In this study, we focus on the fuzzy order acceptance and scheduling problem in identical parallel machines (FOASIPM), which is a scheduling and optimization problem to decide whether the firm should accept or outsource the order. In general, symmetry is a fundamental property of optimization models used to represent binary relations such as the FOASIPM problem. Symmetry in optimization problems can be considered as an engineering tool to support decision-making. We develop a fuzzy mathematical model (FMM) and a Genetic Algorithm (GA) with two crossover operators. The FOASIPM is formulated as an FMM where the objective is to maximize the total net profit, which includes the revenue, the penalty of tardiness, and the outsourcing. The performance of the proposed methods is tested on the sets of data with orders that are defined by fuzzy durations. We use the signed distance method to handle the fuzzy parameters. While FMM reaches the optimal solution in a reasonable time for datasets with a small number of orders, it cannot find a solution for datasets with a large number of orders due to the NP-hard nature of the problem. Genetic algorithms provide fast solutions for datasets with a medium and large number of orders.