguments that because constant conjunctions are not generally observed in the real world of open systems we should be highly skeptical that universal laws exist. This work differs from other critiques of open system arguments against laws of nature by not focusing on laws themselves, but rather on the inference from open systems. We argue that open system arguments fail for two related reasons: 1) because they cannot account for the ‘systems’ central to their argument (nor the implied systems labeled ‘exogenous factors’ in relation to the system of interest) and 2) they are nomocentric, fixated on laws while ignoring initial and antecedent conditions that are able to account for systems and exogenous factors within a fundamentalist framework.     

Recent Developments in Critical Management Science

For much of its history management science had a quantitative and technical emphasis. More recently, there has been a move towards more subjective approaches such as ‘soft OR’ and ‘soft systems’. Currently, there is interest in ‘critical management science’ drawing on critical theory, particularly the work of Habermas. This paper reviews developments in critical management science, in particular critiques of traditional and ‘soft’ management science; Jackson and Keys' system of systems methodology; critical management science methodologies and the problem of power in bringing about change; and the postmodernist critique.     

A unified theory for coherent systems in reliability I. A generalization for some classic theory: Monotone binary coherent systems

Binary coherent system theory has played an important part in reliability. Its extension to (‘degradable’ or ‘multistate’ or) multinary systems has recently been considered in various papers, through various definitions. This paper lays the foundations of a unified theory for coherent systems by first giving unified arguments to apply and to investigate further binary and multinary systems. Monotone binary systems are introduced and examined by generalizing classic deterministic and probabilistic results. Applications of monotone coherence to the multinary case are proposed in a companion paper with a unified viewpoint on multinary coherent systems. As an indication, monotone constraints are defined with a partition of the component set and some total orderings imposed on the elements of the concerned partition. The discrete partition retrieves the classic theory of (free) binary coherent systems; some constraints defined from component levels lead to multinary coherent systems; some other constraints apply to systems submitted to some ‘common stresses’, e.g. the organizing system of a monotone coherent decomposition.     

A Event Occurrence Rules based Compact Modeling Formalism for a Class of Discrete Event Systems

The analysis, failure diagnosis and control of discrete event systems (DESs) requires an accurate model of the system. In this paper we present a methodology which makes the task of modeling DESs considerably less cumbersome, less error prone, and more user-friendly than it usually is. In doing so we simplify the modeling formalism of [4, 5], proposed for obtaining valid models of complex discrete event systems, by eliminating ‘precedence relations’, and capturing them as part of the ‘event occurrence rules’. Under the new modeling formalism the size of the system model is polynomial in the number of signals; whereas the number of states in the commonly used automata models is exponential in the number of signals. We present automated techniques for deriving an automaton model from the model in the proposed formalism. We illustrate the modeling formalism using examples drawn from manufacturing and process control systems.     

Observing mathematical fluency through students’ oral responses

‘Procedural’ fluency in mathematics is often judged solely on numerical representations. ‘Mathematical’ fluency incorporates explaining and justifying as well as producing correct numerical solutions. To observe mathematical fluency, representations additional to a student’s numerical work should be considered. This paper presents analysis of students’ oral responses. Findings suggested oral responses are important vantage points from which to view fluency – particularly characteristics harder to notice through numerical work such as reasoning. Students’ oral responses were particularly important when students’ written (language) responses were absent/inconsistent. Findings also revealed the importance of everyday language alongside technical terms for observing reasoning as a fluency characteristic. Students used high modality verbs and language features, such as connectives, to explain concepts and justify their thinking. The results of this study purport that to gain a fuller picture of students’ fluency, specifically their explanations or reasoning, students’ oral responses should be analyzed, not simply numerical work.