Three classes of Earliness-Tardiness (E/T) scheduling problems

In this work, the tolerance window defined as the variations of gains and penalty associated with the earliness component of the Linear Composite Objective Function (LCOF) of Earliness–Tardiness (E/T) scheduling problems were explored to establish three different classes of the problem. Two variants of E/T problems has been established in the literature; the problems with unknown due-date with the objective of optimizing jobs due-date and the problems with a known due-date for optimizing the E/T cost function. The latter variant considered in this work applies the concept of Just-In-Time (JIT) as the basis for optimizing the E/T cost function. However, while the ideal JIT schedule which tends towards zero LCOF is notional, the deviation is a function of the tolerance window. To the best of the researchers’ knowledge, there is a gap between the measures of the deviation called the delivery reliability or penalty cost function and the tolerance window. This work closes the gap. A numerical example was solved to demonstrate the three problem classes’ utility using the Early Due Date (EDD) algorithm as the hypothetical solution.