Optimising remanufacturing decision-making using the bees algorithm in product digital twins

An end-to-end DT, comprising both product and remanufacturing process DTs, may enable autonomous decision-making. In the DT the decision-making takes place in the DMM.

With reference to (Fig. 1), the DMM will need to accommodate changing business inputs (demands, limitations, and risks) and utilise the beginning-of-life (BoL) and middle-of-life (MoL) data available from the DTs. The outputs are similar to those described in smart recovery decision-making (SRDM)27 and include recovery alternatives as well as product and process operational plans. Reverse logistics options are also considered in the module making use of the product and processing locations, an output that was out of scope in Meng et al.27. The “optimal” solution depends on the inputs and the applied evaluation criteria.

Decision-making module inputs and outputs

Product DT

A product DT comprises a real product in real space, a virtual product in virtual space, and the connections of data and information that tie the ‘products’ together28. The system design used in this work has been described in detail in11.

Process DT

This couples the production system with its digital equivalent29. It is similar to the product DT, as it enables assessment and simulation of potential scenarios feeding key information into the DMM.

Business demands, limitations, and risks

Relate to the business expectations and experiences that are not captured or managed by the product or process DTs but will influence the decision.

Decision on whether to recover an EoL product

This output indicates to the business the worthiness of product recovery.

Reverse logistics options

If the decision to recover an entity or not lies with the business, it can be data-driven. Similarly, if an entity recovery is a foregone activity (contractual, etc.), options on when and where it should be recovered from can be evaluated using DT information. The cost of the reverse logistics operation from an economic, environmental, and social perspective can be assessed using the entity GPS and remanufacturing facility locations.

Recovery options

Relates to the choices that the remanufacturer can make to optimise bottom-line benefits once the entity has been made available. Selecting the most appropriate level of disassembly (complete, partial, targeted, destructive) and reassembly (complete, partial, hybrid, built-to-order, build-to-stock) is key to managing a sustainable business.

Remanufacturing plan (product)

Relates to the requirements of the existing product to start its second life via the remanufacturing process. The remanufacturing bill of materials (rBoM) can be estimated based on the MoL BoM and quality and performance degradation data from the DT. The remanufacturing bill of process (rBoP), much like the manufacturing BoP, defines the activities that need to happen to translate the product from one state to another, balancing triple-bottom-line performance and technical competence. In this case, the rBoP takes the product from EoL back to BoL. The remanufacturing routings can be generated and may include disassembly and rebuilding sequence plans, process steps, machine operations, materials, slave parts and performance targets. Accurate estimations of remanufacturing bills can benefit line balancing, scheduling and production planning30.

Remanufacturing plan (process)

This output considers line balancing, scheduling, planning, demand management, core acquisition and inventory holding, relying heavily on the process DT, targeting the best scheme for managing tasks and demands while being limited by technical constraints.

Module self-evaluation and improvement

A smart decision-making module can make assessments and carry out improvements to optimise itself, but the system should allow for human intervention and preference selection. In the remanufacturing sector, process planning is heavily dependent on the skills and knowledge of experienced individuals, and this needs to be accommodated31.

Before generating the outputs, the decision of whether to remanufacture needs to be made. This will be done by evaluating the triple bottom line as described in the next section.

Model structure

The model (Fig. 2) is built on a scenario where a remanufacturing business can choose whether to recover a HiVE from its MoL/EoL user. If the costs associated with recovery and remanufacturing out-weight the business opportunities from a triple-bottom-line perspective, the business will not recover it (other CE practices may be applicable, but these are out of scope). To make this evaluation, the business needs to identify the best remanufacturing strategy that balances profits, environmental effects, and social impact for the given HiVE location and quality from the DT, within the constraints of existing technological capabilities and management policies. Time will be used as a leading variable that will influence economic, environmental, and social measures. It has been assumed that if a process takes longer, it will require more investment and a larger workforce while generating a greater environmental load. Only the benefits to the business from the point that the HiVE becomes available for remanufacturing until it is ready for its second life meeting the expectation that it will be equivalent to, or better than, the manufactured equivalent, not considering multiple life cycles, are in scope.

