Machine scheduling with earliness, tardiness and non-execution penalties

The study of scheduling problems with earliness–tardiness (E/T) penalties is motivated by the just-in-time (JIT) philosophy, which supports the notion that earliness, as well as tardiness, should be discouraged. In this work, we consider several scheduling problems. We begin by generalizing a known polynomial time algorithm that calculates an optimal schedule for a given sequence of tasks, on a single machine, assuming that the tasks have distinct E/T penalty weights, distinct processing times and distinct due dates. We then present new results to problems, where tasks have common processing times. We also introduce a new concept in E/T scheduling problems, where we allow the non-execution of tasks and consequently, are penalized for each non-executed task. The notion of task's non-execution coincides with the JIT philosophy in that every violation or a breach of an agreement should be penalized. We develop polynomial time algorithms for special cases in E/T scheduling problems with non-execution penalties.