Search

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.

We introduce a methodology for generalizing Data Envelopment Analysis (DEA) to incorporate the role and impact of constituencies in the classification of the model's attributes. Constituencies determine whether entities' attributes in a DEA study are treated as desirable or undesirable. This extension of DEA is the basis for a methodology to answer questions that arise such as: Which constituencies find what entities efficient? Which entities are in the efficient frontier for a specified constituency? and What benchmarking prescriptions apply to inefficient entities for a given constituency? Constituencies allow new applications for DEA analyses of public projects to determine their impact on voters and marketing studies where a product defined by multiple attributes is analysed with respect to diverse markets, are two examples of the type of application for the new methodology. We introduce a DEA LP especially formulated for this new framework with many desirable properties. The new methodology is motivated and validated with a cost–benefit analysis application for a public project.

Performance rating and comparison of a group of entities is frequently based on the values of several attributes. Such evaluations are often complicated by the absence of a natural or obvious way to weight the importance of the individual dimensions of the performance. This paper proposes a framework based on nonparametric frontiers to rate and classify entities described by multiple performance attributes into ‘performers’ and ‘underperformers’. The method is equivalent to Data Envelopment Analysis (DEA) with entities defined only by outputs. In the spirit of DEA, the weights for each attribute are selected to maximize each entity’s performance score. This approach, however, results in a new linear program that is more direct and intuitive than traditional DEA formulations. The model can be easily understood and interpreted by practitioners since it conforms better to the practice of evaluating and comparing performance using standard specifications. We illustrate the model’s use with two examples. The first evaluates the performance of employees. The second is an application in manufacturing where multiple quality attributes are used to assess and compare performance of different manufacturing processes.

In classical scheduling theory job processing times are constant. However, there are many situations where processing time of a job depends on the starting time of the job in the queue. This paper reviews the rapidly growing literature on single machine scheduling models with time dependent processing times. Attention is focused on linear, piecewise linear and non-linear processing time functions for jobs. We survey known results and introduce new solvable cases. Finally, we identify the areas and give directions where further research is needed.

Learning is often perceived as a cost-reducing endogenous by-product of production processes. In many applications this by-product is modeled as a learning curve; that is, a simple function of time or of cumulative production experience. In an earlier paper we presented an alternative explanation where managers decide what resources to devote to knowledge acquisition. In this paper we expand those results to a situation using a more flexible production technology and emphasizing discounted cost. Our model explains resource and output behavior for a firm that is producing specialized units to contractual order. However, the results are quite general and have implications for investment in research, engineering, science and technology, software development, and worker training. We provide examples where the cost-minimizing producer will choose to invest in knowledge creation early in the production program and then have the rate of investment decline over time. Other interesting results are noted by examining the optimal time paths of the control and state variables in a comparative dynamic analysis.

Government cost analysts must often construct models using production data that are limited by a contract between the producer and the government. The producer usually does not share cost data with the government unless the contract requires that data are reported. Also, the data that are reported are often not in the proper form for constructing mathematical models; that is, cost data are often provided by production unit or lot, while economic and accounting data are usually reported by time period. This paper provides a mathematical link between unit or lot data and time series data; that is, between the units domain and the time domain. The analysis is relevant for made-to-order production, the case where a relatively small number of specialized items are produced to contractual order, as in defense and other government contract situations.

This paper explores a class of dynamic cost models that are designed for made-to-order production and are particularly applicable to the airframe industry. In these models we use optimal control theory to describe the time paths of resource use and production rate. The analytic solution for the most general specification of the model is unknown, however the imposition of a restriction on the relation between production rate and experience rate leads to a straightforward solution. The model implies that there exists an optimal trade-off between learning and production rate during the life of a program and that production rate should be changing throughout the life of the program in order to minimize cost. The model is compared with the learning curve, and the applicability of the model is explored by performing various parametric sensitivity analyses. The model's behavior is consistent with the dynamics of actual made-to-order production programs.

