## 4 Assembly Line Balancing Problems with Stochastic or Fuzzy Parameters
### Assembly and Production Line Balancing Problems with Fuzzy Parameters
The formal definition of the considered problem was given with the assembly operation durations presented by triangular fuzzy membership functions. The considered problem is known to be NP-hard, and therefore a meta-heuristic based on the genetic algorithm was developed for its heuristic solution. The performance of the proposed algorithm was studied and discussed over several benchmark instances. The computational results demonstrated a satisfactory performance for the developed algorithm in terms of solution CPU time and quality. The research of the paper [92] addresses both the straight ALBP and the U-shaped ALBP. It is written in this paper that many attempts in the OR literature were made to study the deterministic ALBP and the attention was not given to those with inaccurate data. In [92], a bi-objective fuzzy mixed-integer linear programming was developed, with triangular fuzzy numbers being employed in order to represent uncertainty and vagueness, which are associated with the assembly operation durations arising in the real assembly productions. In the proposed algorithm, two objectives (minimizing the number of available workstations and minimizing the cycle time) were considered with respect to the set of usual constraints presented in Section 2.1. An appropriate strategy was proposed, where two-phase interactive fuzzy programming was used as an algorithm for finding a compromise solution. The validity of the proposed algorithm was evaluated though numerical tests. An experimental comparison study was conducted over several test problems in order to assess the performance of the proposed algorithm. The computational result demonstrated that the interactive fuzzy algorithm can not only be applied to the fuzzy ALBP but was also capable to handle different practical models. The proposed model and algorithm may constitute a framework aiming to assist a decision-maker to deal with inaccurate data in the ALBP. Due to the main role of the efficient assembly and production lines in modern manufacturing systems, the research of the paper [93] was devoted to both straight and U-shaped assembly line balancing problems. The considered ALBP includes conflicting objective functions that should be optimized subject to a set of constraints. This paper endeavors to develop a fuzzy linear programming algorithm. Having dealt with the inaccurate nature of the real assembly production, triangular fuzzy numbers were employed in order to represent fuzzy input data with possible vagueness associated with the assembly operation durations. The developed algorithm can be regarded as a background of fuzzy programming for further practical development in the ALBP. To heuristically solve the fuzzy ALBP, a multi-objective genetic algorithm was developed. Having respected several important characteristics of the fuzzy straight ALBP and fuzzy U-shaped ALBP, the algorithm includes an initial generation, encoding and decoding schemes and a genetic algorithm. The developed algorithm was evaluated based on several benchmark instances and compared with the exact algorithm. The presented computational results demonstrated the efficiency of the developed algorithm over other ones suggested in the OR literature. Sequencing and balancing manual mixed-model assembly lines is challenging in assembly production due to the high complexity and uncertainty of human operators' activities. The control of a predetermined cycle time and the sequencing of assembly production can mitigate large losses due to non-optimal line balancing in the case of open-workstation production, where the human operators can work ahead of a normal schedule and try to reduce a backlog. The objective considered in [94] was to provide a cycle time control algorithm, which can provide the efficiency of the assembly line production in the situations based on an appropriate mixed-sequencing strategy. To handle the uncertainty of human operators' activity durations, a fuzzy mixed-model-based solution has been developed.