Complexity of Scheduling with Proportional Deterioration and Release Dates

Abstract

In this paper, we analyze the computational complexity of single-machine scheduling problems with deteriorating jobs having non-zero release dates. The processing time of each job is a proportional increasing function of its starting time. The objectives are to minimize the total weighted completion time, the number of tardy jobs and the total completion time, respectively. We first show that the total weighted completion time minimization problem and the number of tardy jobs minimization problem are binary NP-hard. Then, we present some optimal properties for the two problems under the restriction that the jobs have identical deteriorating rates. Finally, we show that the total completion time minimization problem with deadline is binary NP-hard, and in the case when the jobs have identical deadlines, agreeable release dates and deterioration rates, it can be solved in \(O(n\log n)\) time.