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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.

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 s...

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.

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.

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.

This paper examines the relationships among several dynamic programming models of the made-to-order production situation. The models consider the impacts of both learning and production rate changes on optimal program costs. The comparisons among the models suggest that a type of economic duality links the solutions. The results of this research suggest a method of transformation which may provide a useful means for finding tractable solutions to similar dynamic programming problems.

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.

The relation between the structural and the reduced-form parameters in a system-of-equations model is used to relate identification to two-stage and three-stage least squares. This provides a straightforward derivation of the estimators as an attempt to satisfy the relation with least squares estimators for the reduced-form parameters.

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.

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 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.