Linear programming is widely used to model production planning decisions. In addition to the optimal solutions, the dual prices provided by those models are of great interest in different situations such as shop-floor dispatching, spare parts inventory management, setup cost estimation, and indirect cost allocation. While those techniques are effective and intuitive in nature, fixed-capacity production planning models are "dual-poor", i.e., dual prices are zero unless resources are fully utilized. Another issue arises regarding the objective function that drives the dual prices of the model. While steady--state queuing models do not consider the finished goods inventory that is held due to insufficient capacity, the linear programming models of production planning do not consider the effects of resource utilization on queue lengths within the production system. Clearly both types of costs, those due to congestion as well as finished goods inventory are relevant. Hence a model that integrates both would appear to be desirable. In this dissertation, we examine the dual behavior of two different production planning models: a conventional fixed--capacity linear programming model and a model that captures queuing behavior at resources in an aggregate manner using non--linear clearing functions. The conventional formulation consistently underestimates the dual price of capacity due to its failure to capture the effects of queuing. The clearing function formulation, in contrast, produces positive dual prices even when utilization is below one, exhibits more realistic behavior, such as holding finished inventory at utilization levels below one, and in multi--stage models, allows for identification of near--bottlenecks as an alternative for improvement in cases where it is economically or physically not possible to improve or add capacity to the bottleneck.
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