## 4 Assembly Line Balancing Problems with Stochastic or Fuzzy Parameters
### Assembly and Production Line Balancing Problems with Fuzzy Parameters
To reduce disassembly costs for enterprises and improve the disassembly efficiency of waste products, the paper [103] investigated a partial sequence-dependent DLBP and established a multi-objective model to minimize the number of used workstations, the total disassembly operation duration, the idle balance index and the number of used disassembly tools. A Pareto-discrete hummingbird algorithm was proposed to address a partial sequence-dependent disassembly line balancing problem. This algorithm includes two stages, as follows: a self-searching stage and an information-interacting stage. With these stages, the exploration and exploitation abilities of the Pareto-discrete hummingbird algorithm may be balanced. The effectiveness and superiority of the Pareto-discrete hummingbird algorithm were verified by comparing it with other algorithms for two instances of the DLBP. The mathematical model and Pareto-discrete hummingbird algorithm were applied to the optimization of a partial sequence-dependent disassembly line of waste laptops. The optimization results showed that the partial disassembly can make the disassembly line smoother and the utilization efficiency of workstations higher than full disassembly. The Pareto-discrete hummingbird algorithm was superior in solving the partial sequence-dependent DLBP. Studies in production engineering focused on disassembly and assembly planning for improving the profitability of remanufacturing. The presentation of assembly and disassembly sequences by analyzing geometrical and technical precedence constraints is an essential necessity of assembly and disassembly planning. A specific and/or graph is used to represent a product's feasible assembly and disassembly sequences, including alternative subassemblies and parallel operations. A lot of researchers have studied the automatic extraction of geometrical precedence constraints by collision analysis within 3D models. Since most of the published approaches focused on collision analysis to identify precedence relations, the generation of and/or graphs for complex products from collision analysis re sults remain inefficient for many industrial cases. In [98], a computer-aided design interface from previous studies is used to extract liaison and moving wedge information from 3D models. A top-down approach and a bottom-up approach for generating complete and/or graphs from the extracted data were introduced. These approaches for computing performances were analyzed on the several test cases and the developed computer-aided design models. The bottom-up approach performed better for the tested samples. It has been found that the amount of moving wedge constraints has a strong effect on the computing performance. It is an indicator to estimate the complexity of products under examination. The exponential behavior of the needed computing resources can be estimated beforehand. For complex products, graph simplifications or alternative graph representations with less information richness were considered. The obtained computational results contribute to automated assembly and disassembly sequence planning from complex products and increasing remanufacturing profitability. In [104], a multi-period integrated decision-making model is investigated for the heavy-duty equipment maintenance, involving disassembly, inspection and assembly, with uncertain numbers of replaced parts within a fixed-time horizon. There are large numbers of subway cars exported from other countries and the maintenance is difficult to be conducted in Hong Kong due to the limited space, machinery and technical support teams. Thus, efficient maintenance planning is required to ensure the quality of transportation services. To resolve this problem, a deterministic mixed-integer optimization model was developed to achieve integrated optimization of disassembly and assembly. The model minimizes the total operation cost, consisting of a purchasing cost and a repair cost subject to capacity constraints.