Figure 2

Relationships between DMM and the remanufacturing functions.

The model assumes that product recovery will not be triggered without product demand, as the core function of this sector is to remanufacture. The decision of whether to recover the product is evaluated in the DMM. Those that are recovered are first disassembled. Disassembly can be either complete, partial, or targeted with components progressing to a reincarnation phase (normally referred to as remanufacturing but not used in this instance to avoid confusion) that can include any combination of cleaning, repairing, machining, assembly, testing and finishing or filtered into reuse, recycling, disposal, or storage material flows. Reincarnation has been used to describe the processes normally associated with remanufacturing, as BoL assets can be made from EoL products and components.

The demand for products and/or components drives the reincarnation and reuse functions. The entire incarnation of product i may be processed through remanufacturing. However, any component j of product i that needs to be replaced due to damage, missing parts, or needing an upgrade can be sourced from the store or component reuse. Alternatively, new components can be procured (or manufactured). Components with poor quality identified after disassembly may be recycled or disposed of and are lost to the system in this scenario. The routing for each approach is different.

Modifying the formulations of32 and Meng et al.33 to evaluate the options available utilising real data from the DT prior to product recovery, the economic, environmental and social impacts of remanufacturing the HiVE can be defined. All variables used can be found in the nomenclature. As the economic indicators of remanufacturing are more mature, development will commence.

Evaluating the economic growth impact in the DMM

In a simplified form from an economic perspective, the potential profit, P, is the sales price of the remanufactured product, SP, minus the total cost of performing the remanufacturing function, CRF (Eq. 1).

With reference to Fig. 2, CRF includes the cost incurred by product recovery and disassembly CPR and CPD, respectively, as well as component storage, CCS, reincarnation activities, CCR, reuse, CCU, recycling CCC, and disposal CCD (Eq. 2). CPA and CPF are the cost of product assembly and finishing (including testing, certifying, and final assembly, labelling and painting, etc. assumed to be a single value specific to the product family). Other miscellaneous costs will be assumed to be absorbed by others in this model.

$$CRF = CPR + CPD + CCS + CCR + CCU + CCC + CCD + CPA + CPF$$


CPR (Eq. 3) can be calculated from the shipping costs, cs, of product i per kilometre, and the distance, l between the product location, available from the DT, and the remanufacturing facility, f.

$$CPR = cs_{i} l_{f}$$


CPD (Eq. 4) relates to whether component j needs to be disassembled from the product nd, the cost of disassembly per unit of time cd, the time it takes to disassemble td, a time function TQ1 given product quality, from the DT, of qi, and the time function TS assuming that more time will be taken to disassemble products into components destined for a second life by remanufacturing or reuse sl, over those that will be recycled or disposed of, nsl. With the CAD, BoM and component relationship information available in the DT, the disassembly sequence can be extracted to match the requirements of the remanufacturing demand. Comprehensive lists of attributes for disassembly in remanufacturing can enable the integration of such systems34.

$$CPD = \mathop \sum \limits_{j} (nd_{j} cd_{j} td_{j} (TSsl_{j} + nsl_{j} )TQ_{1} )$$


CCS (Eq. 5) results from the need to hold components nh, which have been identified as having second life potential but cannot be used in the existing product and are also not recycled or disposed of. If component \(j\) needs to be stored nh, ch is the cost of holding per unit of time and th is the time in storage, then

$$CCS = \mathop \sum \limits_{j} (nh_{j} (ch_{j} th_{j} + cph_{j} ))$$


Following disassembly or recovery from storage, the components can take one of four remanufacturing option routes (decision variables), namely, reincarnation, reuse, recycling, or disposal. rox represents the routes where \(x \in \left\{ {1,\;2,\;3,\;4} \right\}\) respectively. As described previously, the reincarnation processes, CCR (Eq. 6), in the remanufacturing function refer to the repair, upgrade, rebuild, etc. of the product or hybrid of components to match or better the quality of a new equivalent. Having already been disassembled, the components may need to be cleaned, machined (additive or subtractive) or repaired nr. An estimation of the work that may be required could be made in the process DT using the information from the product DT comparing the “as manufactured” with the “current state” instances. Herein offers an opportunity to map product requirements to process capabilities to create suitable production plans. A production line enabled with physical and virtual reconfigurability for individualised product manufacturing, as discussed by Leng et al.35, could complement this.

