Optimization-Based Disassembly Sequence Planning Under Uncertainty for Human–Robot Collaboration

Proper recovery of electronic waste (e-waste) has considerable environmental and economic advantages [1]. A recommended practice for e-waste reduction is to extend the product life cycle through reuse, remanufacture, or recovery of components [2]. Disassembly is an inevitable step for the proper recovery of components from end-of-life (EOL) devices. One question often facing remanufacturers is to identify the best sequence to dismantle a device. Determining the optimal disassembly sequence plan is a challenging decision due to the complexity of product design [3], the need for considering multiple objectives [4], and aligning disassembly objectives with other production planning strategies [5].

A considerable number of studies have been focused on optimizing disassembly sequences to lower the remanufacturing cost [6–8]. Different normative techniques have been developed to find the optimal disassembly sequence. To name a few studies, Tseng et al. [9] developed a flatworm algorithm to lower disassembly times by reducing disassembly direction and required tools. Fu et al. [10] proposed a stochastic bi-objective disassembly planning to maximize profit while minimizing energy consumption. Xia et al. [11] developed a 3D-based multi-objective collaborative disassembly sequence planning method by prioritizing disassembly levels for parts. Lee et al. [12] applied a fuzzy scoring procedure to measure disassembly factors before using a genetic algorithm to select the best sequence. Behdad and Thurston [6] used multi-attribute utility theory to determine the optimal disassembly sequence considering multiple attributes of cost and probability of components damage during disassembly and reassembly. Tao et al. [5] used the disassembly precedence matrix and a Tabu search algorithm to compare different disassembly strategies considering disassembly time, energy consumption, and cost. Ilgin and Taşoğlu [4] combined simulation modeling and genetic algorithm to simultaneously decide the best disassembly sequence and the optimal number of EOL products to recover. Mircheski et al. [13] developed a 3D CAD-integrated software tool to analyze design alternatives in terms of design for disassembly. While the previous studies have investigated disassembly sequence planning, the number of studies considering robotic-assisted disassembly and human–robot collaboration is limited.

Human–robot collaboration in disassembly is becoming a popular topic in recent years. The labor-intensive and repetitive nature of disassembly tasks may lead to human musculoskeletal disorders [14]. Robots can handle monotonous repetitive or hazardous tasks more efficiently than humans [14,15]. Although robots provide higher efficiency, human workers are still needed in disassembly operations for handling tasks that are difficult and inflexible for robots [16].

Previous studies have considered human–robot collaboration when deciding on disassembly sequence planning. For example, Lee et al. [17] considered disassembly rules, disassembly cost, and the position between human worker and robot and used a receding horizon control technique for real-time disassembly planning. Xu et al. [16] applied a discrete bees algorithm to determine disassembly sequence planning by considering time, cost, and difficulty of disassembly. Parsa and Saadat [18] used a genetic algorithm to optimize sequence planning, considering cleanability, repairability, and economy. Xu et al. [19] adopted a multi-objective artificial bee colony algorithm and AND/OR graph to find the optimal disassembly sequence considering disassembly failure risks, disassembly priority, cycle time, and cost. Li et al. [14] considered human fatigue to evaluate disassembly efficiency and used the bees algorithm to arrange tasks among humans and robots. Xu et al. [20] considered the safety strategy and disassembly time and used the improved discrete bees algorithm to allocate disassembly tasks. Their safety strategy is to consider the location between human workers and robots. As a human worker approaches the robot, the operation speed of the robot will slow down to avoid robot accidents.

Although previous studies have considered different factors when allocating tasks in human–robot collaboration, no study has considered disassembly cost, disassembleability, and safety to the best of our knowledge. Combining additional attributes and considering the uncertainty are the primary contributions of this study. We propose an optimization-based disassembly sequence planning by considering three attributes, including cost, disassembleability, and safety. The study uses a multi-attribute utility function to combine these attributes. We consider the disassembly time as an uncertain variable with a Beta probability distribution [21]. Besides disassembly cost (time), we also consider disassembleability, which defines the robotic capability on disassembly [18,22], and operator safety, which is modeled by using the strain index (SI) [23]. Table 1 compares this study with previous studies.

The objective of the study is to find the optimal disassembly sequence and allocate disassembly tasks between humans and robots.

