Trading off due-date tightness and job tardiness in a basic scheduling model

We consider a scheduling problem in which the criterion for assigning due dates is to make them as tight as possible, while the criterion for sequencing jobs is to minimize their tardiness. Because these two criteria conflict, we examine the trade-off between the tightness of the due dates and the tardiness of the jobs. We formulate a version of this trade-off in the case of a stochastic single-machine model with normally distributed processing times. Using lower bounds and dominance properties to curtail the enumeration, we develop a branch-andbound procedure that is capable of solving large versions of the problem, and we report the results of computational experiments involving several hundred test problems.