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This report describes research into the feasibility of developing a Forecasting and Allocation of Army Recruiting Resources Study-Sequential Hierarchical Allocation of Resource Elements (FAARRS-SHARE) system for the U.S. Army Reserve. FAARRS-SHARE provides the Army's active component a means of analyzing the impact of recruiting resources on accessions and the ability to estimate the resources necessary to achieve specific accession levels. This study explores the feasibility of developing a Reserve FAARRS-SHARE system by examining the underlying models for FAARRS-SHARE system and beginning an investigation of new, more appropriate methodologies. Building on new developments in sensitivity/stability analysis in Data Envelopment Analysis (DEA) formulations are developed for estimation of an approximate empirical production function for U.S. Army Reserve recruiting. Parameters of an empirical production function are estimated and reported.

Error bounds are developed for a class of quadratic programming problems. The absolute error between an approximate feasible solution, generated via a dual formulation, and the true optimal solution is measured. Furthermore, these error bounds involve considerably less work computationally than existing estimates.

Sensitivity analysis in data envelopment analysis for the Charnes-Cooper-Rhodes ratio model is studied for the case of the simultaneous proportionate increase of all inputs and proportionate decrease of all outputs of an efficient decision making unit for which efficiency is preserved. Sufficient conditions which preserve efficiency are found and a numerical example illustrating the results is provided.

We suggest several important research topics for semi-infinite programs whose problem functions and index sets contain parameters that are subject to perturbation. These include optimal value and optimal solution sensitivity and stability properties and penalty function approximation techniques. The approaches proposed are a natural carryover from parametric nonlinear programming, with emphasis on practical applicability and computability. Keywords: Semi-infinite programming, Perturbation analysis, Sensitivity analysis, Stability, Parametric non-linear programming, Penalty functions, Mathematical equations., Sponsored in part by Grant NSF-ECS86-19859. Prepared in cooperation with George Washington Univ. School of Engineering and Applied Science, Washington, DC. Dept. of Operations Research.

This note shows how information theoretic methods can be used to obtain simply the fundamental geometric inequality lemma. This lemma is the base used by Duffin, Peterson and Zener (1967) for providing their duality results for geometric programming, and its proof occupies three pages in their book. Their method of proof is a technically impressive procedure. However to illustrate the power of information theoretic methods we shall give a simple proof of this fundamental inequality. The approach we shall take is to show the connection between geometric programming and constrained Khinchine-Kullback- Leibler, or minimum discrimination information (MDI) estimation. Complete duality states for MDI estimation are known (c.f. Brockett, Charnes and Cooper (1980), Charnes, Cooper and Seiford (1978), Charnes and Cooper (1974a,b)). Additionally, in the usual duality state of interest, the statistical properties of the solution are known, facilitating sensitivity analysis. The computation of MDI estimation is easily performed using an unconstrained dual convex program involving only linear and exponential functions.

The objective of this study was to initiate evaluation of the effectiveness of Army advertising. The study employed Data Envelopment Analysis (DEA) and goal programming methodologies to (1) enhance the existing DEA-based mission model, (2) initiate analysis of further advertising variables, and (3) thereby obtain a basis for a future media-allocation model. The objectives were attained and software was provided and implemented on USAREC machines and successfully run by USAREC personnel in at least four demonstrations as well as in current in-house utilizations.

Conventional methods for comparing the relative productivity of schools employ least square regression to find expected achievement of schools with the same input characteristics. The result is that one typically contrasts the relative effects of 'predictor' variables on achievement rather than comparing school units with respect to their input/output efficiency. A newly developed input/output method for comparing the efficiency of decision making units is presented and is applied to elementary schools in an urban school district. The method is found to identify efficient and inefficient schools and provides management information relative to input and output measures., Sponsored in part by Grant NSF-SOC76-15876.

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.

A new approach is proposed for some models of decision-making under uncertainty, using optimized certainty-equivalents induced by expected-utility. Applications to production, investment and inventory models demonstrate the advantages of the new approach. Expected utility theory is 'the major paradigm in decision making.... It has been used prescriptively in management science (especially decision analysis), predictively in finance and economics, descriptively by psychologists... The expected utility (EU) model has consequently been the focus of much theoretical and empirical research.... In spite of its power, elegance and success, considerable criticism has been directed at the EU theory, specially when used descriptively to model the decision processes underlying risky choice. In this context, evidence refuting the validity of the EU model axioms is relevant., Sponsored in part by Grants NSF-SES84-08134 and NSF-SES85-20806.