The cost per unit of time in reincarnation is cr. The time tr to complete these reincarnation activities is affected by the quality of the received component. An estimate of product quality is provided by the DT as qi, but the component quality will depend on the MoL environment and utilisation. A DT at the component level or inferred quality from the performance metrics and/or failure mode data would need to be available to estimate component RUL and quality. This was not demonstrated in the previous chapters, but it is assumed to be possible with improvements in data analytics, diagnostics, and prognostics. To continue, \(q_{j} = q_{i}\) in this model and a time function TQ2 that translates the impact of the different quality levels on time taken to reach qmin will be applied, where qmin is the minimum quality needed for the component to be successfully incorporated into a remanufactured product. Once ready for reassembly, components can be built into products alongside new (procurement) or spare parts (reuse) if needed. CCP (Eq. 7) is the total component purchasing costs where the costs to procure a part or service cp to replace one that will be retained for reuse, has failed, is damaged, is consumable, or upgradable (with the original destined for recycling or disposal) or is missing when the product was recovered are also included.

$$CCR = ro_{j1} = \mathop \sum \limits_{j} nr_{j} \left( {TQ_{2} cr_{j} tr_{j} } \right) + CCP$$



$$CCP = \mathop \sum \limits_{j} cp_{j} (ro_{j2} + ro_{j3} + ro_{j4} + m_{j} )$$


where m is a missing part.

With the parts already disassembled, there may be cost associated with preparing a component for reuse CCU (Eq. 8), related to time tu and quality qj to feed into either the reincarnation frj or reuse fuj flow. Additionally, as P in Eq. (1) only considers the remanufactured product, CCU includes the revenue cruj generated directly from the sale of components.

$$CCU = ro_{j2} = \mathop \sum \limits_{j} nu_{j} \left( {TQ_{3} cu_{j} tu_{j} \left( {fr_{j} + fu_{j} } \right) – cru_{j} } \right)$$


The cost of recycling CCC (Eq. 9) comes from the sum of the costs minus the material sales revenue mrc from the component in question nc. Material-level data and component weights from the DT BoM enable this assessment. Product-level recycling is not considered, as it is assumed that the product is only recovered from the end user if it has remanufacturing potential. It is also assumed that this activity is a transaction, and the process of recycling is out of scope.

$$CCC = ro_{j3} = \mathop \sum \limits_{j} nc_{j} (cc_{j} – mrc_{j} )$$


Similarly, the cost of component disassembly CCD (Eq. 10) includes disposal cost cdp for components set for this route only ndp. No revenue opportunities are expected from the disposal option. Component weights from the DT may support this.

$$CCD = ro_{j4} = \mathop \sum \limits_{j} ndp_{j} cdp_{j}$$


As the aim is to build a unit for the market, the cost of product assembly CPA (Eq. 11) with na representing the components required to assemble the new product, the total costs per unit of time incurred from assembling is expressed in ca and the time is ta.

$$CPA = \mathop \sum \limits_{j} na_{j} ca_{j} ta_{j}$$


Constraints are similar to those used in Meng et al.33 and are documented in Eqs. (11–19). Equation (11) states that each component can either include (1) or not (0) from disassembly, storage, reincarnation, reuse, recycling, or disposal. Equation (12) limits each component to only one of the remanufacturing options \(x\), but at least one component needs to be disassembled and processed through ro1 to meet the product demand Eq. (13), but Eq. (14) ensures that the number of components disassembled is less than or equal to the total number of parts z in the assembled product i. Equation (16) relates to predecessors in the disassembly process. Equation (17) limits the flow of components through reuse to either reincarnation or reuse ready for sale, while Eq. (18) balances the number of components not destined for a second life with those that are recycled or disposed of. Equation (19) constrains the time functions to real numbers greater than zero.

