This paper aims to study allocating tasks problem in a single-station collaborative robot assembly system 4.0 considering the ISO standard. Two products with identical demands are run in a system simultaneously in mixed mode to reduce the idle time and improve the system utilization. The idle time occurs due to balancing difficulties and particularly in this case restrictions in the task vs. robot-worker feasibility matrix. It is not allowed for the resources to assemble a same product simultaneously to avoid any direct contact between resources. Thus, the products are swapped between resources as needed to complete the assembly tasks. Two approaches, a novel mathematical model and the shortest processing time (SPT) rule, are propounded in this study to reduce the cycle and idle times, and enhance the production rate of an assembly system. The two proposed methods rely on dividing the timeline of a station into unknown stages with unknown lengths. The performance of the proposed mathematical model and SPT rule are evaluated by two performance measures: the total number of stations and the % average station utilization. The obtained results are compared to the results of the modified COMSOAL heuristic. The findings revealed that the novel mathematical model dominated results. It guaranteed minimizing the cycle time and maximizing the production rate compared to the SPT rule and modified COMSOAL heuristic. However, many companies value a one-second reduction in cycle time as valuable. This directly relates to the reduction of direct resources costs and the total number of stations.