Showing papers by "Abraham Charnes published in 1992"

Sensitivity of efficiency classifications in the additive model of data envelopment analysis

Abstract: In contrast to existing sufficient conditions for preservation of efficiency under special perturbations and matrix structural assumptions, sensitivity of the additive model's classifications in data envelopment analysis (DEA) is investigated by means of new DEA formulations focusing on the stability (sensitivity) of an organization's classification (whether efficient or inefficient). The formulations for the additive model are linear programming problems whose solutions yield a particular region of stability, a ‘cell’, in which an organization's classification remains unchanged. The largest such cell can always be easily computed for each organization and additionally theoretically characterized simply as optimal solutions of particular linear programming problems.

Chance Constrained Programming Approach to Empirical Analyses of Mutual Fund Investment Strategies

Abstract: Chance constrained programming concepts are used to formalize risk and return relations which are then modeled for use in an empirical study of mutual fund behavior during the period 1984 through 1988. The publicly announced strategies of individual funds are used to form ex ante risk classifications which are employed in examining ex post performance. Negative relations between risk and return held in every year of the period studied. The bearing of these negative risk-return findings for the Bowman paradox, as studied in the strategic management literature, are thus extended from the industrial firms studied by Bowman (and others) and shown to be present even in these investment oriented mutual funds in each of the years of the great bull market from 1984 through 1988. Finally, our use of chance constrained programming enables us to separate risk from return behavior and evaluate their relative strengths as sources of these negative relations, which are found to be more in the returns than the risks.

Non-archimedean infinitesimals, transcendentals and categorical inputs in linear programming and data envelopment analysis

Abstract: Two problems in linear programming associated with data envelopment analysis (DEA) namely, employing non-archimedean infinitesimals, transcendemals (‘big Ms’) and categorical variables (in a new non-archimedean formulation) are addressed. A new more sophisticated pricing procedure as part of an adjacent extreme point algorithm solves these efficiently in the base field. Employing this in Charnes's non-archimedean simplex algorithm led to a ninefold increase in computational speed on large DEA problems with about 1000 decision-making units. Additionally, computational failures due to cycling and/or conditioning instabilities were eliminated.

Semi-infinite relaxation of joint chance constraints in chance-constrained programming Part 1. Zero-order stochastic decision rules†

Abstract: A new class of semi-infinite deterministic (‘determinizations’) dominants and relaxations of joint chance-constraints in chance-constrained programming is developed and specialized to zero-order stochastic decision rule situations. Tight constraint relaxations are obtained where only the partial information of means and variances is known. The tight non-linear semi-infinite relaxations are related to an accessible finite subsystem. When the chance constraints involve linear inequalities, for a large class, the non-linear tight system is proved equivalent to a linear program. Its solutions for the Prekopa-Szantai reservoir construction examples agree well with theirs