Punctuality and idleness in just-in-time scheduling

In scheduling problems with irregular cost functions, such as deviation functions in earliness–tardiness scheduling problems, optimal solutions usually contain some idleness periods during which no activity is processed. Then, minimizing the penalties for not delivering on time and minimizing the idleness cost are two complementary criteria for a schedule. A Dynamic Programming procedure, in which the states are represented by continuous two-dimensional piecewise linear functions, is proposed to compute the cost of the Pareto optimal schedules.