This research effort models decision-making behavior in a dynamic, uncertain environment. We derive consistent estimating procedures that model observed data that results from the decisions. This is accomplished by mating a Bayesian econometric process with a dynamic programming model of contractor behavior. This is used to demonstrate the dramatic increases in precision that can be obtained with just a few observations on program cost. The result of this effort can be used to develop a procedure for using routine data to help manage large programs in much the same way that control charts are routinely used to management production processes today.

A dynamic constraint elasticity of substitution (CES) framework is presented for modeling cost in made-to-order production. The criterion is cost minimization subject to production function constraints. The time paths of the state variables are consistent with those that are generated by actual production programs. In addition to providing an alternative explanation of the learning curve, this model also demonstrates that knowledge brought into the production process affects the rate of learning. This explains why learning is a more important cost determinant for made-to-order as opposed to assembly-line programs.

In this paper we study production programs where a relatively small number of complex units are produced to contractual order, and unit costs fall over time in some systematic way. We call this situation made-to-order production. Aircraft production is a good example. We derive the time path of planned resource use and demonstrate how to obtain approximate solutions for these optimal trajectories. The use of the approximation avoids a “messy” nonlinear optimization problem while providing resource estimates.

(1986). Airframe Cost Estimation Using an Error Components Model. The Journal of Cost Analysis: Vol. 3, No. 1, pp. 39-62.

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.

The basic modeling framework presented in Chapter 3 was developed for a firm producing to an order which specifies a quantity and a delivery date for output. A neoclassical production function was augmented with a learning hypothesis, and the cost of production was minimized to yield optimal time paths of both production and cost. The model presented in this chapter adheres to the same general theoretical framework. However, in the previous Chapters learning was presumed to be an automatic consequence of production experience. In this chapter the firm is permitted to devote resources explicitly to the “knowledge” production. This knowledge in turn permits more efficient production of both knowledge and output. In this way the learning curve is transformed from an automatic result of production to a result of the rational allocation of resources.

There are many possible specifications that embed learning hypotheses within production functions. One approach is to assume neutral technological change and augment a production function with learning as a function of cumulative output. Another possibility is to treat learning as a separate output in a multiple output production function. The output of learning increases the stock of knowledge, and the stock of knowledge enters the production function in the next instance of time as an input.

There are many proposed methodologies for assessing the cost impact of a production rate change. One of the more popular approaches is an application of the Alchian (1959) cost function. Even within this framework there is very little agreement about the relationships among learning, production rate, and program cost. While the models presented in this research require assumptions concerning the cost impact of the above factors in developing models of optimal contractor behavior, others [e.g., Smith (1976), Large, et. al (1974), Bemis (1981, 1983), Cox and Gansler (1981), Crouch (1980), Cox, et. al. (1981), Bohn and Kratz (1984)] address the problem by attempting to statistically estimate the above influences. In these latter studies contractor behavior is not a part of the modeling effort. The purpose of this chapter is to interface the two types of studies and show how estimates of the influences of learning and production rate, which are often statistically unreliable, may be inconsistent with optimal contractor behavior.

In this chapter, discrete models of made-to-order production are presented. For planning purposes the continuous models are appropriate, but our objective is to eventually relate these models to the assembly line or assembly area. This level of disaggregation requires that the models consider discrete production units. In short, this chapter represents the theoretical foundations of our future research. Work is presently underway in this area [see, for example, Camm (1984), Camm and Womer (1984), and Womer and Camm (1984)].

In this chapter two applications of the preceeding model are reported. These applications illustrate two characteristics of the modeling effort. First, in contrast to the approaches to be discussed in Chapter VII, the approach is to estimate parameters from a model which describes the behavior of the firm, rather than use parameter estimates and then describe firm behavior. Second, we tend to approach the estimation probelm by transforming the model to describe the available data rather than artibrarily adjusting the data to fit the model. This approach typically requires different modeling approaches for each data set encountered. As a result the models estimated in the two applications of this chapter differ somewhat from each other even though they are both based on the theory developed in Chapter III.