  Flexible job shop scheduling has been noticed as an effective manufacturing
system to cope with rapid development in today's competitive environment.
Flexible job shop scheduling problem (FJSSP) is known as a NP-hard problem in
the field of optimization. Considering the dynamic state of the real world
makes this problem more and more complicated. Most studies in the field of
FJSSP have only focused on minimizing the total makespan. In this paper, a
mathematical model for FJSSP has been developed. The objective function is
maximizing the total profit while meeting some constraints. Time-varying raw
material costs and selling prices and dissimilar demands for each period, have
been considered to decrease gaps between reality and the model. A manufacturer
that produces various parts of gas valves has been used as a case study. Its
scheduling problem for multi-part, multi-period, and multi-operation with
parallel machines has been solved by using genetic algorithm (GA). The best
obtained answer determines the economic amount of production by different
machines that belong to predefined operations for each part to satisfy customer
demand in each period.
