An　assembly　line　is　a　serial　production　system　that　is　meant　to　produce　high-quality　and　usually　complex　products　in　mass　quantities.　Assembly　lines　play　a　crucial　role　in　determining　the　profitability　of　a　company,　as　they　are　utilised　as　the　final　stage　of　the　system　prior　to　shipping.　In　an　assembly　line　balancing　problem,　the　assembly　tasks　are　allocated　to　workstations　based　on　their　processing　times　after　considering　the　precedence　relationships　between　them.　There　is　a　massive　amount　of　research　in　the　literature　using　deterministic　task　processing　times,　and　many　other　works　consider　stochastic　task　times.　This　research　utilises　the　uncertainty　theory　to　model　uncertain　task　times　and　considers　incompatible　task　sets　constraints.　The　problem　is　solved　using　a　simulated　annealing　algorithm　with　problem-specific　characteristics.　Lower　bounds　are　developed　to　accelerate　the　simulated　annealing　algorithm.　A　restart　mechanism,　which　can　escape　the　local　optimum　obtained　by　neighbourhood　generation,　is　proposed.　A　repair　mechanism　is　integrated　to　combine　the　workstations　so　as　to　further　improve　the　quality　of　solutions.　The　numerical　examples　and　experimental　tests　demonstrate　the　powerful　solution-building　capacity　of　the　proposed　simulated　annealing　algorithm　over　teaching-learning-based　and　genetic　algorithms.　The　methodology　proposed　in　this　research　is　applicable　to　any　industry　(including　the　automotive　industry)　when　the　historical　data　on　task　processing　times　is　very　limited.