Abstract This study evaluates the supplier selection problem encountered when using multiple assembly plants with production capacity constraints to produce multiple products. It also applies assembly sequence planning (ASP) and assembly task assignment to production planning for the overall supply chain to determine optimal supplier combinations and production resource allocation. A multi-objective optimization mathematical model was constructed and a modified multi-objective algorithm was used to solve the optimization model. Developed on the basis of the nondominated sorting genetic algorithm II (NSGA-II), this modified algorithm incorporates an algorithmic and determination mechanism involving the greatest number of following tasks and the longest task time when initial solutions are generated. This increases the efficiency of solutions derived from the NSGA-II, here referred to as the W-NSGA2. The W-NSGA2 is then applied to the actual case of a faucet assembly task, and solutions derived by the W-NSGA2 are compared with those derived by the NSGA-II and the nondominated sorting particle swarm optimizer (NSPSO). Results show that the W-NSGA2 yields better solutions.