Stochastic resource allocation problems (SRAPs) involve determining the optimal configuration of a limited resource to achieve an objective function under given constraints and random effects in manufacturing systems (MSs) and service systems (SSs). The problems are traditionally solved by determining the optimal solution. It is generally preferable to determine as many global optima as possible, or at least a small set of diverse but good candidates, to help the decision-maker rapidly adopt alternative solutions from the set if one solution is unsuitable. However, many local or global optima occur in SRAPs in MSs and SSs due to the interaction between random system factors, such as processing time uncertainty and machine failure rates. Thus, enhancing the searching efficiency of algorithms for SRAPs is a challenge. This study proposes an efficient simulation–optimization approach, called elite-based particle swarm optimization (EPSO), using an optimal replication allocation strategy (ORAS) (i.e., EPSO, to address three types of SRAPs from the literature. Three simulation models were constructed to evaluate the system performance under random factors. We developed a novel EPSO to explore and exploit the solution space. We created an elite group (EG) that includes multiple solutions, and each solution of the EG has a statistically nonsignificant difference from the current optimal solution. The new feature of EPSO updates the velocity and position of the particles in the design space based on multiple global optima from the EG to enhance diversity and prevent premature convergence. We propose an ORAS to allocate a limited number of replications to each solution. Three numerical experiments were performed to verify the effectiveness and efficiency of EPSO compared with other simulation–optimization approaches, namely particle swarm optimization (PSO) and the genetic algorithm (GA) with both optimal computing budget allocation (OCBA) and the ORAS. The experimental results reveal that the solution quality of EPSO improved compared with that of PSO and GA, and the ORAS provides a more efficient allocation of the number of replications compared with the OCBA in the three experiments. Finally, the proposed approach also provides an elite set at the end of the algorithm, instead of a single optimal solution, to support decision-making.