On the value of adaptive solutions to stochastic scheduling problems

Two possible ways of dealing with the presence of unknown system parameters in a stochastic scheduling problem are (i) to give unknowns prior distributions and implement a Bayes (adaptive) policy and (ii) to choose plausible values for the unknown parameters at the outset, thereafter treating them as known. Since adaptive policies are often difficult to construct and/or apply, route (ii) may be favoured if there is little to be lost by it. Hence we seek to quantify the value of an adaptive solution (VAS). For quite general classes of stochastic scheduling problems, both preemptive and nonpreemptive, we are able to relate the VAS to natural measures of the degree of peakedness of the prior distributions and the sensitivity of optimal policies to changes in value of the unknown parameters.