On classifying inputs and outputs in DEA: A revised model

Cook and Zhu [Cook, W.D., Zhu, J., 2007. Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research 180, 692–699] introduced a new method to determine whether a measure is an input or an output. In practice, however, their method may produce incorrect efficiency scores due to a computational problem as result of introducing a large positive number to the model. This note introduces a revised model that does not need such a large positive number.     

Rejoinder to “A note on Galvão's a graph theoretical bound for the p-median problem”

A few comments are added to the note by L. Morgenstern (1983) on a work authored by me (1981) published in European Journal of Operational Research.     

Differential dynamic programming and separable programs

This paper deals with differential dynamic programming for solving nonlinear separable programs. The present algorithm and its derivation are rather different from differential dynamic programming algorithms and their derivations by Mayne and Jacobson, who have not proved the convergence of their algorithms. The local convergence of the present algorithm is proved, and numerical examples are given.The author would like to express his appreciation to Professors H. Mine and T. Katayama for their helpful discussions. The author is also indebted to Professor D. Q. Mayne for drawing his attention to Refs. 1–2.     

Better Than Survival: The Need for Research to Strengthen Planning in Industry and the Public Service

Editor's NoteThis is an invited contribution in our occasional series O.R. Reflections, in which are presented essentially personal views of O.R., based on contributors' own experience. What follows is a slightly revised version of the author's inaugural lecture as Professor of Systems and Operational Research at the University of Warwick on 10th May 1982.The author draws on his experience in industry and in an international research institute (IIASA) o restate the importance of strategic planning if organisations are to do better than mere survival. He argues the need for problem-oriented, inter-disciplinary research to support such activity and suggests that such research, directed towards investment and strategic policy, has a potential value which is quite out of proportion to the money currently invested in it.     

Silent-noisy marksmanship contest with random termination

We consider a marksmanship contest in which Player I has one silent bullet, whereas Player II has one noisy bullet, the first contestant to hit his target wins, and the contest is to be terminated at a random timeT with cdfH(t). The model is a silent-noisy version of our previous paper (Ref. 8), and an extension of silent-noisy duel to nonzero-sum games of timing under an uncertain environment. It is shown that the uncertainty on the termination of the contest has influence on the equilibrium strategies and the equilibrium values, but the silent player has no advantages over the noisy one, in such a nonzero-sum model.The author thanks Professor M. Sakaguchi, Osaka University, who contributed to the research on mathematical decision-making problems and expresses appreciation for his continuous encouragement and guidance. The author also thanks Professor G. Kimeldorf, The University of Texas at Dallas, who invited the author to his university. Finally, the author expresses appreciation to Professors K. Sugahara and W. Fukui, Himeji Institute of Technology, for their encouragement and support.     

Calculating the cone of directions of constancy

This note presents an algorithm that finds the cone of directions of constancy of a differentiable, faithfully convex function.This work was supported by the National Research Council of Canada. The author is indebted to Professor S. Zlobec for suggesting the topic and for his guidance.     

Linear pursuit-evasion games with bounded state spaces

The problem of linear pursuit-evasion games with bounded state spaces is considered. Some sufficient conditions for optimality are established, and an example is given.This research was carried out while the author was a Visiting Associate Research Engineer at the University of California at Berkeley. The research was supported by the Office of Naval Research, Grant No. N00014-69-A-0200-1012. The author would like to express his gratitude to Professor G. Leitmann for discussions and for making possible his visit at Berkeley.     

On the range sets of variational inequalities

This paper investigates the closedness and convexity of the range sets of the variational inequality (VI) problem defined by an affine mappingM and a nonempty closed convex setK. It is proved that the range set is closed ifK is the union of a polyhedron and a compact convex set. Counterexamples are given such that the range set is not closed even ifK is a simple geometrical figure such as a circular cone or a circular cylinder in a three-dimensional space. Several sufficient conditions for closedness and convexity of the range set are presented. Characterization for the convex hull of the range set is established in the case whereK is a cone, while characterization for the closure of the convex hull of the range set is established in general. Finally, some applications to stability of VI problems are derived.This work was supported by the Australian Research Council.We are grateful to Professors M. Seetharama Gowda, Olvi Mangasarian, Jong-Shi Pang, and Steve Robinson for references. We are thankful to Professor Jim Burke for discussions on Theorem 2.1 and Counterexample 3.5.     