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.

In processing networks, ordinary network constraints are supplemented by proportional flow restrictions on arcs entering or leaving some nodes. This paper describes a new primal partitioning algorithm for solving pure processing networks using a working basis of variable dimension. In testing against MPSX/370 on a class of randomly generated problems, a FORTRAN implementation of this algorithm was found to be an order of magnitude faster. Besides indicating the use of our methods in stand alone fashion, the computational results also demonstrate the desirability of using these methods as a high-level module in a mathematical programming system. Keywords include: Networks, Processing networks, Linear programming, and Mathematical programming systems.

The authors of this reprint consider nonlinear programming problem (P) with stochastic constraints. The Lagrangean corresponding to such problems has a stochastic part, which in this work is replaced by its certainty equivalent (in the sense of expected utility theory). It is shown that the deterministic surrogate problem (CE-P) thus obtained, contains a penalty function which penalizes violation of the constraints in the mean. The approach is related to several known methods in stochastic programming such as: chance constraints, stochastic goal programming, reliability programming and mean-variance analysis. The dual problem of (CE-P) is studied (for problems with stochastic righthand sides in the constraints) and a comprehensive duality theory is developed by introducing a new certainty equivalent (NCE) concept. Motivation for the NCE and its potential role in Decision Theory are discussed, as well as mean-variance approximations.

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.

Data Envelopment Analysis is a relatively new method for measuring and evaluating the efficiency of not-for-profit entities with multiple outputs and multiple inputs. Without requiring a priori weights and without requiring explicit specification of interdependencies that may be present between variables it (a) provides and overall measure of performance efficiency from observational data and (b) identifies sources and estimates amounts of inefficiency that may be present in each such source. This paper reports on results from studies of DEA for its possible use in evaluating the performance of 24 Army Health Care Facilities. These DEA results are reviewed and compared with results from alternate methods (often used for efficiency analysis) such as statistical regressions and standards imposed by HCFA.

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.

This note introduces an extension of the Fibonacci series. The new series provides new interpretation for two problems of replenishment which appeared in the April 1986 issue of OR/MS Today which have been stated to be hitherto unsolved. The series offers closed form solutions to both problems.

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.

This study proposes a dynamic goal programming model for planning joint investment in agriculture to achieve self-sufficiency in food production in the Middle East. The issue of equitable allocation of returns to participants in the joint investments is addressed as well. Equitable divisions of profits and equitable assessment of costs to collaborating investors are developed through an associated characteristics function game. Keywords: Dynamic Goal Programming; Game theory.

The work of this contract encompassed significant new developments in network theory and in computational methods to the extent that a system for monitoring performance and for evaluation of policy with regard to Sea-Shore Rotation was produced which was operational in real time. All software developments, documentation, and deliverables were delivered long before the concluding date of the contract. Details of the system and a manual for its usage are included as Appendices 1 and 2. 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 a new model of constrained network goal programming type; newly developed algorithms for use with models of this class; computer software and informatics developed to implement these algorithms, plus the software and informatics for other modules of the system including decision support tools for report generation and monitoring capabilities.

The specialization of the simplex algorithm for the solution of generalized network flow problems rests on the fact that a basis for the problem may be represented graphically as a spanning forest in which each component is either a one-tree or a rooted tree. The design of a specialized algorithm for efficient solution of generalized network problems necessarily depends on data structures chosen to represent the basis. This paper presents the design and detailed algorithmic specification of the primal simplex algorithm for such problems. Computational testing to determine the overhead required by generalized network data structures over pure network data structures indicates that generalized network algorithms are on the order of 2.5 to 3.5 times slower than pure network algorithms. Computational testing with generalized network problems with up to 1000 nodes and 7000 arcs establishes the suitability of the data-structures for efficient implementation of primal simplex calculations. Keywords: Linear programming. (Author), Sponsored in part by Contract MDA903-85-M-6548.

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.

A new solution class extending to games with non-topological product set strategies and multiple payoffs to players is developed without point-to-set mappings or quasi-variational inequalities. Some properties are developed and an illustrative example comparison to existing notions in re Pareto efficiency and Generalized nash equilibria. Keywords: Game theory; Convex sets; operations research.

M. Kress proved for a special class of Location-Scale probability distributions there always exists a probability level for which the Chance Constrained Critical Path (CCCP) remains unchanged for all probabilities greater than or equal to that value. His chance constrained problem has zero-order decision rules and individual chance constraints. This paper extends his results to most of the common probability distributions. Keywords: Chance constrained programming.

