Purpose Parallel two-sided assembly lines are usually designed to produce large-sized products such as trucks and buses. In parallel two-sided assembly lines, both left and right sides of the line are used for manufacturing one or more products on two or more assembly lines located parallel to each other. The purpose of this paper is to develop a new mathematical model for the parallel two-sided assembly line balancing problem that helps to evaluate and validate the balancing operations of the machines such as removal of tools and fixtures and reallocating the operators. Design/methodology/approach The proposed approach is explained with the help of an example problem. In all, 22 test problems are formed using the benchmark problems P9, P12, P16 and P24. The results obtained are compared among approaches of the task(s) shared, tool(s) shared and both tool(s) and task(s) shared for effect on efficiency as the performance measure. The solution presented here follows the exact solution procedure that is solved by Lingo 16 solver. Findings Based on the experiments, line efficiency decreases when only tools are shared and increases when only tasks are shared. Results indicate that by sharing tasks and tools together, better line efficiency is obtained with less cost of tools and fixtures. Practical implications According to the industrial aspect, the result of the study can be beneficial for assembly of the products, where tools and tasks are shared between parallel workstations of two or more parallel lines. Originality/value According to the author’s best knowledge, this paper is the first to address the tools and tasks sharing between any pair of parallel workstations.