John J. Rousseau

Sensitivity and Stability of Efficiency Classifications in Data Envelopment Analysis

A new technique for assessing the sensitivity and stability of efficiency classifications in Data Envelopment Analysis (DEA) is presented. Here developed for the ratio (CCR) model, this technique extends easily to other DEA variants. An organizations input-outut vector serves as the center for a cell within which the organizations classification remains unchanged under perturbations of the data. For the l1, l∞ and generalized l∞ norms, the radius of the maximal cell can be computed using linear programming formulations. This radius can be interpreted as a measure of the classifications stability, especially with respect to errors in the data.

Evaluating solvency versus efficiency performance and different forms of organization and marketing in US property--liability insurance companies

Abstract Solvency is a primary concern for regulators of insurance companies, claims paying ability is a primary concern for policyholders, and return on investment is a primary concern for investors. These interests potentially conflict, and the decision-makers for the firm must trade off one concern versus another. Here we examine the efficiency of insurance companies via data envelopment analysis using solvency, claims paying ability, and return on investment as outputs and using a financial intermediary model for the insurance company. The effect of solvency on efficiency is then examined. These efficiency evaluations are further examined to study stock versus mutual form of organizational structure and agency versus direct marketing arrangements, which are examined separately and in combination.

DEA evaluations of the efficiency of organizational forms and distribution systems in the US property and liability insurance industry

The efficiency effects of different forms of ownership (stock versus mutual) and types of marketing system (agency versus direct) are studied using 1989 data for the US property-liability insurance industry. Data envelopment analysis (DEA) results are obtained from the recently developed RAM (Range Adjusted Measure) model and then extended for comparison with studies by others. Using agency theory (and like approaches) these studies assume that operations all occur only on the efficient frontier. The need for that assumption is obviated by using operations provided by DEA to project all observations onto their efficient frontiers. A use of (non-parametric) rank-order statistics then produces results which differ from these other studies.

An effective non-Archimedean anti-degeneracy/cycling linear programming method especially for data envelopment analysis and like models

A non-Archimedean effective anti-degeneracy/cycling method for linear programming models, especially Data Envelopment Analysis (DEA), processing networks and advertising media mix models is herein developed. It has given a tenfold speed increase plus elimination of cycling difficulties over conventional Marsden or Kennington/Ali LP software modules in a 1000 LP DEA application.

Extremal Principle Solutions of Games in Characteristic Function Form: Core, Chebychev and Shapley Value Generalizations

In 1966, W. Lucas [1] exhibited a 10 person game with no von Neumann-Morgenstern solution. D. Schmeidler [2] then originated the nucleolus, proved it exists for every game, is unique and is contained in the kernel and the bargaining set (thereby establishing the first elementary proof of their existence). Charnes’ idea of defining solutions by use of uni- or poly-extremal principles involving comparison of coalitional worths and payoffs thereto was specialized by Charnes and Kortanek [3] to non-Archimedean linear programs characterizing and generalizing the nucleolus and to the class of convex nucleus solutions given by minimizing a convex function of the coalitional excesses subject to simple conditions like the payoff vector being a division of the grand coalition value or an imputation.

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

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 Charness 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.

Identification of Pareto-efficient facets in data envelopment analysis

Abstract In Data Envelopment Analysis (DEA), identification of the Pareto-efficient frontier of an empirical production possibility set is a prerequisite step toward determining rates of change of outputs with changes in inputs along its piecewise linear facets. These rates of change, which will be different on different facets, have important economic and managerial implications in trade-off analysis, forecasting and resource allocation. Accurate and complete identification of the component members of each facet remains an open question. Such identification is important in certain procedures for determining these rates of change. This paper develops three modifications to the pivoiing criteria of the simplex algorithm, commonly used to solve DEA problems, as alternative strategies for more completely identifying facet members of the Pareto-optimal frontier common to several production possibility sets in DEA. Experimental results from implementing these strategies are presented.

Reply to Luo and Huang

1 Carlson ML and Rousseau JJ (1989). EOQ under date-terms supplier credit. J Opl Res Soc 40: 451–460. 2 Schwarz LB (1972). Economic order quantities for products with finite demand horizons. AIIE Trans 4: 234–236. 3 Schwarz LB (1977). A note on the near optimality of ‘5-EOQ’s worth’ forecast horizons. Opns Res 25: 533–536. 4 Sivazlian BD and Stanfel LE (1975). Analysis of Systems in Operations Research. Chap. 5. Prentice Hall: Englewood Cliffs, NJ. 5 Lev B and Soyster AL (1979). An inventory model with finite horizon and price change. J Opl Res Soc 30: 43–54. 6 Hannan EL and Smith LA (1981). Economic order quantities for a finite demand horizon with a single price change—a note. N Z Opl Res 9: 1. 7 Lev B and Weiss HJ (1990). Inventory models with cost changes. Opns Res 38: 53–63. 8 Kingsman BG (1983). The effect of payment rules on ordering and stockholding in purchasing. J Opl Res Soc 34: 1085–1098.

Optimal design of syndicated panels: A mathematical programming approach

Abstract A new design concept for syndicated panels is proposed which explicitly handles tradeoffs between the economics of the panel (i.e., costs and revenues) and its econometrics (risk of sampling errors). Economic and statistical criteria are directly incorporated, leading to new mathematical programming formulations for deciding panel composition and size. These models provide insights into the complexities of panel design that are not available from traditional statistical methods. Much of the published literature does not address syndication or panel sampling and attendant complications such as demographic shifts and turnover standards. The present paper provides new methods, with worked examples, for optimizing the design when such conditions are present and thereby extends the range of situations for which optimal designs can be obtained. The traditional ‘cost of a sample unit’ is disaggregated to separate costs of sample recruitment, retention and maintenance, thus linking the sampling considerations to the optimization of the operation of the panel.