Queues, stochastic demand and the value of excess capacity in the steel industry

Abstract

The purpose of this study is to demonstrate the value of excess or reserve capacity in the steel industry. The model presented indicates a difference between gross and net arrivals resulting from the balking process. Waiting time between placement and shipment of an order is shown to be a determinant of balking values. The distribution of queue lengths is empirically estimated as is the corresponding distribution of joining probabilities. The value of reserve capacity to consumers results from the ability of capacity to reduce waiting time. Marginal value of capacity to consumers is shown to be the reduction in waiting time due to an increase in capacity times the value of consumers' time. The marginal value of capacity is positive and is estimated from the data. It is also shown that producers place a positive value on reserve capacity. The decrease in waiting time due to an increase in capacity results in an increase in net arrivals or orders. Marginal revenue of capacity is identified as this increase in net arrivals times product price. The value of marginal revenue of capacity is shown to be positive and is empirically estimated. The firm determines its optimal level of capacity by equating this marginal revenue of capacity with the marginal cost of capacity. Estimates of the marginal cost of capacity are also provided.