$$fr_{j} ,\;fu_{j} , \;m_{j} ,\;nd_{j} , \;nsl, \;nh_{j} , \;nr_{j} , \;nu_{j} , \;nc_{j} ,\;ndp_{j} sl \in \left\{ {0,1} \right\}$$


$$\mathop \sum \limits_{x} ro_{jx} = 1 \quad \forall j$$


$$\mathop \sum \limits_{j} nd_{j} \ge ro_{j1} \ge 1$$


$$\mathop \sum \limits_{j} nd_{j} \le z$$


$$nd_{j} \ge nd_{k} \quad \forall j \in P_{k}$$


$$\mathop \sum \limits_{j} (fr_{j} + fu_{j} ) = 1\quad \forall j$$


$$nsl_{j} = \mathop \sum \limits_{j} \left( {nc_{j} + ndp_{j} } \right)$$


$$\lambda = TS, \;TQ_{1} , \;TQ_{2} , \;TQ_{3 } \{ \lambda \in {\mathbb{R}} |\lambda > 0\}$$


Evaluating the environmental stewardship impact in the DMM

The potential environmental benefits, E result from the environmental savings made through remanufacturing a product and making it available to the customer, as opposed to one made from virgin material and processes ES, minus the impact to the environment from the remanufacturing function, ERF (Eq. 20).

Referencing Fig. 2, ERF includes the environmental impacts of product recovery, EPR, disassembly, EPD, component storage, ECS, reincarnation activities, ECR, reuse, ECU, recycling, ECC, disposal, ECD, assembly, EPA and product finish, EPF (Eq. 21). EPF is the environmental impact of product finishing assumed to be a single value specific to the product family. Other miscellaneous environmental impacts, such as those from facility systems, will be assumed to be absorbed by others in this model.

$$ERF = EPR + EPD + ECS + ECR + ECU + ECC + ECD + EPA + EPF$$


Environmental impacts can be categorised as energy (J) and material consumption (kg), emissions to air and water (kg), and waste generation (kg)36. These can be referred to as environmental impact \(e\alpha_{{\text{y}}}\), where \(\alpha\) is the action (shipping, disassembly, storage, etc.) and \(y \in \left\{ {1,\;2,\;3,\;4,\;5} \right\}\) reflects the impact categories. EPR (Eq. 22) can then be calculated from the environmental impacts of shipping es, which will likely include the energy consumption from fuel and emissions to air (Eq. 19) for the journey between the product and facility locations available from the DT.

$$EPR_{y} = es_{yi} l_{f}$$


EPD (Eq. 23) relates to the environmental impact of disassembly of component j per unit of time ed and the time it takes to disassemble td. Energy consumption is likely to be a key impact in both automated and semi-automated disassembly processes in remanufacturing I4.0 of the future, as electronic and/or pneumatic tooling will be prevalent and demanding of substations or compressor units. The scale of the impact will be proportional to utilisation time. Joining methods and attributes such as tightening torques can be extracted from the DT to estimate separation, tooling and fixturing energy requirements.

$$EPD_{1} = \mathop \sum \limits_{j} (nd_{j} ed_{y1j} td_{j} (TSsl_{j} + nsl_{j} )TQ_{1} q_{i} )$$


ECS (Eq. 24) results from the potential need to preserve components for storage. This can often utilise materials and generate solid waste from bagging, or if a protective coating is applied directly, emissions to water via application or energy consumption and pollutants from the wash-off process. Depending on the time in storage, multiple applications or layering of methods may be required. Material properties of components can be extracted from the ‘as designed’ DT to direct preservation methods. Therefore, if component j needs to be stored, eh is the environmental impact of holding per unit of time and th is the time in storage.

