The stochastic single machine scheduling problem with earliness and tardiness costs

This paper studies the static single machine scheduling problem with earliness and tardiness costs where job processing times are random variables and due dates are distinct and deterministic. The objective is to identify an optimal sequence which minimizes the total expected earliness plus tardiness cost. A case where processing times are normally distributed is fully explored. We demonstrate that variations in processing times increase cost and affect sequencing decisions. Three heuristics for finding an optimal sequence are proposed. The illustrative example and computational results indicate that optimal sequences and their expected costs are significantly different from those provided by the classical deterministic single machine models. Furthermore, our computational experiments show that two of the proposed heuristics perform well in identifying optimal sequences.