Kettele, using dynamic programming, developed a simple algorithm for the optimal redundancy problem in reliability and life testing problems with a single constraint. Proschan Bray gave a generalization of Kettele's dynamic programming algorithm to include multiple constraints. To solve a much broader class of optimization problems barlow Proschan generalized the Kettele algorithm to apply to strictly increasing separable function problems with a single constraint. This paper considers a still more general optimization model and develop a Further Generalized Kettele Algorithm to apply to multiple constraints, etc. As an example, and integer Lexicographic programming model will be solved. Furthermore, another form of the more general optimization model is pointed out in section 4 of the paper.

Models employed in evaluation or stipulation of regulatory policies involving competition and/or differing objectives of competing parties have sometimes been seriously deficient in accounting for interactions between the parties' strategies or in allowing for multiple objectives. Classical game-theoretical models, wherein the strategy set is the topological product of the individual parties strategy sets, do not encompass such situations. The new dominance cones method and class of situations (Charnes, Cooper, Huang, Wei) is herein further extended to such extensions of classical games. This is applied to an example of Harker without requiring hi variational and quasi-variational inequalities or point-to-set mappings. Keywords: game theory.

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.

The authors derive an explicit determinantal formula for the least squares (LS) solution of an overdetermined system of linear equations. From this formula it follows that the LS solution lies in the convex hull S of points, each of which is a solution of a square subsystem of the whole system. The results are extended to weighted LS solution; it is shown that the convex hull S in which the solution must lie is independent of the weighting matrix.

In this paper, three special pursuit games on cyclic graphs are solved. These games are relevant to unsolved problems initiated by a game without a value. The following problems are proposed: (i) For a finite or infinite game without a saddle point, how should the players make their decisions? Here, we suppose that the game is played once. Thus mixed strategies are not considered. (ii) For an infinite game without a value v, i.e., V1

Pincus' 1968 formula for the (unique) global minimum of a continuous function on a concept set in superscript n is extended to finite multiple optima and to discrete and special variance. The impacts of these on association ergodic irreducible aperiodic Markov chain computational (Pincus 1970)-currently called 'simulated annealing'-is exemplified and assessed leading to grave concern about what current simulated annealing process may coverage to, instead of optima. Reprints. (jhd), Availability: Published in International Journal of Systems Science, v20 n8 p1521-1533 1989.

Low-resolution data flow computing offers a practical compromise between conventional control-flow computing models and the specialized architectures required for fine-grain data flow processing. We give a formal specification of an arbitration facility that simultaneously partitions and statically assigns operations to processors. This general model is based on differences in the processors, diversity of data links in the network, size of tokens flowing between nodes in the data flow graph, memory limitations on the processors, and considerations to promote parallelism. A network model solves the static problem for bipartite and tree structured data flow graphs. Based on this centralized static allocation scheme, data tokens are automatically routed to processors, the run-time scheduling process is distributed among the processors. Dynamic arbitration implemented as a centralized facility takes inadequate advantage of network capabilities. A general decentralized (distributed) dynamic arbitration scheme maps tasks to processors at run-time, with the association of tasks to processors based on intertask communication and network data link characteristics. Task migration is supported by treating both data and code as tokens. No centralized control or mass storage are required in this communication-efficient arbitration model. (rrh), Sponsored in part by Grants NSF-SES84-08134 and NSF-SES85-20806.

Low-resolution data flow computing offers a practical compromise between conventional control-flow computing models and the specialized architectures required for fine-grain data flow processing. We give a formal specification of an arbitration facility that simultaneously partitions and statically assigns operations to processors. This general model is based on differences in the processors, diversity of data links in the network, size of tokens flowing between nodes in the data flow graph, memory limitations on the processors, and considerations to promote parallelism. A network model solves the static problem for bipartite and tree structured data flow graphs. Based on this centralized static allocation scheme, data tokens are automatically routed to processors, and the run-time scheduling process is distributed among the processors. Dynamic arbitration implemented as a centralized facility inadequate advantage of network capabilities. A general decentralized (distributed) dynamic arbitration scheme maps tasks to processors at run-time, with the association of tasks to processors based on intertask communication and network data link characteristics. Task migration is supported by treating both data and code as tokens. No centralized control or mass storage are required in this communication-efficient arbitration model. (KR)

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.

