SINGLE-MACHINE SCHEDULING PROBLEM WITH FUZZY PRECEDENCE RELATION

This paper considers the single machine scheduling problem with fuzzy precedence relation. A precedence relation is a binary relation between jobs, that is, 'Job J(j) precedes job J(i)' means that processing of job J(i) cannot be started till completion of job J(j), which reflects the technical ordering with respect to production, etc. The fuzzy precedence relation relaxes this restriction and it reflects the satisfaction level with respect to precedence between two jobs. Two objectives are considered, i.e., L(max) (maximum lateness) to be minimized, and minimal satisfaction level with respect to fuzzy precedence relation to be maximized. Analogously to ordinary multi-criteria problems, we define nondominated schedules and find them. In order to calculate nondominated schedules, we first define a schedule vector and then a nondominated schedule vector. Our aim is to propose an efficient algorithm for calculating nondominated schedules. Finally, we discuss further research problems in this direction.