Minimizing Total Completion Time subject to Release Dates and Sequence Dependent Processing Times

We consider the problem of scheduling jobs with release dates and sequence-dependent processing times on a single machine to minimize the total completion time. We show that this problem is equivalent to the Cumulative Traveling Salesman Problem with additional time constraints. For this latter problem, we give a dynamic programming formulation from which lower bounds are derived. Two heuristic algorithms are proposed. Performance analysis of both lower bounds and heuristics on randomly generated test problems are carried out. Moreover, the application of the model and algorithms to the real problem of sequencing landing aircraft in the terminal area of a congested airport is analyzed. Computational results on realistic data sets show that heuristic solutions can be effective in practical contexts.