An analysis of Klimov's problem with parallel servers

We introduce a family of undiscounted branching bandits on parallel servers under controls which can impose priorities between customer classes. This family can be used to model a wide range of multi-class queueing scheduling problems, with the capacity to incorporate problem features such as machine breakdowns, complex patterns of preemption/non-preemption and semi-Markov extensions. An index policy (which we call Klimov's rule) is developed which is optimal in the particular case of a single server. An expression for its cost suboptimality is given for parallel servers. Under additional conditions on the nature of the stochastic evolution of the systems concerned, the policy is shown to be asymptotically optimal in a heavy traffic limit. These general results are utilised to develop an analysis of the index policy for a parallel server version of Klimov's classical M/GI/1 system with Bernoulli feedback. This work was supported by the Engineering and Physical Research Council through the award of grant GR/M09308. The author would also like to express his appreciation to Professor I. C. Paschalidis for helpful discussions on Klimov's problem and to Professors J. Niño-Mora and G. Weiss for many discussions and much encouragement     

On the solvability of noncoercive linear variational inequalities in separable Hilbert spaces

In this paper, we build an existence theory for linear variational inequalities associated with an operator which generalizes in Hilbert space the class of copositive plus matrices. We show how this theory can be used to study some important engineering problems governed by noncoercive variational inequalities.Thanks are due to Professor V. H. Nguyen for many valuable discussions. The author thanks the Associate Editor and the referees for their helpful suggestions     

Farkas' theorem of nonconvex type and its application to a min-max problem

This note is concerned with the generalization of Farkas' theorem and its application to derive optimality conditions for a mix-max problem. Farkas' theorem is generalized to a system of inequalities described by sup-min type positively homogeneous functions. This generalization allows us to deal with optimization problems consisting of objective and constraint functions whose directional derivatives are not necessarily convex with respect to the directions. As an example of such problems, we formulate a min-max problem and derive its optimality conditions.The author would like to express his sincere thanks to Professors S. Suzuki and T. Asano of Sophia University and Professor K. Shimizu of Keio University for encouragement and suggestions.     

An application of coding theory to a problem in graphical enumeration

This note was written while the first author was visiting the Department of Combinatorics and Optimization of the University of Waterloo as an Adjunct Professor. He would like to thank his colleagues there for their hospitality. The second author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.     

A note on flow shop scheduling problems with deteriorating jobs on no-idle dominant machines

The main results in a recent paper [M. Cheng, S. Sun, L. He, Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines, European Journal of Operational Research 183 (2007) 115–124] are incorrect because job processing times are variable due to deteriorating effect, which is not taken into account by the authors. In this note, we show first by counter-examples that the published results are incorrect, and then we provide corrected results.     

BOOK REVIEWS

Book reviewed in this article: America at Work Series: Machines for America; Power for America; Wings for America, by Marshall Dunn, Author of “Science and Modern Progress” and “Up to Civilization,” and Lloyd N. Morrisett, Professor of Education, University of California, Los Angeles. Factors Affecting Student Achievement and Change in a Physical Science Survey Course, by Waldo Lyle Brewer, Ph.D. The Practical Outline of Mechanical Trades for Home Study, edited by William L. Schaff, Assistant Professor of Education, Brooklyn College. Practical Physics, by Marsh W. White, Ph.D., Editor, Professor of Physics; Kenneth V. Manning, Ph.D., Assistant Supervisor of Physics Extension; Robert L. Weber, Ph.D., Assistant Professor of Physics; R. Orin Cornett, Ph.D., Lecturer in Electronics, Harvard University Heat and Thermodynamics, by Mark W. Zemansky, Ph.D. Mathematics for the Sheet Metal Worker, by Clayton E. Buell, B.S., M.Ed. Educators Guide to Free Films, Third Edition, Compiled and Edited by Mary Foley Horkheimer; and John W. Differ, M.A. Methods of Teaching in Town and Rural Schools, by E. L. Ritter and L. A. Shephers Radio Education Pioneering in the Mid-West, by Albert A. Reed, LL.D., Formerly Deputy State Superintendent of Public Instruction, Lincoln, Nebraska; Director-Emeritus, University Extension Division, University of Nebraska; Professor Emeritus, Secondary Education, University of Nebraska. Piloting and Maneuvering of Ships, by Lyman M. Kells, Ph.D., Associate Professor of Mathematics; Willis F. Kern, Associate Professor of Mathematics; and James R. Bland, Associate Professor of Mathematics Navigation, by Lyman M. Keils, Ph.D., Professor of Mathematics; Willis F. Kern, Associate Professor of Mathematics; and James R. Bland, Associate Professor of Mathematics     

