## 4 Dynamic Human-Robot Collaborative Disassembly Line Balancing  
This section addresses a serial-paced HRDL and one of its dynamic line-balancing problems. The HRDL is formed by multiple human-robot collaborative workstations connected in a series by a conveyor system. Multiple types of used products in the same batch can enter the HRDL for complete disassembly at the same time. The disassembly operations are assigned to each workstation in sequence to disassemble these products completely, according to their precedence relationships. The state of each component in the same product is allowed to change in different batches. We assume that they can be identified by sensor feedback before the disassembly of the product begins. It is specified that multiple robots and humans can work at the same workstation. They share the same workspace and resources. Considering the workspace and resource constraints, there is an upper limit to the number of robots and humans that can be accommodated at each workstation. For each disassembly operation assigned to a workstation, at least one feasible task sequence in its corresponding task graph can be used to complete it at any time. Generally, humans have high flexibility, while robots are superior in strength and accuracy and more suitable for performing unsafe tasks. In the HRDL, a task can only be assigned to a robot or a human that meets its requirement. The D-HRDLB problem is raised to balance the HRDL to work efficiently in different environments. This problem is assumed to be stationary for each environment. It contains four subproblems for each environment: (a) how to find the optimal disassembly sequence for each product; (b) how to find the optimal task sequence for each selected disassembly operation; (c) how to assign the selected tasks to the appropriate robots or humans; and (d) how to allocate the robots and the humans that have been assigned tasks to an ordered sequence of workstations. These four subproblems need to be optimised simultaneously under a series of constraints, such as precedence and sequence constraints. In this study, three optimisation objectives are considered: minimising the cycle time, minimising the total number of robots and humans in use, and minimising the number of humans in use. In addition, the number of workstations is fixed and predetermined. Figure 3 shows an example of a D-HRDLB problem in the \(\ell\)th environment. In Figure 3, an HRDL consists of three human-robot collaborative workstations. A used flashlight is completely disassembled on this line. At the starting time instant of the \(\ell\)th environment, the multimodel sensing system detects that component three (bulb) of the flashlight is lost; thus, the HRDL changes from the \((\ell-1)\)th environment to the \(\ell\)th environment. Since the selected task sequence for the disassembly operation--seven (\(B_{7}\)) in the \((\ell-1)\)th environment--is no longer feasible, for the \(\ell\)th environment, the planning system needs to redetermine the feasible task sequences for \(B_{7}\) and recalculate the Pareto-optimal solutions. One of the Pareto-optimal solutions in the \(\ell\)th environment is shown in the lower part of Figure 3. The D-HRDLB problem in changing environments can be formally defined by a dynamic multiobjective optimisation model. In the formulation, the feasibility of a task and the set of operators used to perform a task are taken as dynamic factors leading to changing environments. The indices, sets and parameters, and decision variables for modelling the D-HRDLB problem are given in Table 1, Table 2, and Table 3, respectively. To simplify the model expression, the TD-TAOGs corresponding to multiple types of products are merged into a general TD-TAOG by default.