Janet M. Wagner

Groundwater quality management under uncertainty: stochastic programming approaches and the value of information

A stochastic optimization model for containment of a plume of groundwater contamination through the installation and operation of pumping wells is developed. It considers explicitly uncertainty about hydraulic conductivity in the aquifer and seeks to minimize the expected total cost of operating the pumping wells plus the recourse cost incurred when containment of the contaminant plume is not achieved. Four different formulations of the model are examined, ranging from simply replacing all uncertain parameters by their expected values to a full stochastic programming with recourse model involving nonsymmetric linear quadratic penalty functions. The full stochastic programming with recourse model, which minimizes the expected total costs over a number of realizations of outcomes of the random parameters, is nonlinear and possibly nonconvex and is solved by an extension of the finite generation algorithm. The value of information about the uncertain parameters is defined through the differences between the values of the optimal solutions to the different formulations. A sample problem is solved using all four formulations. The results indicate that the explicit incorporation of uncertainty does make a difference in the solutions obtained. The work indicates that stochastic programming with recourse is a useful tool in management under uncertainty, and that it can be used with reasonable computational resources for problems of moderate size.

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

Abstract One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.

A stochastic optimization model for planning capacity expansion in a service industry under uncertain demand

A stochastic optimization model for capacity expansion for a service industry that incorporates uncertainty in future demand is developed. Based on a weighted set of possible demand scenarios, the model generates a recommended schedule of capacity expressions, and calculates the resulting sales under each scenario. The capacity schedule specifies the size, location, and timing of these expansions that will maximize the companys expected profit. The model includes a budget constraint on available resources. By using Lagrangian relaxation and exploiting the special nested knapsack structure in the sub‐problems, an algorithm was developed for its solution. Based on the initial computational results, this algorithm appears to be more efficient than linear programming for this special problem.

Advances in physician profiling: the use of DEA

Abstract Insurers, health plans, and individual physicians in the United States are facing increasing pressures to reduce costs while maintaining quality. In this study, motivated by our work with a large managed care organization, we use readily available data from its claims database with data envelopment analysis (DEA) to examine physician practices within this organization. Currently the organization evaluates primary care physicians using a profile of 16 disparate ratios involving cost, utilization, and quality. We employed these same factors along with indicators of severity to develop a single, comprehensive measure of physician efficiency through DEA. DEA enabled us to identify a reference set of “best practice” physicians tailored to each inefficient physician. This paper presents a discussion of the selection of model inputs and outputs, the development of the DEA model using a “stepwise” approach, and a sensitivity analysis using superefficiency scores. The stepwise and superefficiency analyses required little extra computation and yielded useful insights into the reasons as to why certain physicians were found to be efficient. This paper demonstrates that DEA has advantages for physician profiling and usefully augments the current ratio-based reports.

Containing groundwater contamination: Planning models using stochastic programming with recourse

Abstract This paper examines the problem of operating pumping wells in order to contain an area of groundwater contamination when the aquifer properties of the area are uncertain. A stochastic program with simple recourse is formulated, involving a non-convex quadratic objective subject to linear constraints. This problem is solved using an extension to the Finite Generation Algorithm that will find an at least locally optimal solution to a problem involving a non-convex quadratic objective function. A numerical example is presented and analyzed.

Models for planning capacity expansion of convenience stores under uncertain demand and the value of information

Several stochastic optimization models for planning capacity expansion for convenience store chains (or other similar businesses) are developed that incorporate uncertainty in future demand. All of these models generate schedules for capacity expansion, specifying the size, location, and timing of these expansions in order to maximize the expected profit to the company and to remain within a budget constraint on available resources. The models differ in how uncertainty is incorporated, specifically they differ in the point in the decision-making process that the uncertainty in the demand is resolved. Several measures of the value of information are defined by comparing the results from the different models. Two sample problems are given and their solutions for the various approaches compared.

Efficiency in Public Higher Education Systems: A Statewide Comparison Using Data Envelopment Analysis

As state funding for public higher education has declined, there is a rising demand for accountability. Past studies have relied on indicator ratios to look at the relationship between funding and performance measures. This approach has some inherent problems that make it difficult to identify inefficiencies. This chapter will study efficiency in state systems of higher education by applying data envelopment analysis (DEA). DEA methodology converts multiple variables into a single comprehensive measure of performance efficiency and has the ability to perform benchmarking for the purpose of establishing performance goals. The advantages of DEA modeling will be shown by comparing results with those from a recent study of higher education finance based on publicly available data. DEA is shown to be feasible and implementable for studying state systems of higher education, and provides useful information in identifying “best practice” state systems and guidance for improvement. The value of DEA modeling to state policy makers and education researchers is discussed.