Single machine parallel-batching scheduling problem with fuzzy due-date and fuzzy precedence relation

A problem of single machine parallel-batching problem with fuzzy due-date and fuzzy precedence relation is investigated. Each job has a positive processing time. Set-up times are assumed to be identical for all batches. All batch sizes cannot exceed a common upper bound. The length of a batch is equal to the largest processing time among all jobs in the batch. Fuzzy due-date denotes the degree of satisfaction with respect to completion times of jobs. Fuzzy precedence constraint expresses the satisfaction level about precedence between two jobs. The objective is to minimise maximum completion time, maximise the minimum value of desirability of the fuzzy due-date and the minimum value of desirability of the fuzzy precedence. First, we propose a fuzzy due-date and ordinary precedence model, which maximises the minimum satisfaction degree of fuzzy due-date. An efficient iterative algorithm based on Procedure HL is designed. On that basis, another efficient algorithm to seek non-dominated solution is presented for the main problem in this paper. The non-dominated solution is defined to be consists of batch size, batch number and allocation of jobs to batches. The whole solution procedure needs at most [GRAPHICS] computational time. Finally, we illustrate the procedure with a numerical example.