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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.learning augmented planning models, dynamic optimization, optimal control theory, knowledge creation

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This paper deals with a model of the firm engaged in production to order. Models of this situation frequently conclude that the size of the order and production rate each influence the costs of production. Despite this fact, empirical work on production costs focus almost exclusively on either production rate or the size of the order as explainers of variations in costs. In this paper, a model is developed which is consistent with both these facts. The model permits production rate to be a decision variable in the manufacturer's production planning. The model is solved for an optimal production plan which requires production rate to change throughout the life of the program. The planning situation, where alternative order sizes are considered, is then contrasted with the production situation, where unit costs are related to cumulative output given a production plan. This approach provides guidance for the use of data on past programs in the estimation of cost functions and the evaluation of future production plans.production/scheduling, production/scheduling: work studies and learning