$$ECS_{y} = \mathop \sum \limits_{j} (nh_{j} eh_{yj} th_{j} )$$


The four remanufacturing option routes remain the same as in section “Evaluating the economic growth impact in the DMM”. As already presented, within the reincarnation activity, components may need to be cleaned, machined (additive or subtractive) or repaired before assembly, testing and finishing can occur. Many of these processes will come with environmental impact and the potential for all five categories being represented. Examples include powering spindles, water for coolant systems in machine tools, the heating and use of wash solutions in cleaning, the addition of new materials or replacement parts, product testing emitting emissions, wastewater and heat energy, or volatile organic compounds from paint applications. Estimations for these activities can be made by comparing the current and future state DTs.

The environmental impact per unit of time in reincarnation is er ECP (Eq. 26) is the environmental impact associated with the procurement of a part or service to replace one that will be retained for reuse, has failed, is upgradable, or is missing ep.

$$ECR_{y} = ro_{j1} = \sum\limits_{j} {nr_{j} (TQ_{2} q_{j} er_{yj} tr_{j_{yj}}) + ECP}$$



$$ECP_{y} = \sum\limits_{j} {ep_{yj} (ro_{j2} + ro_{j3} + ro_{j4} + m_{j} )}$$


Similar to the equivalent costing equations in section “Evaluating the economic growth impact in the DMM”, there could be some environmental impact generated as a result of preparing a component for reuse eu, and these ought to be evaluated, as reusing a product does not guarantee an environmental benefit37. However, these impacts are likely to be less than those associated with reincarnation, recycling and disposal, as this option is generally associated with a lower level of product change, energy expenditure and value leakage38. As E in Eq. (20) only considers the remanufactured product, ECU (Eq. 27) captures the environmental benefits associated with reusing the component over a new component eru.

$$ECU_{y} = ro_{j2} = \mathop \sum \limits_{j} nu_{j} (TQ_{3} eu_{yj} tu_{j} (fr_{j} + fu_{j} ) – eru_{yj} )$$


The environmental impacts of component recycling ECC (Eq. 28) come from the energy and materials used and wastes generated when returning a component to useable material. The total benefits associated with reusing the material over virgin material erc are also considered.

$$ECC_{y} = ro_{j3} = \mathop \sum \limits_{j} nc_{j} (ec_{yj} – erc_{j} )$$


Similarly, the environmental impact of disposal edp includes emissions to water and solid waste for those components set for this route only ndp. As disposal is recognised as the last option in the CE loop39, no environmental benefits are expected. The weight of solid waste can be predicted using the material and CAD data, while the water waste estimate may need to come from a measured or inferred value, both made available in the current state DT.

$$ECD = ro_{j4} = \mathop \sum \limits_{j} ndp_{j} edp_{yj}$$


The environmental impacts incurred from assembly and testing, etc. are expressed in ea. The ‘as manufactured’ DT can support here.

$$EPA = \mathop \sum \limits_{j} na_{j} ea_{yj} ta_{j}$$


Constraint equations Eqs. (12–19) are applicable.

Evaluating the social wellbeing impact in the DMM

As previously discussed, the social pillar of sustainability is the least researched to date. Therefore, the equations that drive this element of the evaluation will be based on the three distinct social groups, the employee, customer, and community40. The first will be based on job opportunities similar to that proposed by Meng et al.33, but instead of being dependent on the weight of recoverable material, it will use time. This works on the assumption that tasks requiring longer to perform than others within the scope already defined are proportional to the number of people who could be employed to complete the task. In this regard, the more people who can be employed, the better it is for society.

The second element is driven by the relationship between the customer/user and remanufacturer and made possible by the DT. With a suitable HMI, the customer can make the DT data available to EoL service providers when they no longer require the product so that remanufacturers can evaluate processing options. The remanufacturer uses these data to decide whether to recover the HiVE. This places data-driven decision-making at the forefront of remanufacturing planning, but if the remanufacturer decides not to recover the HiVE, it may become an unwanted burden to the user. This would be seen as having a negative social impact.

