A five facets frame for the design of heuristics

The author suggested to distinguish between the ‘engineering approach’ and the ‘mathematical approach’ in connection with the design of heuristics. Stainton and Papoulias extended the scope by suggesting the ‘relational approach’. Based upon this extension, a five facets frame is presented here which is suggested to precede and accompany the ‘technical’ design of the heuristic. The facets are: coverage by participation, experience by doing, abstraction by structuring, extension by comparison, exploration by creativity.     

Using DEA to assess NATO burden-sharing

As the member making many of the most visible contributions to NATO, the USA has often claimed that they shoulder the heaviest ‘burden’ in maintaining the objectives of the alliance. This claim has been backed by research which has concentrated on contributions such as defence expenditure and benefits such as protection from external threats. However, modern alliances entail the exchange of multiple forms of alliance benefits and liabilities and therefore the study of ‘burden-sharing’ in these alliances is a more complicated accounting problem than has been acknowledged by previous research. In this paper, burden-sharing is studied using Data Envelopment Analysis (DEA). This is a novel application of DEA. Instead of calculating relative ‘efficiencies’, the analysis produces a ‘net-burden index’ for each member nation of NATO. The results of the analysis indicate that whilst the USA shoulders a heavy burden, some other member nations, including Canada and Spain, may in fact shoulder a heavier burden.     

On the nature of OR: taking stock

This paper argues that OR, having reached its maturity, must now play to its strengths. In strategic terms this means competing in those areas where OR's core competences can be brought to bear. Using a competence model it is suggested that OR's core products are (i) the development and implementation of the quantitative, algorithmic ‘smart bits’ and (ii) the ‘helpful ways’ of managing intervention processes. These core products are supported and sustained by three core competences labelled process, analytic, and context. Individuals and small groups of practitioners develop ‘strands of practice’ and larger groups ‘webs of practice’ on the basis of their core competences. It is argued that this is giving rise to the emergence of three archetypes of OR service, namely the OR technical consultancy, the OR process consultancy, and the full service OR consultancy. Both the technical and process consulting are built around ‘strands of practice’ of individuals and find their natural home in small service providers. The full service OR consulting practice, in the past located in internal OR groups, will in the future be located within the large management consultancies, which are capable of managing ‘webs of practice’. The implications for the worlds of OR practice and academia are examined.     

Mathematics,Applicable versus Pure‐and‐Applied

‘Applicable mathematics’ is based on the idea that mathematics provides a source of models of proposed and postulated states of affairs. The use of the model is essentially to simulate exploration of the possibilities of the situation to which the model relates. Two main areas where this ‘investigation of the implications of possibilities’ is needed are in discussing putative scientific hypotheses and in discussing the implications of proposed or suggested social and technical innovation. Much of what has been customarily called ‘pure mathematics’ can be regarded as second‐order applicable mathematics, i.e. mathematics which adds to and strengthens our over‐all model building capability.

     

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.     

An optimization model for aggregation of prescribed burn units

Fire is a natural component of many terrestrial ecosystems; however, uncontrolled intense wildfires can cause loss of human life and destruction of natural resources. Prescribed burning is a management activity undertaken for the purposes of both wildfire hazard reduction and the preservation of fire-adapted ecosystems. Achievement of prescribed burn targets is made difficult by operational constraints such as limited personnel, equipment and suitable weather for undertaking burning. Prescribed burn program implementation may benefit from efficiencies gained in undertaking larger burns. Here, we present a mixed-integer programming formulation for aggregation of prescribed burn units. The model minimizes the total prescribed burn perimeter requiring management, by aggregating existing ‘fundamental’ burn units into larger compact and contiguous units or ‘clusters’. This problem is a special case of the ‘supervised regionalization’ or the ‘\(p\)-regions problem’. The model’s functionality is demonstrated on a test landscape and a number of extensions and implementation issues are discussed.     

