Fuzzy scheduling of job orders in a two-stage flowshop with batch-processing machines

In this paper, we present a mixed-integer fuzzy programming model and a genetic algorithm (GA) based solution approach to a scheduling problem of customer orders in a mass customizing furniture industry. Independent job orders are grouped into multiple classes based on similarity in style so that the required number of setups is minimized. The family of jobs can be partitioned into batches, where each batch consists of a set of consecutively processed jobs from the same class. If a batch is assigned to one of available parallel machines, a setup is required at the beginning of the first job in that batch. A schedule defines the way how the batches are created from the independent jobs and specifies the processing order of the batches and that of the jobs within the batches. A machine can only process one job at a time, and cannot perform any processing while undergoing a setup. The proposed formulation minimizes the total weighted flowtime while fulfilling due date requirements. The imprecision associated with estimation of setup and processing times are represented by fuzzy sets.