Minimising a weighted quadratic function of job lateness in the stochastic single machine scheduling problem

We study a static single machine scheduling problem in which processing times, due-dates, and penalties for not completing jobs on time are distinct arbitrary random variables. The objective is to identify an optimal sequence, which minimises the expected weighted sum of a quadratic function of job lateness. The problem is NP-hard to solve; however, based on a precedence relation structure among adjacent jobs, we develop an exact algorithm. Our computational results demonstrate that the algorithm solves large problem instances quickly. Furthermore, the proposed problem is general in the sense that its special cases reduce to some classical deterministic or new stochastic single machine models.