Herbert F. Lewis

Two-Stage DEA: An Application to Major League Baseball

We show how to use DEA to model DMUs that produce in two stages, with output from the first stage becoming input to the second stage. Our model allows for any orientation or scale assumption. We apply the model to Major League Baseball, demonstrating its advantages over a standard DEA model. Our model detects inefficiencies that standard DEA models miss, and it can allow for resource consumption that the standard DEA model counts towards inefficiency. Additionally, our model distinguishes inefficiency in the first stage from that in the second stage, allowing managers to target inefficient stages of the production process.

Multi-period job selection: planning work loads to maximize profit

We examine the profitability of job selection decisions over a number of periods when current orders exceed capacity with the objective of maximizing profit (per-job revenue net of processing costs, minus weighted lateness costs), and when rejecting a job will result in no future jobs from that customer. First we present an optimal dynamic programming algorithm, taking advantage of the structure of the problem to reduce the computational burden. Next we develop a number of myopic heuristics and run computational tests using the DP as benchmark for small problems and the best heuristic as benchmark for larger problems. We find one heuristic that produces near-optimal results for small problems, is tractable for larger problems, and requires the same information as the dynamic program (current and future orders), and another that produces good results using historical information. Our results have implications for when it is more or less worthwhile to expend resources to maintain past records and obtain future information about orders.

Organizational capability, efficiency, and effectiveness in Major League Baseball: 1901–2002

Effective organizations need capabilities relevant to their missions and must manage those capabilities efficiently. We anticipate capability is more important in industries in which labor is highly paid, while efficiency is more important in industries in which labor is inexpensive. We explore the contributions of capability and efficiency to effectiveness for Major League Baseball teams from 1901 through 2002. Our analysis measures team capability using offensive and defensive statistics and uses Network Data Envelopment Analysis to derive efficiency scores to capture managerial performance. We define effectiveness as the teams winning percentage. Both capability and efficiency are significant contributors to regular season effectiveness. Capability is more important. Finally, we examine the post-season performance of post-season teams between 1903 and 2002. Our analysis measures post-season performance based on the teams winning percentage and that of its opponent. Post-season performance is unrelated to capability and managerial performance, accounting for about 1% of post-season success.

Unoriented two-stage DEA: The case of the oscillating intermediate products

Data envelopment analysis (DEA) allows us to evaluate the relative efficiency of each of a set of decision-making units (DMUs). However, the methodology does not permit us to identify specific sources of inefficiency because DEA views the DMU as a “black box” that consumes a mix of inputs and produces a mix of outputs. Thus, DEA does not provide a DMU manager with insight regarding the internal source of the organization’s inefficiency.

Player Salaries, Organizational Efficiency, and Competitiveness in Major League Baseball

The dramatic growth of free agency in Major League Baseball has caused great concern about the competitiveness of some teams, particularly those in smaller markets. The authors use a two-stage data envelopment analysis model as part of a larger analysis to determine the minimum total player salary required to be competitive in each nonstrike year since 1985. They then examine trends in this salary and determine how many teams were noncompetitive each year because of low total player salary. Finally, they examine the relationship between competitiveness and market size. The authors find evidence that the number of times that a team has been noncompetitive because of low total player salary between 1985 and 2002 is negatively related to the size of the market in which it plays. The authors also find that large market teams are more likely to overspend on player salaries than are small market teams.

An Efficiency-Based Multicriteria Strategic Planning Model for Ambulatory Surgery Centers

Ambulatory surgery centers (ASCs) provide a low-cost alternative to traditional inpatient care. In addition, with health care reform imminent, it is likely that many currently uninsured people will soon acquire health care coverage, significantly increasing the demand for health services. ASCs are among the providers that can expect to see a substantial amount of this new pent-up demand and, therefore, ASCs are likely to continue their current growth into the foreseeable future. Those ASCs that plan accordingly by optimizing procedure mix and volume will benefit most from the increased demand. We propose a two-stage efficiency-based multicriteria decision model to guide an ASC in identifying its optimal procedure mix. The first stage uses Data Envelopment Analysis (DEA) to calculate the efficiency of each procedure based on the resources required to perform the procedure, the revenue it generates, and its risk of complications. The second stage uses the DEA factor efficiency scores in a bottleneck program to optimize the mix of procedures while satisfying the ASC’s resource and operational constraints. The criteria are to (1) maximize reimbursement while (2) minimizing the total number of complications. We demonstrate the approach using a data set based in part on data from an actual ASC.

Using DEA Factor Efficiency Scores to Eliminate Subjectivity in Goal Programming

Many real-world problems require decision makers to consider multiple criteria when performing an analysis. One popular method used to analyze multicriteria decision problems is goal programming. When applying goal programming, it is often difficult if not impossible to determine the target values and unit penalty weights with any level of confidence. Thus, in many situations, managers and decision makers may be forced to specify these parameters subjectively. In this paper, we present a model framework designed to eliminate the arbitrary assignment of target values and unit penalty weights when applying goal programming to solve multicriteria decision problems. In particular, when neither of these parameters is available, we show how to integrate factor efficiency scores determined from data envelopment analysis into the model. We discuss an application of the methodology to ambulatory surgery centers and demonstrate the model framework via a product mix example.

Performance Measurement of Major League Baseball Teams Using Network DEA

Data envelopment analysis (DEA) has been extensively applied to measure the performance of individual athletes and teams in a variety of sports as well as to analyze nations competing in the Olympics. Most of the models presented in the literature are single-stage DEA models which treat the underlying process of converting inputs into outputs as a “black box.” In many situations, analysts are interested in investigating the sources of inefficiency within the organization in order to improve organizational performance. To accomplish this, researchers have developed two-stage and network DEA methodologies.

On the tour partitioning heuristic for the unit demand capacitated vehicle routing problem

The tour partitioning heuristic for the vehicle routing problem assumes an unlimited supply of vehicles. If the number of vehicles is fixed, this heuristic may produce infeasible solutions. We modify the heuristic to guarantee feasibility in this situation and we analyze the worst-case performance of the modified heuristic.

Measuring and Managing the Productivity of U.S. Public Transit Systems: An Unoriented Network DEA

Governments at all levels face budget shortfalls, and consequently public transit systems in the U.S. must compete with other public services for financial support. In order to depend less on public funding, it is critical that public transit systems focus on their operational performance and identify any sources of inefficiency. In this chapter, we present an unoriented network DEA methodology that measures a public transit system’s performance relative to its peer systems, compares its performance to an appropriate efficient benchmark system, and identifies the sources of its inefficiency.