Total completion earliness problem of single machine scheduling in fuzzy environments

In the fuzzy environment that the processing times and the due-dates of jobs are fuzzy parameters, the total completion earliness problem of single machine scheduling is investigated. In the case that the jobs have a common due-date and the same membership grade of earliness, an optimal scheduling is obtained in which the total completion earliness is maximized. In another case that the jobs have a common due-date and different membership grades of earliness, a necessary condition is given such that a schedule is optimal, and a corresponding branch and bound algorithm is proposed by which an optimal schedule can be found.