Voluntary Operational Research

Operational Research has traditionally been carried out in organizations which are able and willing to pay for it; this tends to restrict it to the larger industrial, commercial or governmental bodies. In this paper we reflect on an O.R. project done on behalf of a group of charities, to whom, as with most voluntary organizations, the skills of operational researchers are not usually available.It seems likely that voluntary organizations will have an increasing role as leisure time increases, and in any case the widening scope and complex context of their activities means that they could benefit from the kind of help that operational researchers can give. At the same time, O.R. workers who care about a particular voluntary organization may want to offer their skills to it. However, the skills of operational researchers are not as obviously relevant to voluntary organizations as is the professional expertise of lawyers and accountants. Undertaking O.R. projects as a voluntary helper rather than as a paid consultant, and in voluntary organizations rather than the more usual clients for O.R., has significant implications for the approach and methods used.We discuss these issues in the light of our recent experiences of carrying out ‘voluntary Operational Research’.     

The contiguity of probability measures and asymptotic inference in continuous time stationary diffusions and Gaussian processes with known covariance

We establish contiguity of families of probability measures indexed by T, as T → ∞, for classes of continuous time stochastic processes which are either stationary diffusions or Gaussian processes with known covariance. In most cases, and in all the examples we consider in Section 4, the covariance is completely determined by observing the process continuously over any finite interval of time. Many important consequences pertaining to properties of tests and estimators, outlined in Section 5, will then apply.     

Introducing the Microcomputer into the O.R. Department

This paper reviews the typical main-frame computer services that are currently available and by accepting the alleged advantages of microcomputers postulates the ideal computing requirements of O.R. departments. Experience of microcomputers in O.R. departments, within the N.C.B. and elsewhere, is considered in relation to these ideal requirements. It is concluded that although some main-frame computer services will remain essential to O.R. and accepting that the main-frame can give a reasonable general computing service, the micro offers additional advantages. These include: lower cost and/or better service, the ability to configure the equipment exactly to meet O.R. needs; full control over applications and priorities; and portability - which means that computing power can now be taken direct to the manager by the O.R. department.     

The Role of Management Science

Many of the arguments that are found in the literature on the theme "O.R./M.S. in crisis" stem not just from alternative definitions of O.R./M.S., but from differences in strongly held views about its scope and role in organisations, and these are then reflected in the vehemence with which certain definitions are defended or criticised. It is when the hopes and aspirations of O.R./M.S. are compared with what is being achieved in practice, that we realise the degree to which O.R./M.S. has failed to live up to its original promise. In most organisations, O.R. analysts are expected and are happy to act as technicians and not as advisers, so that technique orientation and concern with tactical problems are constantly reinforced. In addition, managers in various functions have become aware of the potential contribution of analytical modelling in their own spheres and have begun to recruit analysts direct, resulting in the possible fragmentation of O.R. and the loss of its unique identity. The responsibilities of O.R./M.S. obviously relate not only to its organisational status, but also to an examination of and an identification with organisational goals. Many O.R. analysts are plainly more comfortable when these goals are clearly defined for them, an attitude which people from other professions will readily endorse, but if O.R./M.S. has any aspirations to get involved in strategic problems, it will have to pose questions about the validity and appropriateness of organisational goals and try to influence the formulation of problems accordingly.     

Constraint satisfaction problems: Algorithms and applications

A constraint satisfaction problem (CSP) requires a value, selected from a given finite domain, to be assigned to each variable in the problem, so that all constraints relating the variables are satisfied. Many combinatorial problems in operational research, such as scheduling and timetabling, can be formulated as CSPs. Researchers in artificial intelligence (AI) usually adopt a constraint satisfaction approach as their preferred method when tackling such problems. However, constraint satisfaction approaches are not widely known amongst operational researchers. The aim of this paper is to introduce constraint satisfaction to the operational researcher. We start by defining CSPs, and describing the basic techniques for solving them. We then show how various combinatorial optimization problems are solved using a constraint satisfaction approach. Based on computational experience in the literature, constraint satisfaction approaches are compared with well-known operational research (OR) techniques such as integer programming, branch and bound, and simulated annealing.     

