Scheduling of deteriorating jobs with release dates to minimize the maximum lateness

In this paper, we consider the problem of scheduling n deteriorating jobs with release dates on a single (batching) machine. Each job’s processing time is a simple linear function of its starting time. The objective is to minimize the maximum lateness. When the machine can process only one job at a time, we first show that the problem is NP-hard even if there are only two distinct release dates. Then we present a 2-approximation algorithm for the case where all jobs have negative due dates. Furthermore, we prove that the earliest due date (EDD) rule provides an optimal solution to the case where all jobs have agreeable release dates, due dates and deteriorating rates, and that the EDD rule gives the worst order for the general case, respectively. When the machine can process up to b(b=∞) jobs simultaneously as a batch, i.e., the unbounded parallel-batch scheduling model, we show that the problem is NP-hard and present one property of the optimal schedule for the case where all jobs have agreeable release dates and due dates.