The feasible disassembly sequences for a given product can be presented in the form of a graph, as shown in Fig. 1, for a simple product with three components. Each path has different costs, safety, and difficulty.

This section describes the three attributes incorporated in the objective function and the proposed optimization model based on the concept of a multi-attribute utility function.

The scaling constant K is found in Eq. (2). Since some attributes such as disassembly time are uncertain, instead of utility function U(y) the expected utility is used as shown in Eq. (3). For details, see Refs. [24–26].

Each attribute is normalized to unify the unit and range. Also, each attribute is utility independent of other attributes. According to Clemen and Reilly [27], an attribute is a utility independent of another attribute, if preferences for uncertain choices possessing different attribute levels are independent of the values of another attribute. For example, disassembly cost and disassembleability are preferentially independent and utility independent since, regardless of the value of disassembly cost, the user always prefers lower complexity (higher disassembleability) over higher complexity. Even in the case of uncertain choices involving different values of disassembleability, the user’s preference among the uncertain cases is independent of disassembly cost. We should note that the concept of preferential independence and utility independence is separate from how attributes are calculated.

The t_U and t_L are the range of disassembly time, p, q are shape parameters, and Γ is the gamma function.

Besides disassembly cost, operator safety is another important attribute. The SI, proposed by Moore and Garg [23], is a well-known tool to evaluate the risk of developing musculoskeletal disorders in distal upper extremities, including the hand, wrist, forearm, and elbow. Given that the e-waste disassembly task requires a lot of upper limb movements, such as disconnecting cables and loosening screws, the SI score is a suitable method to quantify human physical stress in our study. The disassembly tasks are assigned to human and robot based on SI scores to release human physical stress.

Disassembleability describes the level of complexity of each task. Tasks with high complexity are not feasible to be performed by a robot. The parameters describing disassembleability are introduced in Refs. [18,22] which include: (1) component size (CS), (2) component weight (CW), (3) requirement of tools (T), (4) accessibility (AC), (5) component shape (CSH), (6) operation complexity (OC), (7) positioning (P), and (8) operation force (OF). The scores of each parameter are described in Table 4.

If DS is higher than 14.2 or the robot's capability, the tasks are assigned to the human worker since they exceed the robot's capability [18,22]. The threshold 14.2 is calculated by dividing the summation of the maximum disassembleability of each parameter by 2 e.g., (4 + 2.4 + 3 + 2 + 1.4 + 6.5 + 5 + 4)/2. The threshold 14.2 is calculated based on the equations provided in Refs. [18,22] and disassembleability parameters are listed in Table 4 for HRC. It should be noted that besides the DS value, other feasibility considerations should be taken into account. For example, if the object is too small or heavy even though the DS is lower than 14.2, the robot still cannot hold and locate the position, therefore the tasks should be assigned to human workers.

The multi-attribute utility function U_j shows the overall utility of disassembly operation j, which incorporates the three individual utility functions of cost, disassembleability, and safety. U_j will be used to formulate the objective function of the optimization model. The objective is to maximize the overall utility of the whole sequence. A binary decision variable x_j is defined to determine whether disassembly operation j should be conducted or not. The safety SI scores are used to assign each task to the human worker or robot. Due to the high complexity and uncertainty, tasks with high DS values are given to the human worker. The index set, decision variable, and model parameters are expressed as follows:

Equation (14) shows the expected disassembly cost based on Eq. (9). Equations (15) and (16) reflect the normalization of SI and DS scores for each task between 0 and 1. Equations (17)–(19) are a set of inequalities that represent an if–then statement when solving the task assignment between human and robot. When the task has high safety and disassembleability, it can be assigned to either robot or human; if the expected disassembly cost of the robot is less than the cost of human worker, α_j will be 0. In addition, the SI scores and DS determine α_j based on safety and disassembleability.

The data collected from the disassembly of a Dell desktop computer are used as a case study.

Three main components are targeted for disassembly (2a), i.e., component A—heatsink assembly, component B—optical disc drive & hard drive assembly, and component C—memory module. The heatsink assembly, as illustrated in Fig. 2(b), is made up of a fan shroud (A1) and a heat sink (A2), whereas component B consists of an optical disc drive (B1) and a hard drive (B2).

The number of possible disassembly sequences of the three components is six as a permutation problem.

