Control and Cybernetics a New Optimal Algorithm for a Time-dependent Scheduling Problem *

Abstract: In this article a single machine time-dependent scheduling problem with total completion time criterion is considered. There are n given jobs, j1, . . . , jn, and the processing time pi of the i-th job is given by pi = 1 + bisi, where si is the starting time of the i-th job, i = 1, . . . n. If all jobs have different and non-zero deterioration rates and bi > bj ⇒ bi ≥ bmin+1 bmin bj+ 1 bmin , where bmin = min{bi}, then an optimal schedule can be found in O(n logn) time. The conducted computational experiments show that the presented algorithm performs very well even on data not satisfying the assumed constraints.