Using a mathematical programming model to examine the marginal price of capacitated resources

Accurate information on dual prices of capacitated resources is of interest in a number of applications, such as cost allocation and pricing. To gain insight we focus on the dual prices of capacity and demand in a single-stage single-product production-inventory system, and discuss their interpretation. In particular, we examine the behavior of two different production planning models: a conventional linear programming model and a nonlinear model that captures queuing behavior at resources in an aggregate manner using nonlinear clearing functions. The classical linear programming 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 and exhibits more realistic behavior, such as holding finished inventory at utilization levels below one.