Assignment scheduling problem with precedence constraints and un-symmetrical fuzzy processing times

A single machine due date assignment scheduling problem with asymmetric processing time and
precedence constraints in fuzzy environment is investigated in the present work, to minimize total earliness and
tardiness penalties. It is polynomially solvable with processing time at the same width ratio, and the precedence
constraints are out-tree. Further, when the general constraints are involved, a 2-approximate algorithm is put
forward based on linear relaxation method.