Implicit costs and prices for resources with busy periods

Conventional cost accounting gives a marginal value to excess average capacity of a resource of zero. In point of fact, a typical actual machine alternates in time between periods in which it is overutilized (busy periods) and periods in which it is underutilized (idle periods). During busy periods this imputed price is positive; in idle periods the price is zero. Averaging these short-term prices over time procedures the correct nonzero long-term price for machine time for cost-accounting purposes. There are two common approaches for estimating such prices (costs): (a) the busy period pricing method of Morton et al., and (b) the average waiting-line pricing method of Banker et al. The average waiting-line method can speedily give a formula for long-term prices given an analtyic differentiable formula for yearly expected costs. In these cases, at about the same effort, the busy period can average analytic short-term prices to obtain the identical formula. However, the more general busy period method has a number of advantages: (a) explicit short-term prices are obtained in the process, (b) an approximation to long-term prices can be given which requires the estimation of no difficult parameters and (c) a general procedure is provided for finding exact/heuristic solutions to more complicated models, such as for seasonality. Banker et al. make repeatedly the erroneous statement that positive prices are caused by stochasticity. Indeed, stochasticity can produce busy periods, and thus positive prices, but so can simple seasonality, or any large clump of known orders. Even mild seasonality can make the stationary approach highly inaccurate. The paper has several purposes: (a) to review and extend the basic busy period methodology, (b) to derive some new stationary stochastic pricing results, (c) to derive/illustrate some seasonal pattern results, (d) to discuss issues for companies with orders partially known in advance (represented by master schedules), and (e) to make a few suggestions for future research.