The final element relates to community impact and is based on the relationship between reused or remanufactured components and recycled material to those being discarded. The greater the quantity, volume or weight of material going through remanufacturing or recycling compared to disposal, the better it is for society.

Starting with the employees, of the remanufacturing activities segregated in Fig. 2, there are four that include time variables. These are disassembly, storage, reincarnation, and reuse. Assuming all man-hours H are valued the same, then J is the function that relates process time to man-hours.

$$H = \mathop \sum \limits_{j} J_{j} (td_{j} + ts_{j} + tr_{j} + tu_{j} )$$


With regard to the burden B of managing a product offered to the remanufacturing business, the impact is positive if the remanufacturing business recovers it or negative if it does not.

$$B = \in \left\{ { – 1,\;1} \right\}$$


Finally, the volume-based ratio of reused, remanufactured, and recycled material Vr to those going to disposal Vd is R.

$$R = \frac{{V_{r} }}{{V_{d} }}$$


A single value related to the social impact S is required. To ensure that each element is represented accordingly, a weighted deviation method based on Dehghanian and Mansour41 can be used as described in Eq. (34).

$$WD_{s} = \mathop \sum \limits_{n = 1}^{3} w_{n} \left( {\frac{{\left| {f_{n}^{\left( s \right)} – f_{n}^{*} } \right|}}{{f_{n}^{*} }}} \right)$$


The weighted deviation (WD) utilises the distance between the solution and the ideal to find the best match for the decision-maker’s requirements. If n represents the three elements H, B and R, wn are the weightings applied to n by the business. \(f_{n}^{\left( s \right)}\) and \(f_{n}^{\left( * \right)}\) are the nth objective function values of the solution, s, and the ideal, *. The lower the WD, the closer it is to the decision-maker’s request.

This model has focused on the CE’s triple bottom line but does not include the extended ‘technological advancement’ or ‘performance management’ elements, as clarity on how these elements may be quantified is lacking in the literature. Research development, the advancement of high-tech products and conformance to guidelines, regulations and policies are all relevant and have the potential to influence the desire to remanufacture with incentives or secondary market drivers. Additionally, not considered in the model are resource allocation and availability, both of which are assumed to be finite.

Model evaluation method

The DMM aims to optimise the disassembly sequence and provide the most cost-effective remanufacturing function for each component based on the data documented in the “Raw data” tab within Kerin et al.42. The raw data include a high-level list of parts and disassembly process predecessors, a component interference matrix built as per Percoco and Diella43 and a set of values for populating the calculation. These values assume the remanufacturing facility is based in the UK where this research was conducted.

A MATLAB version of the BA disassembly planning tool by Hartono23, displayed as a flow chart in Fig. 3, is utilised in the DMM to calculate the best disassembly sequence solution, the routing, and the cost associated with each targeting the minimisation of CRF.

Figure 3
figure 3

Flow chart of the Bees Algorithm used in the DT23.

The BA consists of five parameters that need to be set in the initialisation. In this work, the number of scout bees (n) = 10, the number of selected sites (m) = 5, the number of elite sites (e) = 1, the number of selected site bees (nsp) = 5, and the number of elite site bees (nep) = 10. The stopping criterion is the maximum number of iterations. The feasible disassembly sequence is generated by scout bees from the predecessor list and the component interference matrix (“Raw data” tab in Kerin et al.42). The n scout bees are sorted by their fitness values and those that are fittest are considered to have located the elite site (e) and selected sites (m). The nep bees search the elite site and its neighbourhood and the nsp bees forage the selected sites and their surroundings. The remaining bees (n–m) randomly explore the wider solution space. The bees are sorted by their fitness values and the best disassembly sequence plans are saved until the specified maximum iteration number is reached. The neighbourhood search strategies use swap, insert and mutation operators. The solutions consist of a disassembly sequence, disassembly recovery mode, and objective function.


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