All six sequences are tested to be feasible in our pilot studies. However, the removal of subassemblies had to be in a specific order due to physical constraints. Specifically, to remove the heatsink assembly (A) from the computer, the fan shroud (A1) had to be removed before the heat sink (A2) so that cable A2 could be disconnected from the system board. Similarly, to remove component B from the computer, one had to remove the optical disc drive (B1) first to get access to the hard drive (B2). Figure 3 shows the possible disassembly sequences.

To evaluate the SI and DS scores, a participant was tasked with removing the heatsink assembly, the optical disc drive, the hard drive, and the memory module from the desktop computer. Adequate training was given to the participant before the formal data collection. The manufacturer’s service manual guided the disassembly procedure. The participant was videotaped during the data collection, performing the disassembly task. After the task was accomplished, the participant was interviewed about their subjective rating of force-related variables, i.e., IE of SI and OF of DS, for every work element. The disassembly of each component is composed of different tasks as shown in Table 5.

Two researchers independently analyzed the video taken during the data collection to obtain the remaining variables. Instead of computing the SI score for the entire job, SI scores for every work task were calculated in the study to validate our optimization model. Furthermore, a default rating value of 4 was assigned to DD, representing a worker performing a given task for 4–8 h [30].

Table 6 shows the disassembly time for human and robot. In this example, the lower bound of disassembly time, t_L for human is determined from experiments. The upper bound of disassembly time for human, t_U, and disassembly times of robot are assumed.

The disassembly time by the robot is assumed to be greater than human due to the current software and hardware limitations in handling disassembly tasks. The robotic technology for disassembly tasks is not well developed, and most disassembly operations are still conducted manually, so we assume a higher operation time for robots to handle tasks. This may change in the future with more advancements in robotics.

Table 7 summarizes the SI and DS scores for each task. While SI and DS are the same for components A and B removal, the disassembly of component C was highly dependent on the disassembly order of components A and B removal.

As shown in Fig. 2(a), if component C is removed before B and A, the limited space could negatively impact variables such as HWP of SI scores and AC and P of DS. Moreover, poor hand/wrist posture and accessibility made the force exertion difficult, increasing the subjective ratings of IE of SI and DS. Consequently, the SI scores and DS are higher when component C was removed before A and B, performing tasks J16 and J17, and they dropped if A or B was removed before C, performing tasks J12 and J13.

The input parameter d in disassembly cost is assumed to be 5 and 2 for human and robot, respectively, and parameter c is 0.01 in Eq. (6). Due to the limited scope of this study, each disassembly operation is run only once; however, one experiment is not adequate to obtain the exact shape of the distribution function. In practice, comprehensive data collection is needed to empirically gather disassembly time, fit the proper distribution, and estimate the parameters of distribution functions. The relation between disassembly cost and time is plotted in Fig. 4.

The robot costs less than human due to its capability in handling long-term monotonous, repetitive tasks [14,15]. The scaling constants K, k₁, k₂, and k₃ are considered as 1.68, 0.17, 0.3, 0.23. The tasks with SI scores higher than 18 are assigned to the robot to reduce musculoskeletal disorders damage to the human worker (Table 7). In this study, normalization is used since each attribute has different ranges and units. Note that k_i are constants in the range of (0, 1). The scaling constants are of the nature of utility where k_i refers to the utility (preference) of an alternative in which the ith attribute is at its best level and the rest of the attributes are at their worst levels. For example, 0.3 shows the utility of a disassembly sequence alternative for the decision maker in which the safety is the highest but the cost and disassembly are at their worst levels (highest cost and highest complexity).

This section shows the optimal sequence and work assignment results. Also, several sensitivity analyses on parameters of the cost function (d and c) have been conducted.

The utility of each attribute and the task assignment among human and robot is shown in Table 8. Some utilities are 0 due to normalization. These tasks reflect either a high SI or high DS score. For example, U_3,j of task J3 equals 0, meaning this task has high values of DS that the robot cannot implement.