Policy analytics need more than a spreadsheet: a case study in funding formulae

This article presents two case studies, concerning the allocation of £Billions by a mechanism communicated via spreadsheet models. It argues that technical analytic skills as well as policy development skills are a vital component of governance. In the UK, Central Government uses funding formulae to distribute money to local service providers. One commonly stated goal of such formulae is equity of service provision. However, given the complexity of public services, together with variations in need, delivery style and the exercise of stakeholder judgement as to which needs should be met and how, such formulae frequently obscure the process by which equity has been taken into account. One policy ‘solution’ to managing such tensions is to seek ‘transparency’. With respect to funding formulae, this commonly involves publishing the underlying data and formulae in spreadsheets. This paper extends the argument that such ‘transparency’ requires an audience that understands the policy assumptions (and related conceptualisations), data sources, methodological approaches and interpretation of results. It demonstrates how the search for policy ‘transparency’ is also met by the technical quality assurance goals that the operational research community would recognise as best practice in the development both of software generally and spreadsheet models specifically. Illustrative examples of complex formulae acting to subvert equity are drawn from the English Fire and Rescue Service and Police Service allocation formulae. In the former, an increase in the amount of deprivation, as measured by one of six indicators, has the perverse effect of decreasing the financial allocation. In the latter, metropolitan areas such as London are found to gain most from the inclusion of variables measuring sparsity. The conclusion from these scenarios is that the steps needed to for technical quality assurance and policy transparency are mutually reinforcing goals, with policy analysts urged to make greater use of technical analytic skills in software development.     

Interaction between data analysis and telecommunications

We consider interaction between data analysis and telecommunications from both sides, examining the contribution of each discipline to the other. The fast changes in telecommunications have some important consequences. First, the importance of statistics in the design of a network is growing, given the evolution of technology towards more digitalization and the resulting changes in dimensioning the network. Second, the technical tools of statistics are deeply modified, and there is concern about how to take this into account—particularly how to take advantage of the new economy of ‘value added services’ which uses the network as a ‘market place’.     

The effects of exogenous variables in efficiency measurement—A monte carlo study

A Monte Carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis (DEA) method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control. In making efficiency measurements and comparisons, one must separate the effects of the environment (the exogenous factors) and the effects of the productive efficiency. There are two basic approaches to account for the effects of exogenous variables: (1) an one-step procedure which includes the exogenous variables directly in estimating the efficiency measures, and (2) a two-step procedure which first estimates the relative ‘gross’ efficiencies using inputs and outputs, then analyzes the effects of the exogenous variables on the ‘gross’ efficiency. The results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one-step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for. However, the effects of exogenous variables are significant for the two-step approach, especially for the DEA methods.     

Decomposition of technical and scale efficiencies in two-stage production systems

Conventional data envelopment analysis (DEA) models are used to measure the technical and scale efficiencies of a system when it is considered as a whole unit. This paper extends the efficiency measurement to two-stage systems where each stage has one process and all the outputs from the first process become the inputs of the second. An input-oriented DEA model for the first process is developed to separate the process efficiency into the input technical and scale efficiencies, and an output-oriented model is developed for the second process to separate the process efficiency into the output technical and scale efficiencies. Combining the two models, the system efficiency is expressed as the product of the overall technical and scale efficiencies, where the overall technical and scale efficiencies are the products of the corresponding efficiencies of the two processes, respectively. The detailed decomposition allows the sources of inefficiency to be identified.     

A class of balanced allocation problems

This paper considers the problem of ‘balanced’ allocation of incoming jobs to a set of machines with varying efficiencies. A variance criterion is used for defining the extent of imbalance. This research also deals with the case when the rate of disposal of jobs by a machine is not deterministic but a random variable. A few alternative criteria for imbalance are also proposed.     

