## 4 Assembly Line Balancing Problems with Stochastic or Fuzzy Parameters
### Stochastic Assembly and Production Line Balancing Problems
Instead of simply trying to evaluate and maximize a single robustness measure, authors of [74] showed that the robust scheduling problem can be enriched. The robust schedule is a multi-faceted issue, which can be used in order to study different points of view, such as stability, sensitivity and the level of service. It is important since the main objective is to support a decision-maker to be able to preserve the different points of view in a robust schedule. It was also illustrated how these robust scheduling problems can be effectively utilized by a decision-maker in solving a real-world scheduling problem with inaccurate data. Mixed-model assembly lines are usually operated with inaccurate data, such as stochastic product sequences. Balancing such assembly lines can be challenging as their estimation can be difficult to determine in the case when asynchronous pace and buffers have to be taken into account. Several works have addressed problem versions with a target throughput, while a few authors have studied a version of throughput maximizations of the mixed-model ALBP. The paper [75] addresses the ALBP with a fixed number of workstations and a buffer between each pair of the connected workstations. A so-called make-to-order environment was studied and modeled as a stochastic sequence of products with a known rate of the demands. A cycle time simulator was conducted, and a heuristic algorithm was proposed to exploit the cycle time simulator for assessing the cycle time of an assembly line and to provide good line balances. The heuristic algorithm was applied to a dataset with several buffer layouts. The calculated solutions were compared to those of the OR literature. The comparisons showed that the obtained line balances outperform the benchmark ones. The line balance quality difference was greater for tested instances with more buffers, which highlights the capacity to conveniently exploit buffers in the mixed-model assembly lines. Two-sided assembly lines are used in the factories producing large-sized products. In most OR literature, the assembly operation durations are assumed as deterministic, while these assembly operations may have varying durations in many practical applications, which cause the reduction of performance quality or the infeasibility of the schedule. The ignorance of the specific constraints, including a positional constraint, zoning constraint and synchronism constraint, may result in the invalidation of the constructed schedule. In the paper [76], in order to solve such a stochastic two-sided ALBP with multiple constraints, a hybrid teaching learning-based optimization algorithm is proposed, which allows combining a teaching learning-based optimization for a global search and a neighborhood search with seven neighborhood operators for a local search. A priority-based decoding algorithm was developed in order to ensure that the selected assembly operations satisfy most of the constraints identified by the priority rules and to reduce the idle times related to a sequence dependence among assembly operations. Experimental results on benchmark instances demonstrated the efficiency and universality of the developed decoding algorithm and the comparison among other algorithms showed its effectiveness. The quality of the balance of the mixed-model assembly line is related to the determined production sequence of assembly operations. Two problems are incompatible in time since balancing is realized simultaneously with planning the assembly line, while assembly operation sequencing is an operational problem closely related to possible market demand fluctuations. In the paper [77], an exact procedure to solve the integrated assembly line balancing problem and assembly operation sequencing problem showed that the demands are stochastic. The searched optimal line balance is required to be flexible in order to cope with possible demand scenarios. A paced assembly line was considered, and the utility work was used as recourse for workstation border violations.