J3 is focused on loosening the captive four screws. This task needs high positioning with the small object screws with high complexity and uncertainty. Thus, the task is assigned to the human worker. Some tasks are decided by expected cost when the tasks have low SI scores and high disassembleability. For example, J4 is to lift the heat sink assembly and remove it from the computer with low SI scores and low DS. The task is assigned to robot due to cost-efficiency. Although the robot's disassembly time is higher than that of human worker, the expected disassembly cost of robot is less than the expected cost of human, as discussed in Fig. 4. However, tasks with high SI and DS scores, for example, J9, are assigned to human. Although J9 has a safety issue, it is still assigned to human due to the high operational complexity and infeasibility.

The optimal sequence is shown in Fig. 5. Paths 1–2–8–14 and 1–3–9–14 have the same overall utilities, 8.49, so either path is optimum. Path 1–2–8–14 removes component A before B, and Path 1–3–9–14 removes B before A. Paths 1–4–10–14 and 1–5–11–14 have the same utility, 8.34. Both paths remove component C after A or B. Paths 1–6–12–14 and 1–7–13–14 have the lowest utility of 7.70 since component C is removed first in both paths with limited space.

This section describes a sensitivity analysis of the cost function parameters for the robot. Three different combinations of parameters d and c for different conditions are considered. The human cost function is the same as in the previous section, with parameters d = 5 and c = 0.01. Figures 6–8 show the three different conditions for the robot cost function.

In the first condition, the cost of the robot is either higher or lower than human; in the second condition, the robot's cost is lower at the beginning but will be higher than human as the disassembly time increases. The third condition is the opposite of the second condition.

Table 9 summarizes the results of these three conditions for the work assignments between human and robot. In condition 1, when the parameters change slightly and the robot cost function is close to the human, the results are the same as in the previous section. However, the work assignments will change when the cost function deviates from humans. In condition 2, the work assignments are changed from the human worker to the robot as parameter c increases. In condition 3, the work assignments are switched from robot to human as parameter c decreases.

In practice, the cost function may vary depending on the type of products, robots, and factory configurations. When estimating the cost of operating a robot, various factors such as procurement cost, utilization rate, the efficiency of scheduling, tooling, and setup time should be considered.

The proposed optimization model and the demonstrating case study have several limitations. The operator safety is calculated based on the Strain Index which is focused on the upper extremities. However, disassembly could involve lifting heavy objects which would have an impact on the lower body. Future work should be focused on a diverse set of disassembly tasks that require human movement and lifting of a wide range of objects. More complex case studies on washing machines, printers, and home appliances would enhance the proposed work. Also, another assumption was that a robot can repeatably perform disassembly tasks, however, various factors ranging from environmental conditions to robot degradation and product-to-product variability influence the robot's performance. Future work is needed to incorporate the impact of variable conditions on robot and human performance.

The study proposes an optimization-based disassembly sequence planning framework for human–robot collaboration. It uses the multi-attribute theory to combine three attributes of cost, the complexity of disassembly, and safety to determine the optimal sequence. The disassembly cost is modeled as an uncertain variable with a beta distribution. The safety and disassembleability are modeled using SI and DS scores. The model determines the task assignments among human and robot and determines the optimal disassembly sequence. An example of a desktop computer is used to show the application of the proposed model. In addition, a sensitivity analysis of the robot cost function is discussed.

This study can be extended in several ways. First, the SI scores and DS are currently decided subjectively using standard metrics and conducting lab experiments. However, computer vision techniques can be utilized to quantify the SI scores and DS by observing human and robot disassembly operations. Second, the model can be extended to a real-time sequence planner. Third, other attributes such as the distance between the removal component and the robotic arm position can be further considered in the real-time sequence planner. Fourth, experimental studies can be conducted to provide real disassembly time by robot and the feasibility analysis of each disassembly task.

This material is based upon work supported by the National Science Foundation–USA under Grant No #2026276. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

t =

disassembly time

t_U, t_L =

upper and lower bounds of disassembly time

C_max =

maximum disassembly cost

C_min =

minimum disassembly cost

U_j =

the overall utility of task j

d, c =

constant parameters in the disassembly cost function

p, q =

shape parameters of the beta distribution

DS =

disassembleability scores

SI =

strain index scores

SI_max =

maximum strain index

SI_min =

minimum strain index

DS_max =

maximum disassembleability score

DS_min =

minimum disassembleability score

f(y) =

the probability density function of attribute y

U(y) =

the utility function of attribute y

C_j(t) =

disassembly cost of task j

Γ =

Gamma function