Some properties of efficient solutions for vector optimization

In this paper, we discuss the optimality conditions for vector optimization problems. Properties of efficient and weakly efficient solutions are studied, and some new necessary conditions are obtained. Most of them are related to the mapping properties of the derivative operatorf(x) of the objective functionf. Almost all of our results are based on the methods of functional analysis and the theory of degree.The authors would like to thank Professor Y. D. Hu, Deputy General Secretary of the Chinese Operations Research Society, for his help and directions. Also, the authors would like to thank Professors T. K. Sung and Y. J. Chang, Chairmen of the authors' present department, for their sincere concern and encouragement. Finally, the authors are grateful to Professor G. Leitmann for his valuable comments, suggestions, and his careful editing of an earlier version of this paper.     

In Praise of Unicorns

The general thrust of this paper will be to put the recent ‘King is Dead’ controversy into its proper perspective, to review the consequences of Russell Ackoff's criticisms of the 1978 Conference, to look with a critical yet benevolent eye on university courses in the light of these criticisms and to suggest a menu of unsolved problems which might indicate exciting developments in our subject.The paper will start with a discussion of the three disasters which have hit Operational Research in the last twenty years. It is the contention of the speaker that the ‘King is Dead’ controversy was largely a controversy about nothing of significance and, by sapping the energies of those who could otherwise have been constructively employed, was itself one of these disasters (the other two can be left as exercises for the reader).The criticisms of Russell Ackoff were of a much more substantial nature. The author does not agree completely either with Ackoff's diagnosis or his suggestion of the way the patient should be treated. The paper will suggest ways in which the universities have reacted to these criticisms and the extent to which they are moving away from the mind-bending dullness and boredom which seems to run through so much Operational Research teaching. The place of universities in contemporary society will be discussed with particular emphasis on research and on the need to serve the community.We shall discuss an outline of some of the major unsolved problems which at present are largely ignored by Operational Research scientists. None of these problems involves or needs the development of formal mathematics and for that reason they are much more difficult than the normal problems on which mathematicians give their advice. The paper will try to convey the sense of intellectual excitement which is needed to be reintroduced into Operational Research, particularly in order to move away from the nervous, defensive and apologetic posture assumed by so many Operational Research scientists as a reaction to recent criticisms.     

Note on group consistency in analytic hierarchy process

We study the paper of Xu [Z. Xu, On consistency of the weighted geometric mean complex judgement matrix in AHP, European Journal of Operational Research 126 (2000) 683–687] for the group consistency in analytic hierarchy process of multicriteria decision-making. The purpose of this note is threefold. First, we point out the questionable results in this paper. Second, for three by three comparison matrices, we provide a patchwork for his method. Third, we constructed a counter example to show that in general his method is wrong. Numerical examples are provided to illustrate our findings. If there are four or more alternatives, then we may advise researchers to ignore his results to avoid questionable estimation of group consistency.     

Optimal retailer's ordering policies in the EOQ model under trade credit financing

The main purpose of this note is to modify the assumption of the trade credit policy in previously published results to reflect the real-life situations. All previously published models implicitly assumed that the supplier would offer the retailer a delay period, but the retailer would not offer the trade credit period to his/her customer. In most business transactions, this assumption is debatable. In this note, we assume that the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer's replenishment model. Furthermore, we assume that the retailer's trade credit period offered by supplier M is not shorter than the customer's trade credit period offered by retailer N(M?N). Under these conditions, we model the retailer's inventory system as a cost minimization problem to determine the retailer's optimal ordering policies. Then a theorem is developed to determine efficiently the optimal ordering policies for the retailer. We deduce some previously published results of other researchers as special cases. Finally, numerical examples are given to illustrate the theorem obtained in this note.     

Reply to comments by Soleimani-damaneh and Mostafaee (2006) and Zhang (2006)

In Fukuyama [Fukuyama, H., 2000. Returns to scale and scale elasticity in data envelopment analysis. European Journal of Operational Research 125, 93–112], I investigated some mathematical structure on scale elasticity and returns to scale. Soleimani-damaneh and Mostafaee [Soleimani-damaneh, M., Mostafaee, A., in press. A comment on “Returns to scale and scale elasticity in data envelopment analysis”. European Journal of Operational Research. doi:10.1016/j.ejor.2006.11.042] and Zhang [Zhang, B., in press. A Note on Fukuyama (2000). European Journal of Operational Research. doi:10.1016/j.ejor.2006.11.040] claim that some results, which are related to homogeneity, are incorrect. This note replies to their comments by demonstrating that Fukuyama (2000) results are still valid.