Minimizing maximum earliness and number of tardy jobs in the single machine scheduling problem

This paper studies the problem of simultaneous minimization of the two criteria of maximum earliness and number of tardy jobs on a single machine. The goal is to generate the set of efficient sequences with respect to the two criteria. A heuristic algorithm named as H1 is developed for this problem and its efficiency is evaluated against a heuristic algorithm reported in the literature. The two algorithms are executed and applied to a set of instance problems. The computational results for instances with problem sizes of up to 150 jobs show that the H1 heuristic works far more efficiently than the competing heuristic. An exact procedure based on the branch-and-bound approach is also presented for the problem, in which the H1 heuristic is used as the upper bound. A lower bound and some dominance rules proposed in this paper cause the branch-and-bound algorithm to become even more efficient. Computational results of instances with sizes of up to 35 jobs prove the efficiency of the branch-and-bound approach in the optimal solution of the instances.