In a production flow line with stochastic environment, variability affects the system performance. These stochastic nature of real-world processes have been classified in three types: arrival, service and departure process variability. So far, only service process – or task time – variation has been considered in assembly line (AL) balancing studies. In this study, both service and flow process variations are modelled along with AL balancing problem. The best task assignment to stations is sought to achieve the maximal production. A novel approach which consists of queueing networks and constraint programming (CP) has been developed. Initially, the theoretical base for the usage of queueing models in the evaluation of AL performance has been established. In this context, a diffusion approximation is utilised to evaluate the performance of the line and to model the variability relations between the work stations. Subsequently, CP approach is employed to obtain the optimal task assignments to the stations. To assess the effectiveness of the proposed procedure, the results are compared to simulation. Results show that, the procedure is an effective solution method to measure the performance of stochastic ALs and achieve the optimal balance.

In the literature, line balancing is mostly investigated in deterministic environments. But production systems inevitably contain stochastic situations. In this study, the stochastic type-II assembly line balancing problem (ALBP) is considered. Firstly, a chance-constrained nonlinear mixed integer programming (MIP) formulation is developed from the well-known deterministic form. Then, a new linearized stochastic model is proposed by using some transformation approaches to reduce model complexity, and the model is solved. Finally, constraint programming (CP) models for deterministic ALBPs, nonlinear chance-constrained stochastic ALBPs and linearized chance-constrained stochastic ALBPs are developed, respectively. Problems from the literature are utilized to test the effectiveness of the proposed models and the results are compared with a bidirectional heuristic algorithm. The numerical results show that the CP models are more effective and successful for solving the stochastic ALBP. Some managerial implications are also suggested for industrial environments that consistently face ALBPs.

In this study, the U-type assembly line balancing problem (UALBP) with assignment restrictions (AR-UALBP) is considered. Linked and incompatible distance and station restrictions are taken into account. New mathematical programming (MP) and constraint programming (CP) models are proposed. The objective function of the models is minimizing the cycle time for a given number of workstations. In addition to this objective, line efficiency and CPU time are also considered as other performance measurements. Numerical experiments on some problems from the literature are performed to evaluate the effectiveness of the proposed models. The results are compared with the results of the CP model of the straight ALBP with assignment restrictions and also the results from MP and CP models are compared with each other. The numerical results indicate that the proposed CP and MP models are more effective in obtaining better and optimal results when solving the AR-UALBP.