Single machine scheduling with start time dependent processing times: Some solvable cases

This paper considers a generalized one machine maximum lateness problem with fuzzy duedate and controllable machine speed. There are one machine and n jobs J1, J2,...,Jn to be processed on the machine. A membership function is associated with each job Jj, which describes the degree of satisfaction with respect to completion time of Jj. Further machine speed can be changeable jobwise. The objective is to find an optimal schedule and optimal jobwise machine speeds and to minimize the total sum of costs associated with jobwise machine speeds and dissatisfaction with respect to completion times of jobs. We propose a polynomial time algorithm for solving the above problem under some assumptions.