Migration from Sequence to Schedule in Total Earliness and Tardiness Scheduling Problem

To be competitive, services must be delivered with high punctuality. To schedule punctual services, the classical scheduling theory offers to minimize total earliness and tardiness of services. In this study, we developed an optimal fully polynomial time algorithm to transform a given sequence, permutation of jobs, into its minimum cost schedule counterpart, timing of jobs, for the single machine scheduling with the objective total earliness and tardiness. We provide the fundamental necessary and sufficient optimal properties for the objective of sub-sequences of jobs, called clusters. The algorithm first decomposes a sequence into several clusters, and then it applies a recursive scheme to join the clusters and to generate their minimum cost schedule counterparts. The complexity status sheds light on the competitiveness of our algorithm in comparison with other state-of-the-art algorithms in the literature.