On Measuring the Contribution of OR

Cost-benefit analysis offers a common-sense approach to measuring the contribution of OR but encounters difficulties which have been recognized by Ackoff. Ackoff's concept of adaptivity appears to offer a neat solution to those difficulties but can be seen to provide only a methodology and to lack a background theory. The authors argue that: in general the development of background theory should precede the development of a methodology; for OR the background theory required is one of decision-making; and that the social sciences provide the resource from which an adequate theory of decision-making can be developed.     

Measuring the relative balance of DMUs

In basic Data Envelopment Analysis (DEA) models, the weights of performance criteria are endogenously determined, assigning to each decision-making unit (DMU) its best possible efficiency score. This property is widely considered to be a major strength of the method, but it is also a source of considerable problems concerning performance assessment and performance control. Such problems result from the possibility of zero-value weights that exclude criteria from the evaluation. Unlike approaches that deal with this issue by incorporating value judgments into the analysis, we suggest a complementary balance score that is derived from the given data set. This score evaluates the extent to which a DMU avoids concentration on only some of the crucial performance criteria. One of the possible decisions resulting from a balance analysis is to reduce the set of DMUs considered to serve as benchmarks. For this case, a modified CCR–O model is presented.     

Measuring the height of a polynomial

Conclusions  Mahler’s measure is alive and well in several quite diverse contexts. The differing points of view seem to generate a healthy friction. If the general level of health is measured by the quantity and quality of unsolved problems, then it may help to list these.

Measuring the impact of primal heuristics

In modern MIP solvers, primal heuristics play a key role in finding high-quality solutions. However, classical performance measures reflect the impact of primal heuristics on the overall solving process badly. In this article, we introduce a new performance measure, the “primal integral”, which depends on the quality of solutions and on the time when they are found. We compare five state-of-the-art MIP solvers w.r.t. the newly proposed measure, and show that heuristics improve their performance by up to 80%.     

Measuring the tameness of almost convex groups

A 1-combing for a finitely presented group consists of a continuous family of paths based at the identity and ending at points in the 1-skeleton of the Cayley 2-complex associated to the presentation. We define two functions (radial and ball tameness functions) that measure how efficiently a 1-combing moves away from the identity. These functions are geometric in the sense that they are quasi-isometry invariants. We show that a group is almost convex if and only if the radial tameness function is bounded by the identity function; hence almost convex groups, as well as certain generalizations of almost convex groups, are contained in the quasi-isometry class of groups admitting linear radial tameness functions.

     

Measuring the efficiency of decision making units

A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs.     

Measuring the True Profitability of Sales Promotions

The effectiveness of a promotional campaign is often exaggerated because managers ignore consumer expectations or lead effects. In a case study, these lead effects are analysed using a system dynamics model, autoregressive time-series analysis and econometric techniques.     

Measuring Stiffness

Many problems have been proposed for the testing and evaluation of mathematical software for the solution of the initial value problem for a system of ordinary differential equations. The stiffness of a given problem is of great significance for testing, but the concept is at best somewhat vague and the few quantitative measures of stiffness being used are of limited value. A relatively precise and quantitative way is proposed to answer the questions: How does the stiffness vary in the course of the integration of a given problem? Is a given problem A stiffer than a given problem B, and if so, by how much?     

Measuring the Size(2)

There are three different common w(?)measure the size of a three dimensional figure. Consider the shoe box below. We can measure the total length of its edges. Like perimeter, this is one-dimensional. We can measure its surface area,which is two-dimensional. Or we can measure its volume,which is three-dimensional. The shoebox has edges of lengths 14inches,5inches,and 7inches, There are four edges of each length. (some are hidden from view.)The total length of all edges is 4·15"+4·7"+4·14",or 104inches.     

