## 4 Assembly Line Balancing Problems with Stochastic or Fuzzy Parameters
### Assembly and Production Line Balancing Problems with Fuzzy Parameters
As the production process was modular, the fuzzy sets represented the uncertainty of the activity durations related to processing the modules. Both optimistic estimates and pessimistic estimates of the completion of activities were extracted from the fuzzy model and incorporated into a predictive control algorithm to ensure the constrained optimization of the predetermined cycle time. The applicability of the proposed algorithm was demonstrated using a wire-harness manufacturing process with a paced assembly conveyor. The developed algorithm can handle continuous assembly conveyors as well. The computational results confirmed that the developed algorithm is applicable in the cases where a production line of the supply chain is not well-balanced, and the activity durations are uncertain. The paper [95] is devoted to both multi-objective straight assembly line balancing problems and U-shaped ALBP with fuzzy operation duration. Four objectives were considered (minimizing numbers of workstations, maximizing fuzzy assembly line efficiency, minimizing the fuzzy idleness percentage and minimizing the fuzzy smoothness index). Two problems were formulated, including uncertainties, variability and imprecision that usually occur in a real-world production. The durations of assembly operations were determined by triangular fuzzy numbers. To heuristically solve this fuzzy problem, a hybrid multi-objective genetic algorithm has been developed. A one-fifth success rule was deployed for selection and mutation operators to improve this genetic algorithm. The results in the genetic algorithm application were controlled in convergence and diversity by means of controlling the selective pressure rate. A fuzzy controller to the selective pressure was employed for the genetic algorithm toward its better implementation. The Taguchi design of the computational experiments was used for the parameter control and calibration. The numerical examples were presented to compare the performance of the proposed algorithm with the existing ones. The computational results showed a better performance of the proposed algorithm. Similar ALBP, modified algorithms and closed results are presented in the paper [96]. Balancing the workloads of available workstations is a key point in the efficiency of the assembly line. An initial line balance can be broken by the changing processing abilities of machines because of their degradation, and therefore re-balancing of the assembly line is inevitable. The impacts of unexpected events on assembly line re-balancing are usually ignored in the OR literature. Using the advanced sensor technologies and Internet of Things, the machine degradation can be continuously monitored, so condition-based maintenance can be implemented to improve the health state of the machine. Using the technology of robotic process automation, workflows of the assembly process can be smoothed, workstations can work autonomously and a higher level of process automation can be achieved. Real-time information of the processing abilities of machines will bring about opportunities for automated workload balance via an adaptive decision. In [97], a fuzzy control system was developed to make real-time decisions to balance the workloads based on the processing abilities of the workstations, given the policy of condition-based maintenance. Fuzzy controllers were used to decide whether to re-balance the assembly line and how to adjust the production rate of each workstation. The conducted numerical experiments showed that the buffer level of the assembly line with the fuzzy control system was lower than that of the assembly line without a control system (the buffer level of the assembly line with another control system was the lowest). The product demands can be satisfied by assembly lines, except the one with another control system since there were too many production losses sacrificed for the low buffer level. The stability analysis of the control performance to the numerical parameter settings was conducted.