This paper presents a survey of current research in the area of distributed systems and discusses some possible areas of future research. The trend toward data base management systems which are responsible for the creation, accessing, and maintenance of a large collection of information containing complex interrelationships is prevalent in centralized systems today. It seems that the same advantages which led to the growth of data base management systems in centralized systems can be applied in distributed systems as well. Most current research (particularly in the area of modeling) views a distributed system in terms of independent data files. The authors address some of the problems involved when the distributed system is viewed in terms of an integrated data base.

Decision making is defined in terms of four elements: the set of decisions, the set of outcomes for each decision, a set-valued criterion function, the decision maker's value judgment for each outcome. Various confidence structures are defined, which give the decision maker's confidence of a given decision leading to a particular outcome. The relation of certain confidence structures to Bayesian decision making and to membership functions in fuzzy set theory is established. A number of schemes are discussed for arriving at 'best' decisions, and some new types of domination structures are introduced.

Newton's method for finding a stationary point of f:R(n) -> R has second order of convergence. However, it necessitates computation and inversion of second order derivatives matrix. We present new classes of algorithms. One of these has second order of convergence while using first order information only.

The rate of convergence of line search algorithms based on general interpolating functions is derived, and is shown to be independent of the particular interpolating function used. This result holds for the root finding problem f(x) = 0 as well. We show how inverse interpolation can be used in conjunction with the line search problem, and derive its rate of convergence. Our analysis suggests that one-point line search algorithms (in particular Newton's method) are inefficient in a sense. Two-point algorithms using rational interpolating functions are recommended.

The principal economic assumptions of this paper are neoclassical behavior assumptions on a consumer group which owns the resources and a collection of producers employing these resources. A saddle value problem is formulated to characterize equilibrium in the economy in the sense that at equilibrium prices producers determine production plans to maximize profits and that these outputs and inputs are exactly those demanded and supplied respectively by the consumer group. The saddle value problem is shown to be equivalent to a dual pair of uniextremizations termed the consumer group's problem and the producers' problem. The neoclassical economic assumptions yield sufficient conditions which are among the most general ones for guaranteeing a saddle point and simultaneously a perfect duality for the dual programming pair. Economic interpretations are given for all the variables of the consumer group's problem and for all the variables of the producers' problem even at non-optimal stages in each problem. The approach is an infinite dimensional extension of the Charnes' constrained game linear programming equivalents in finite dimensions, Sponsored in part by the National Science Foundation.

The L sub infinity norm has been widely studied as a criterion for curve fitting problems. This paper presents an algorithm to solve discrete approximation problems in the L sub infinity norm. The algorithm is a special- purpose linear programming dual method which employs a reduced basis and multiple pivots. Results of the computational experience with a computer code version of the algorithm are presented.

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.

Modelling and solving large scale networks are crucial to many practical military applications. The purpose of this note is to identify important elements of successful models and methods based on breakthroughs in network areas that have been validated in over a hundred computer hours of empirical testing and 15 man years of code development resulting in the modelling of large scale military manpower assignment problems and designing computer codes for solving large scale assignment, transportation, and transshipment problems.

This document formulates the generalized constrained maximum entropy problem often used in a decision making context as an extended dual convex programming problem. The dual problem is then presented. In this dual setting the primal Lagrange multipliers are precisely the dual variables, and are easily calculated directly by virtue of the simple structure of the dual problem. An example involving the selection of best equipment for an oil spill is presented as an illustration. The authors contrast their solution with those given by previous authors. (Author)

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.

This paper presents a new algorithm to solve a network problem with equal flow wide constraints. The proposed solution technique is motivated by the desire to exploit the special structure of the side constraints and to maintain as much of the characteristics of pure network problems as possible. Our solution technique for the equal flow problem consists of solving two sequences of pure network problems. One sequence yields tighter lower bounds on the optimal value by considering the Lagrangean relaxation of the equal flow problem in which the side constraints are dualized. The second sequence yields upper bounds on the optimal value for the problem and maintains a feasible solution at all times. This sequence is obtained by considering a reformulation of the equal flow problem based on parametric changes in the requirements vector. The procedure has the added attractive feature that it provides a feasible solution which is known to be within a percentage of the optimal at all times. As such, the algorithm terminates when a solution with a prespecified tolerance on the objective function value is obtained. On NETGEN problems, using the first 150 arcs to form 75 equal flow side constraints, we found that the new algorithm is approximately 3 times faster than existing techniques and requires only 50% of the storage.

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.

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.