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Mathematical and statistical theory together with data analysis of the Wharton Center for Applied Research(WCAR) Final Report on the FY 1984 Advertising Mix Test shows that: (1) The conclusions with respect to budgetary amounts and proportions in the WCAR report are not supported by the evidence. (2) The models and analyses utilized by WCAR are not correct and tend to be misleading. (3) Serious questions are present with respect to the data and design. It is concluded that no reliance should be placed on the WCAR Report and, in particular, reliance should not be placed on any of the budgetary recommendations made with respect to advertising in this report. Keywords: Advertising Policy Evaluation; Interactive Statistical Models; Significance Tests; and Economic Isoquant Theory.

Ridge regression has been extensively reviewed in the literature of applied statistics as a method for dealing with problems of collinearity in least squares regressions. In this paper, ordinary least squares and least squares combined with ridge regressions are examined and compared with ordinary goal programming and goal programming combined with constraints on regressand values that admissible statistical estimates must satisfy. The comparisons are effected by means of an example in chemical processing that has been extensively treated in the ridge regression literature. Keywords: Least squares; ridge regression; least absolute values; goal programming; constrained regression; Reprints.

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (= Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is also obtained for each DMU from the observed values of its multiple inputs and outputs without requiring uses of a priori weights. There are many different ways of specifying DEA reference sets. A partition into 6 classes is provided for such observations in which 3 are scale inefficient and 3 are scale efficient with the latter containing substs of DMUs that are also technically (= zero waste) efficient. Keyswords: Efficiency; Fractional programming; Linear programming; Multi-dimensional efficiency analysis.

A new class of constrained stochastic network models is formulated in a manner that can be used to support a variety of analyses of optimal design modifications for special weapons systems under budgetary and other constraints. In this paper only single aircraft systems are treated. Component modifications to the B52G system are considered in a prototype example.

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (= Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is also obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions. A partition of DMUs into six classes is established via primal and dual representation theorems and three classification theorems which do not depend on non-archimedian analysis. Earlier theory is extended to explain the consequences of zero inputs and outputs and to utilize zero virtual multipliers (shadow prices). Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (= zero waste) efficient. Keywords: dual linear programs; multicriterion efficiency analysis. (Author), Sponsored in part by Grant NSF-SES85-20806.

Concepts of efficiency analysis are extended through the Data Envelopment Analysis (DEA) method to include new theoretical characterizations of Pareto optimal production functions, solutions of such problems as economies of scale, non-concavity and isotonicity, discretionary and non-discretionary inputs, multiplicative efficiency formulations (piecewise Cobb-Douglas), and comparisons to alternatives such as ratio and regression analysis. Keywords: Army planning, Manpower, Multiplicative efficiency, Log efficiency, Data envelopment analysis, Piecewise Cobb-Douglas forms, Production functions, Pareto optimality, Efficiency analysis, Statistical regression, Ratio analysis, Simulation, and Validation.

Management accountability as an added dimension for management science research is examined from the standpoint of possible uses in some of the newer comprehensive auditing approaches to propriety, effectiveness and efficiency evaluations of management and organization behavior. Attention is centered on non-market activities and not-for-profit organizations. Goal focusing is examined, for example, as a relatively recent extension of goal programming for use in effectiveness evaluation and as an alternative to utility theoretic approaches in national goals accounting systems designed to deal with programs or objectives involving numerous kinds of off-market activities. The bulk of the paper, however, is devoted to a new mathematical programming model for deriving analytic representations of extremal frontiers or envelopes from empirical data and for measuring the efficiency of not-for-profit entities. An illustrative application to a recently completed large-scale social experiment in educating disadvantaged children in the U.S. public schools is used to show how distinctions may also be drawn between program efficiency and management efficiency. The appendix develops a canonical form for the types of statistical distributions involved. It also provides a beginning for dealing with statistical properties of the extremal relations obtained by applying these kinds of mathematical programming models to observational data., Sponsored in part by Grant NSF-SOC76-15876. Prepared in cooperation with Carnegie-Mellon Univ. School of Urban and Public Affairs, Contract N00014-75-C-0932.

