Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine

We consider a scheduling problem in which the jobs are generated by two agents and have time-dependent proportional-linear deteriorating processing times. The two agents compete for a common single batching machine to process their jobs, and each agent has its own criterion to optimize. The jobs may have identical or different release dates. The batching machine can process several jobs simultaneously as a batch and the processing time of a batch is equal to the longest of the job processing times in the batch. The problem is to determine a schedule for processing the jobs such that the objective of one agent is minimized, while the objective of the other agent is maintained under a fixed value. For the unbounded model, we consider various combinations of regular objectives on the basis of the compatibility of the two agents. For the bounded model, we consider two different objectives for incompatible and compatible agents: minimizing the makespan of one agent subject to an upper bound on the makespan of the other agent and minimizing the number of tardy jobs of one agent subject to an upper bound on the number of tardy jobs of the other agent. We analyze the computational complexity of various problems by either demonstrating that the problem is intractable or providing an efficient exact algorithm for the problem. Moreover, for certain problems that are shown to be intractable, we provide efficient algorithms for certain special cases

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

AbstractIn 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