Weight assurance region in two-stage additive efficiency decomposition DEA model: an application to school data

In this paper we use the additive efficiency decomposition approach in two-stage data envelopment analysis. Initially, we evaluate the variable returns to scale version and face a structural difficulty of the model. In an extreme case, weights ξ₁ or ξ₂, which represent the relative importance of the performance of the first and second stages, respectively, become zero for a number of decision making units (DMUs). As a result, individual stage efficiencies for these DMUs are undefined. We propose a weight assurance region model to restrict ξ₁ and ξ₂, which ensures that both weights are always positive, and therefore individual stage efficiency is always defined. Furthermore, the proposed model is appropriate for policy making in the presence of a priori information about the relative importance of each stage in the overall process. We employ the new model to evaluate the efficiency of secondary education in 65 countries and construct an overall ‘school efficiency’ index. In the first stage we measure the ‘learning environment efficiency’ and in the second we measure the ‘student’s performance efficiency’.     

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.     

Resource allocation based on cost efficiency

In this paper, we consider a resource allocation (RA) problem and develop an approach based on cost (overall) efficiency. The aim is to allocate some inputs among decision making units (DMUs) in such way that their cost efficiencies improve or stay unchanged after RA. We formulate a multi-objective linear programming problem using two different strategies. First, we propose an RA model which keeps the cost efficiencies of units unchanged. This is done assuming fixed technical and allocative efficiencies. The approach is based on the assumption that the decision maker (DM) may not have big changes in the structure of DMUs within a short term. The second strategy does not impose any restrictions on technical and allocative efficiencies. It guarantees that none of the cost efficiencies of DMUs get worse after RA, and the improvement for units is possible if it is feasible and beneficial. Two numerical examples and an empirical illustration are also provided.     

A framework for group decision support systems: Combining AI tools and OR techniques

Work on the implementation of Group Decision Support Systems has to exploit recent advancements of computer science. Existing frameworks for single-user Decision Support Systems, based on well-established Operations Research methods such as Multicriteria Decision Making techniques, have to be integrated with successful technical developments in electronic communication and computing. Starting from the presentation of the related Operations Research background, this paper proceeds by discussing challenges coming from the areas of Computer-Supported Cooperative Work and Information Systems on the World Wide Web platform. Based on this discussion, a framework for an ‘open’, computer-mediated Group Decision Support System is proposed. The term ‘open’ is related to a platform-independent system, which can efficiently support alternative types of goals and control protocols between its users.     

The Role of Heuristic Proof in Mathematics Teaching

With the great emphasis now being placed on the importance of ‘rigour’ in new mathematics programmes, many educators have been led to disparage intuition as the vitally important tool that it is in developing mathematical insights. Increasingly one sees evidence, even in technical schools, of pupils actually being discouraged from arriving at mathematical perceptions through unorthodox (and uncontrollable!) channels of analogy involving considerable divergent thinking or through consideration of physical models with which they are familiar.

As a mathematician, this pre‐occupation with ‘purism’ greatly disturbs the author. Mathematicians do not create through the formal apparatus ‐‐ they only apply formalism after ‘guessing’ results intuitionally. We have become overconcerned with the way the package is wrapped and less concerned with what is in it. Especially, the role of heuristic argument is widely misunderstood and misused in schools and colleges. The author hopes that this article will help to rectify this sorry state of affairs.     

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.     

Conditioning in fuzzy environment

The concepts of ‘conditional fuzzy algebra’ and ‘conditional evaluation of possibility’ are introduced when the conditioning event is either in the initial algebra or does not belong to it. In the latter case a ‘wider’ fuzzy environment in which ‘old’ and ‘new’ elements could be considered together is constructed, and a new evaluation of possibility which allows to evaluate the elements of such new environment is defined.     

基于数据包络分析方法的上市银行盈利效率研究

银行是我国金融市场的主导力量。银行的一举一动对金融市场,乃至整体经济运行均有重要的影响。特别是在经济进入新常态,金融深化改革的新环境下,研究银行的效率,既是银行发展的内在需要,也是宏观经济的必然需求。本文基于银行所有者的角度,以资本金和不良贷款作为投入,利息收入和非利息收入作为产出,测算2015年16家上市银行的盈利效率,结果表明:上市银行盈利的纯技术效率普遍较高,规模效率受规模因素影响较显著;国有商业银行的规模效率低,导致其技术效率偏低。对于大型银行,规模已经成为影响盈利技术效率的重要因素之一。     

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.