This document consists of the following five reports: 1) Goal Programming/Constrained Regression Review of the Bell System Breakup; 2) Rejoinder. natural Monopoly and Bell System: Response to Charnes, Cooper and Sueyoshi; 3) A Preface and Post Script to Evans and Heckman Studies for the Bell System Breakup; 4) Exhibit I: A Guided Tour of A Family of Studies on the AT&T Breakup; 5) Exhibit II: On Errors in the Evans and Heckman Bell System Breakup Studies. Keywords: Efficiency; econometric models., Sponsored in part by Grants NSF-SES85-20806 and NSF-SES84-08134

DEA's (Data Envelopment Analysis) first formulated model was a non- linear ratio (or fractional) programming problem, as reported in Charnes, Cooper and Rhodes where it was also shown that the fractional programming transformation first given in Charnes and Cooper could be used to obtain a corresponding dual pair of linear programming problems for use in evaluating the efficiency of not-for-profit entities-such as schools, hospitals and government (including military) agencies. These formulations were to be used to secure efficiency evaluations from observed data on the multiple outputs and multiple inputs generated by the activities of the entities to be studied. Numerical evaluations with operational significance were to be secured without requiring recourse to a priori weights (or other transformations) and without requiring explicit specification of parametric functional forms for the relations that might obtain between the inputs and the outputs. Specification was to be required only for the outputs and the inputs to be considered and the DMUs (Decision Making Units) which are responsible for converting inputs into outputs and whose convex or conical combinations constitute the relevant set for obtaining the relative efficiency evaluations that are wanted.

Plans are said to be strategic when they are to be used to guide or control other plans. For instance, a strategic marketing plan may be formulated to guide the development of marketing plans for each of several product lines. Much of the literature dealing with strategic management focuses only on the latter in terms of an overall corporate strategy which sets directions or objectives intended to relate corporate developments to future environments in which the company will (or should) operate. Keller (1983) is particularly strong in asserting that the focus of strategic planning should be on the latter and this should be done from the standpoint of top management involvement without cluttering detail. In treatments like the one we are undertaking, however, it is necessary to allow for variations encountered in practice as well as in the literature., Sponsored in part by Grants NSF-SES87-22504. Revision of report dated Jan 89.

This study is concerned with developing tools which can be applied to managerial performance evaluation and/or for directing audit activities for profit-making as well as not-for-profit entities using multiple inputs to produce multiple outputs. This is accomplished by building on basic concepts of Data Envelopment Analysis (DEA). In particular, the customary CCR ratio forms: as described in Charnes, cone-ratio form of Chames, Cooper, Wei and Huang (1986) . Numerical examples are supplied along with mathematical developments and geometric portrayals of what is involved, and this is followed by an example application to the evaluation of large commercial U.S. banks as drawn from Sun (1987). Keywords: Efficiency Multi attribute optimization; Polyhedral cones; Polar cones; Data envelopment analysis., Prepared in cooperation with Maine Univ.

Data Envelopment Analysis (DEA) began in generalization of the usual scientific-engineering efficiency valuation of a single input, single output system as the ratio of the output input (in the same physical measure, e.g., energy) to multi-input, multi-output systems (or organizations or production units) without known physical laws or the same measure for all inputs and outputs. This was accomplished by (i) reduction of the multi-inputs and outputs to single virtual inputs and outputs, (ii) replacing absolute efficiency by efficiency relative to all members of a sample of units (called DMU's) having the same inputs and outputs, (iii) evaluating a unit's relative efficiency as the maximum of the ratio of its virtual output to virtual input subject to virtual outputs being less than or equal to virtual inputs for each (all) of the DMU's. The origin, history, current status and problems of Data Envelopment Analysis (DEA) on empirical multi-input, multi-output data are surveyed in relation to efficiency valuation, production function determination and stochastic frontier estimation.

