Mathematical Model For U-shaped Assembly Line Balancing Problem Under Uncertainties

Compared with the traditional straight-line assembly line, U-shaped assembly lineis widely employed in a JIT manufacturing system. The research on the U-shapedassembly line balancing helps to improve production efficiency and reduce productioncosts. This paper focus on the U-shaped assembly line balancing problem and themathematical models with deterministic and stochastic operation time are studied inorder to improve the efficiency and effectiveness of the U-shaped assembly lines. Themain work is listed as follows:First of all, since the resulted solutions from the existing mathematical model maybe infeasible due to either-or constraints, a new station-oriented mathematical model isdeveloped based on the logistics and transport properties of the U-shaped assemblylines, in order to ensure logistics intergrades on the inlet and outlet of the U-shapedassembly line. The proposed model can make sure that the precedence constraints aresatisfied and all the found solutions are feasible.Secondly, a mixed integer linear programming model for mixed U-shaped assemblyline with deterministic operation times is built with the objective of minimizing thenumber of opened stations. Furthermore, the strengthen constraints and learning effectsare also involved into this model. Experimental results on the well-known benchmarkproblems demonstrate the effectiveness of the proposed model.At last, a multi-objective chance-constrained and piecewise-linear programmingmodel for U-shaped assembly lines with stochastic operation is developed in order toensure ordering of U-shaped production and improve the efficiency and stability of theU-shaped assembly line. The multiple constraints, including strengthen constraints, toolconstraints, and materials distribution constraints are all taken into account. Since thismodel is nonlinear and needs a large amount of time to be solved, it is transformed intoa mixed integer linear programming model via linearization transformation,non-dimensionalization changing. An experimental case from a car engine heat dissipating is utilized to verify the effectiveness of the proposed model.In addition, the parameters of this model are also analyzed and the threshold valuesof the parameters are provided in order to further explore the practicability.