Fuzzy Single Machine Scheduling Problem with Mixed Precedence Constraints and Fuzzy Due Dates

A problem of scheduling jobs on a single machine subject to fuzzy due dates and mixed precedence constraints is discussed. Fuzzy due dates denote the degree of satisfaction with respect to completion times of jobs. The mixed precedence constraints consist of crisp and fuzzy precedence relations. The fuzzy precedence expresses the satisfaction level with respect to precedence between two jobs. The objective is to maximize the minimum satisfaction level of fuzzy due dates and mixed precedence constraints. Through searching the nondominated solutions of the bi-criteria problem, the optimal schedules can be found.