Norman Keith Womer

A dynamic cost function for an airframe production program

Abstract This research represents an extension of previous work in the area of estimating military airframe program costs. The effort is unique in that it yields a model of the production process that considers the impact of learning, production rate, and (implicitly) facility size on total program costs. To provide an empirical test of model validity the parameters are estimated for the C141 airframe program. The models use as a prototype for models of ongoing production programs is illustrated by estimating the cost impact of exogenous changes in the program delivery schedules, e.g. the “crashes” and “strech-outs” that frequently characterize military airframe production programs.

Solving stochastic resource-constrained project scheduling problems by closed-loop approximate dynamic programming

Project scheduling problems with both resource constraints and uncertain task durations have applications in a variety of industries. While the existing research literature has been focusing on finding an a priori open-loop task sequence that minimizes the expected makespan, finding a dynamic and adaptive closed-loop policy has been regarded as being computationally intractable. In this research, we develop effective and efficient approximate dynamic programming (ADP) algorithms based on the rollout policy for this category of stochastic scheduling problems. To enhance performance of the rollout algorithm, we employ constraint programming (CP) to improve the performance of base policy offered by a priority-rule heuristic. We further devise a hybrid ADP framework that integrates both the look-back and look-ahead approximation architectures, to simultaneously achieve both the quality of a rollout (look-ahead) policy to sequentially improve a task sequence, and the efficiency of a lookup table (look-back) approach. Computational results on the benchmark instances show that our hybrid ADP algorithm is able to obtain competitive solutions with the state-of-the-art algorithms in reasonable computational time. It performs particularly well for instances with non-symmetric probability distribution of task durations.

Some Propositions on Cost Functions.

Abstract : In this paper, a model is developed for a firm producing to an order which specifies a quantity and a delivery date for output. The order serves to constrain a production program which minimizes the discounted cost of producing at a constant output rate. The model is formed by augmenting a homogenous production function with a learning hypothesis and deriving a cost function. The cost function is then compared to several results due to Alchian, Hirshleifer, and Oi.

The unit learning curve approximation of total cost

Abstract Learning curve theory has been integrated into mathematical models which previously did not take learning into account. Researchers have in general used one of two approximations of total cost based on the integral of the unit learning curve when developing larger models. An error analysis of the two approximations is presented.

A generalization of the learning curve

Abstract This paper presents a generalization of models that relate required resources to accumulated experience. These learning curve models are often used as planning tools in made-to-order production programs. This is especially true in the acquisition of major defense items. However, learning curves are deficient in that they only consider a single cost determinant, cumulative experience. The model presented in this paper considers both cumulative experience and production rate as cost determinants. As a decision application it is shown how the model may be used to generate the type of program cost data that is used in planning for made-to-order programs.

Benefit-cost analysis using data envelopment analysis

Benefit-cost analysis is required by law and regulation throughout the federal government. Robert Dorfman (1996) declares ‘Three prominent shortcomings of benefit-cost analysis as currently practiced are (1) it does not identify the population segments that the proposed measure benefits or harms (2) it attempts to reduce all comparisons to a single dimension, generally dollars and cents and (3) it conceals the degree of inaccuracy or uncertainty in its estimates.’ The paper develops an approach for conducting benefit-cost analysis derived from data envelopment analysis (DEA) that overcomes each of Dorfmans objections. The models and methodology proposed give decision makers a tool for evaluating alternative policies and projects where there are multiple constituencies who may have conflicting perspectives. This method incorporates multiple incommensurate attributes while allowing for measures of uncertainty. An application is used to illustrate the method.

A Method for Repricing Aircraft Procurement Programs

Planned annual procurement quantities for defense weapon systems are often altered after production starts. Department of Defense analysts support the decision process by providing cost estimates for alternatives to ongoing procurement programs. This paper presents a method for repricing aircraft programs under a proposed change in quantity. The method is an extension of the standard learning curve model that accommodates the redistribution of fixed costs at the contractors plant.

Measuring efficiency with a linear economic model

This paper modifies and interprets Data Envelopment Analysis (DEA) using a linear economic model. This approach is similar to the cone input/output and assurance region approaches to DEA, but it is implemented so that the multipliers are measured in the same units across all linear optimization problems. This approach allows one to interpret alternatives as profit maximizing organizations and the DEA multipliers as prices that are comparable across the alternatives. This is a useful extension of the assurance region concept, but more important, is that our approach enhances communication with decision-makers. The improved communication is illustrated by applying the model to the siting of a long-term health care facility. This application is interesting because the multiplier bounds make practical sense, and because the problem has dimensions that sometimes lead to interpretation problems with the traditional DEA model. For example, the site characteristics do not result from coordinated decisions, some sites exhibit zero values for some variables, and the problem has many variables compared with the number of potential sites. Problems with these dimensions have, at times, been deemed unsuitable for DEA, but they are handled without problem by the linear economic model.

Production Rate and Contractor Behavior

Abstract There has been much interest in recent years in the relationships among learning, production rate, and program costs. These relationships are of particular interest in military acquisitions research where, because of the nature of the funding process, the government must assess the cost impact of numerous production rate changes. One approach that is often used to analyze the problem is an empirical application of the “Alchian cost function.” Department of Defense analysts routinely use these models for planning purposes. The purpose of this paper is to demonstrate that the models as being applied imply nonsensical contractor behavior.

An error components model of cost overruns and schedule slip on army R&D programs

What has been causing cost overruns and schedule slippages in Army major weapon-system R&D programs during the past ten years? This article addresses this question with emphasis on the effectiveness of an Army acquisition strategy entitled Total Risk Assessing Cost Estimating (TRACE). An empirical study employed a questionnaire and interviews with key personnel from all of the major Army Program Management Offices involved with R&D. The major research question was the following: What explanatory variables have been affecting R&D cost overruns and development time? This includes an evaluation of TRACE as a potential explanatory variable. Data was collected and analyzed using an error components multiple regression model. The major explanatory variables that appeared to explain cost overruns were technological risk of the program, education and experience of key program management office personnel, and the degree of “buy in” by the prime contractor. Strong statistical results indicate that TRACE is having little or no effect on cost overruns. In the case of development time, the major explanatory variables were seen to be technological risk of the program, testing, TRACE, education, and length of the R&D contract.