A job shop scheduling heuristic for varying reward structures

In this paper, a job shop scheduling problem of assigning preemptive tasks with precedence constraints to flexible resources is defined. A significant characteristic of this problem is that each task has a reward structure that defines the amount of reward based on its completion time. The objective is to maximize the total reward in the job shop. An optimal solution to this problem cannot be realistically obtained, as even significantly simpler problems are strongly NP-hard; therefore, a heuristic is proposed to obtain applicable solutions. The method is based on calculating (heuristic) penalty indices for each task as a function of time in order to allocate tasks to resources. A mathematical programming technique is then used to optimally minimize the penalty. This approach combines sound management science principles in order to emphasize analytical solutions to complicated real-life problems.