Measuring cubeness in the limit cases

In this paper we show that the recently introduced family of the cubeness measures C_β(S)(β>0) satisfy the following desirable property: lim_β→∞C_β(S)=0, for any given 3D shape S different from a cube. The result implies that the behaviour of cubeness measures changes depending on the selected value of β and the cubeness measure can be arbitrarily close to zero for a suitably large value of β. This also implies that for a suitable value of β, the measure C_β(S) can be used for detecting small deviations of a shape from a perfect cube. Some examples are given to illustrate these properties.     

Measuring the effects of reinsurance by the adjustment coefficient

In this paper we consider the optimal levels of reinsurance in cases where the cedent has a choice between a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The optimality criterion that we use is that the insurer's adjustment coefficient should be maximized, subject or not to a constraint on the insurer's expected net profit. The solution is given, assuming that the claims have a compound Poisson distribution, that the quota-share premium is calculated on a proportional basis with a commission payment and that the excess of loss reinsurance premium is calculated according to the expected value principle.     

Measuring the effects of knowledge in military campaigns

A particularly difficult problem in command and control is that of identifying the relationship between intelligence, decision and combat outcome. The problem centres on three things: (1) an adequate representation of the situation confronting the commander on the battlefield; (2) an adequate measure of combat outcome; and (3) an appropriate metric linking knowledge of the first to the second. In this paper, we focus on the third of these by developing a measure of the knowledge possessed by the commander at the time he takes his decision and by relating this to combat outcomes. Combat outcomes are represented using traditional attrition-based metrics and the combat situation is simply the size, location and identity of enemy units. Therefore, the possible number of identified enemy units arrayed against the friendly commander constitutes the set of hypotheses on alternative situations. Surveillance assets provide the commander with evidence that is used to update the probability distribution. Knowledge if then represented as the product of two components: residual knowledge, the knowledge gained from the updated probability distribution, and detection knowledge, the knowledge from the detection itself. Information entropy was used to develop a metric that reflects the degree to which the commander understands the situation confronting him. The metric was applied in a UK Ministry of Defence study of a proposed Airborne STand-Off Radar (ASTOR) to measure the effects of improved surveillance on combat outcomes.     

Measuring the Rarely Visited Sites of Brownian Motion

We study the almost sure asymptotic behaviors of the Lebesgue measure of the points which are hardly visited, in the sense of Földes and Révész,⁽⁷⁾ by a linear Wiener process.     

Measuring the Efficiency of Prescribing by General Practitioners

Data envelopment analysis (a mathematical programming technique) has often been applied to measuring the efficiency with which outputs are produced. The technique derives efficient combinations of outputs for given inputs: constant returns to size may be assumed or one may choose to examine whether decreasing or increasing returns hold true. An analysis of the cost of prescribing drugs for 106 general practices in the Lincolnshire Health Authority for the year 1993/1994 reveals the statistical problems that are encountered in applying this technique.     

Measuring the national competitiveness of Southeast Asian countries

National competitiveness is a measure of the relative ability of a nation to create and maintain an environment in which enterprises can compete so that the level of prosperity can be improved. This paper proposes a methodology for measuring the national competitiveness and uses the 10 Southeast Asian countries for illustration. The basic idea is to deconstruct the complicated concept of national competitiveness to measurable criteria. The observations (data) on the criteria are then aggregated according to their importance to obtain an index of national competitiveness. For data collected from questionnaire surveys, a calibration technique has been devised to alleviate bias due to personal prejudice. In data aggregation, the importance is expressed by both a priori weights and a posteriori weights. These two types of weights consistently show that Singapore, Malaysia, and Thailand have the highest national competitiveness, while Myanmar, Cambodia, and Laos are the least competitive countries. The performance of each country in every criteria measured also provides directions for these countries to make improvements and for investors to allocate resources.     

Measuring the level sets of anisotropic homogeneous functions

In this note we investigate some basic properties of the level sets of functions which are homogeneous with respect to nonisotropic dilations. In particular we obtain a formula for the volume of the level sets in terms of the area on the level surfaces. We relate the results to some well known mean value formulas for solutions of PDE’s.