Bicriterion jobshop scheduling with total flowtime and sum of squared lateness

In this paper sufficient conditions for optimality for the single machine job scheduling problem with a linear combination of total flowtime and sum of squared lateness as the objective function are developed. Based on the sufficient conditions a lower bound for the objective function for a given schedule is derived. A branch-and-bound procedure incorporating the lower bound has also been developed. In addition, we also show how to fathom nodes in the branching tree using the a-priori precedence relationships among the jobs that can be determined using the sufficient conditions. Computational experiments for the branch-and-bound and its results are also presented.