Minimizing weighted flowtime in a two-stage flow shop with fuzzy setup and processing times

In this paper, we present a mixed integer fuzzy programming approach to scheduling of customer orders for various furniture styles. Jobs are grouped into multiple classes based on different factors such as fabric type, furniture style and order due dates to reduce number of setups. The family of jobs at each stage of operation can also be partitioned into batches, where each batch consists 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 how batches are formed at each stage 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 flow time while fulfilling due date requirements. Numerical experimentation reveals that the proposed solution approach can efficiently schedule up to 16 jobs