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.