Relations between sea duty and shore duty in the U.S. Navy involves large numbers of variables and constraints, along with projected rates of attrition, promotion, demotion, and transfer, which need to be simultaneously considered over a series of periods. Mechanisms for evaluating possible changes in policies and other requirements are also required. This paper reports on a constrained network goal programming model with an accompanying algorithm and a computer code (called BIGNET) which makes it possible to deal with all of these aspects of the Navy's sea-shore rotation problems in the ultra high speed processing times that are characteristic of network codes. An accompanying appendix contains a numerical example with accompanying details of the way the model can be implemented.

This paper serves as and introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses to study DEA efficiency measures with and illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating sources of inefficiency by means of artificially generated data, and (3) and extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested. Additional keywords: Reprints; Mathematical models; Numerical analysis; Fractional programming. (Author)

Sensitivity analyses may be regarded as a mathematical programming counterpart of significance testing in statistics since each is concerned with examining allowable ranges of variation in the data. In statistical analysis, this may take the form of examining ranges of possible chi sq values obtained from the data relative to a fitted function from and hypothesized class of statistical distributions. In linear programming, it may take the form of ascertaining ranges within which data may be varied without requiring a change in the set of vectors that constitute an optimum basis. Additional keywords: Reprints.

The recently implemented U.S. court decision to break up Bell (=American Telephone & Telegraph Co.) to accord with U.S. anti-trust laws is also proving to be influential in other countries. Econometric studies commissioned by the Anti-Trust Division of the U.S. Justice Department used flexible functional forms to demonstrate that the evidence failed to show that Bell was a natural monopoly. This same evidence is reviewed via goal programming/constrained regression models to reach an exactly opposite conclusion. The two approaches are compared and shortcomings and deficiencies in the econometric modeling, statistics and statistical (optimization) principles utilized in Bell System studies are examined in detail. Additional keywords: Cost models; Econometric models; Economic and statistical tests; Tables(data); Operations research. (Author), Presented at the Congress of European Operational Research (7th), Bologna, Italy, 16-19 Jun 85.

A previous paper emphasized overall efficiency ratings obtained from DEA. Only passing attention was given to identifying underlying sources and amounts of inefficiency in the observed inputs and outputs. This paper will reverse that emphasis and also try to supply perspective by reference to alternative approaches that have been used for these purposes. Ratio analyses (including index numbers) and statistical regressions are the example alternatives that will be examined. Keywords: reprints.

The construction and analysis of Pareto-efficient frontier production functions by a new Data Envelopment Analysis method is presented in the context of new theoretical characterizations of the inherent structure and capabilities of such empirical production functions. Contrasts and connections with other developments, including solutions of some remaining problems, are made re aspects such as informatics, economies of scale, isotonicity and non-concavity, discretionary and non-discretionary inputs, piecewise linearity, partial derivatives and Cobb-Douglas properties of the functions. Non-Archimedean constructs are not required. Key Words include: Pareto-Koopmans Efficiency, Efficiency Analysis, Frontier Production Functions, Data Envelopment Analysis., Revision of report dated Nov 84. Sponsored in part by Grant NSF-SES84-08134.

Goal Programming Sea Shore Rotation; This paper is an exposition of the (GPSSR) system to support management of policy and execution of the U.S. Navy's Enlisted Personnel Sea Shore Rotation Program. Its components include (1) a new model of constrained network goal programming type; (2) newly developed algorithms for use with models of this class; (3) computer software and informatics developed to implement these algorithms, plus the software and informatics for other modules of the system including (4) decision support tools for report generation and monitoring capabilities. Originator supplied keywords include: Goal programming; Sea shore to rotation; Valve arc method; Constrained networks., Revision of report dated Sep 84. Prepared in cooperation with Carnegie-Mellon Univ. School of Urban and Public Affairs, under contract N00014-82-C-0411.

In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale (in multiple input and multiple output situations). The results are discussed and related not only to classical (single output) economic but also to more modern versions of economics which are identified with 'contestable market theories'.