The variation of one machine scheduling problem

A generalization of one machine maximum lateness minimization problem is considered. There are one achine with controllable speed and n weighting jobs $J_{j}$, j=1, 2, ..., n with ambiguous duedates. Introducing fuzzy formulation, a membership function of the duedate associated with each job $J_{j}$, which describes the satisfaction level with respect to completion time of $J_{j}$. Thus the duedates are not constants as in conventional scheduling problems but decision variables reflecting the fuzzy circumstance of the job completing. We develop the polynomial time algorithm to find an optimal schedule and jobwise machine speeds, and to minimize the total sum of costs associated with jobwise machine speeds and dissatisfaction with respect to completion times of weighting jobs. jobs.