Manufacturer's optimal pricing and lot-sizing policies under trade-credit financing

In the year 2006, Teng et al considered an appropriate economic production quantity (EPQ) model in which the manufacturer receives the supplier's trade credit and provides trade credit to the customer simultaneously. The following two payment methods were discussed by Teng et al: The main purpose of this paper is summarized below: Finally, with a view to further motivating the interested researchers for using the methodology and mathematical analytic techniques in several other contexts in the field, we have chosen to include, in Section 12, a number of related recent works in the field.     

THE CALCULUS OF GENERATING FUNCTIONS AND THE FORMAL ENERGY FOR HAMILTONIAN ALGORITHMS

1.DarbouxTransformationConsidercotangentbundleT*R"acRZnwithnaturalsymplecticstructureandtheproductofcotangentbundles(T*R")x(T*R")=R4nwithnaturalproductsymplecticstructureCorrespondingly,weconsidertheproductspaceR"xR"rsRZn.ItscotangentbunT*(R"xR")=T*Rzn=R'nhasnaturalsymplecticstructure')PreparedbyQinMengzhaoChoosesymplecticcoordinatesz~(p,q)onthesymplecticmanifold,thenforsymplectictransformationg:T*R"~T*R",wehaveitisaLagrangiansubmanifoldofT*R"xT*RninR4n~(R'",J4.).NotethatonR4nth…     

O.R. and the Systems Movement: Mappings and Conflicts

The ‘crisis’ debate in O.R. expresses concern at the divergence between textbook O.R. and what practitioners actually do. The debate is examined by comparing O.R., systems analysis and systems engineering. They are all wedded to logic in situations in which logic may not be paramount. The science in O.R. applies only to aggregate results, but the practitioner must deal with a specific situation. The tradition of systems thinking which emerged from organismic biology is described. It leads to a way out of the O.R. ‘crisis’, by providing a formal structuring of a paradigm of learning rather than optimization. O.R. can aspire to match natural science, and pass the problems by; or it can close the textbook/practitioner gap by changing its concept of ‘being scientific’.     

Anthropology and O.R.: The Place of Observation in Management Science Process

This paper is an argument to combine the methods of observation with O.R. techniques to form the basis of a management science process. The paper begins by defining a typology showing where observation methods seem to be most appropriate in O.R. interventions. This is followed by a section outlining some of the techniques and problems of observation as seen from the field of anthropology. Using this theory, combined with personal experience, an observation process is developed. An example of using the process is then given.     

Nonprobabilistic entropies and indetermination measures in the setting of fuzzy sets theory

Our purpose in this paper is first of all to build an axiomatic generalization for the nonprobabilistic entropy of De Luca and Termini in the setting of fuzzy sets theory.We then build from this entropy an indetermination measure which can be used like discriminant function in Pattern Recognition when patterns are described by means of fuzzy sets.     

A Kuhnian Crisis in Management Science?

A survey of the Journal of the O.R. Society in 1978 shows that Ackoff's papers were part of a quite widespread and often pessimistic debate about the practical success of O.R. A similar survey for 1968 shows, on the other hand, a widespread mood of optimism. It is suggested that O.R. is now in a period of crisis analogous to that described by Kuhn in the Natural Sciences, when the dominant framework of assumptions appears to fail in relation to important problems. When such failures persist, alternative frameworks are proposed challenging the hitherto accepted view, and an increasingly wide-ranging debate develops. Many of the features of such debates, as outlined by Kuhn, seem to be present in the current controversy within O.R. More specifically, it seems possible in O.R. and related fields to identify three rival sets of proposals, which may be labelled official, reformist (e.g. Ackoffian) and revolutionary. However, the debate in O.R. differs from that in the Natural Sciences because it is not just about the best means of understanding the empirical world. It is also about the type of social world to be constructed through the framework of assumptions adopted. Our view is that in the current debate, proponents of the reformist stance will probably win. However, this may be very much an interim solution.     

Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand

This paper presents an inventory model for deteriorating items over a finite time horizon where the demand increases linearly with time. The method is developed by assuming that the successive replenishment cycle lengths are the same. Many O.R. scientists/researchers obtained an optimal replenishment schedule where the replenishment cost is constant in each cycle length over the finite time horizon. In this paper, we relax the assumption of fixed replenishment cost. The replenishment cost per replenishment is taken to be linearly dependent on the lot-size of that replenishment. Shortages are allowed and are fully backlogged. As a special case, the results for the model without shortages are derived. Finally, two numerical examples are presented to illustrate the model.     

The Art of Course Planning: Soft O.R. in Action

This article is a case study described from two viewpoints: that of an analyst and that of a ‘decision-maker’. It describes the use of two ‘soft O.R.’ methods in helping the members of a university O.R. group to plan revisions to a postgraduate Diploma course, resulting in the implementation of an improved course. One author conducted the exercise while the other was a member of the client group. Given that case studies are usually written by the analyst alone, it is hoped that a client's eye-view will be useful as feedback for practitioners and can also introduce some of the concepts and terminology of soft O.R. to those engaged in more mathematical O.R. activities.     

Fuzzy processes

In this paper, contributions to fuzzy probability and to differential equations with fuzzy parameters are made.After an introductory section, a review of fuzzy sets and fuzzy algebra is given in Section 2. The main new results of the investigation are contained in Section 3.In Section 3, Zadeh's definition of the probability of a ‘fuzzy event’ the average value of a fuzzy function are extended into the time domain. It is then shown that not only grades of membership, but also probabilistic processes with notions of fuzziness contained, can be defined which obey ordinary, matric, or integro-differential equations. Applications are also given in Section 3.     

Artificial Intelligence—An Overview of Similarities with O.R.

A brief outline of A.I. is provided, noting problems, techniques and objectives which are similar to those found in O.R. It is intended that this will indicate to O.R. workers which A.I. areas might be worth following up as relevant to their own work and which problems in A.I. might be attacked by the O.R. community as part of the development of intelligent support systems.     

多数满意陪审团定理的极大和极小概率

证明了在群体中,当各个体正确判断方案满意性的概率越分散,由多数满意规则确定的相应群体正确判断方案满意性的概率将越大.根据这一结果得到：在所有的个体正确判断方案满意性的平均概率相同的情况下,由多数满意陪审团定理决定的群体正确判断方案满意性的极大概率和极小概率的表达式.     

Fuzzy Pattern Recognition Approach to Construction Contractor Selection

Contractor selection is a complex process crucial to ensuring the success of construction projects. Existing methods by which owners select a suitable contractor have been inadequate because it is difficult for decision-makers to evaluate contractor bids against inexact qualitative criteria. The purpose of this paper is to propose a Multiple-layer Fuzzy Pattern Recognition (MFPR) approach to solve contractor selection problem. Integrating judgments, experience and preferences of decision-makers, this paper uses the paired comparison method to decide relative membership degrees of qualitative criteria as well as weights of the criteria set, a case study for a channel construction project was used to demonstrate the feasibility of this approach. The findings clearly indicate that the techniques may successfully harmonize different opinions and reach a group consensus.     

Metric properties and exceptional sets of β-expansions over formal Laurent series

This paper is concerned with the metric properties of β-expansions over the field of formal Laurent series. We will see that there are essential differences between β-expansions of the formal Laurent series case and the classical real case. Also the Hausdorff dimensions of some exceptional sets, with respect to the Haar measure, are determined. Authors’ addresses: Bing Li and Jian Xu, School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China; Jun Wu, Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China     

The Assessment of Diurnal Storage Requirements for Gas Supply Systems

The British Gas Corporation is preparing for substantial capital expenditure to provide additional gas storage capacity, which is required to balance out the within-day variations of demand, Conversion to natural gas, with its higher calorific value, resulted in a substantial increase in the effective volume of gas storage available. This surplus has been eroded by the rapid growth in demand over the decade since conversion, and new investment in storage will be required if current forecasts of growth are correct. The assessment of the storage requirements has therefore become more important, and more sophisticated methods are being developed. In this paper the factors affecting the need for storage are examined, the methods adopted in incorporating these factors into a simulation model are discussed, and the results from the models are presented. Consideration is given to the national policy aspects of the problem and to the interactions between O.R. and other staff within B.G.C. during the development of the project.