The effect of returns volume uncertainty on the dynamic performance of closedloop supply chains
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Abstract
We investigate the dynamics of a hybrid manufacturing/remanufacturing system (HMRS) by exploring the impact of the average return yield and uncertainty in returns volume. Through modelling and simulation techniques, we measure the longterm variability of endproduct inventories and orders issued, given its negative impact on the operational performance of supply chains, as well as the average net stock and the average backlog, in order to consider the key tradeoff between service level and holding requirements. In this regard, prior studies have observed that returns may positively impact the dynamic behaviour of the HMRS. We demonstrate that this occurs as long as the intrinsic uncertainty in the volume of returns is low —increasing the return yield results in decreased fluctuations in production, which enhances the operation of the closedloop system. Interestingly, we observe a Ushaped relationship between the inventory performance and the return yield. However, the dynamics of the supply chain may significantly suffer from returns volume uncertainty through the damaging Bullwhip phenomenon. Under this scenario, the relationship between the average return yield and the intrinsic returns volume variability determines the operational performance of closedloop supply chains in comparison with traditional (openloop) systems. In this sense, this research adds to the still very limited literature on the dynamic behaviour of closedloop supply chains, whose importance is enormously growing in the current production model evolving from a linear to a circular architecture.
Keywords
Bullwhip effect Closedloop supply chains Fill rate Hybrid manufacturing/remanufacturing system Supply chain dynamicsIntroduction
The traditional linear economic model, which covers from resource extraction to disposal, is evolving into a new one, which collects and brings used products into a circular system. As a consequence, supply chains are currently developing from openloop to closedloop architectures in an attempt to capture the environmental, financial, and societal opportunities derived from these circular economic models [2, 15, 20]. However, these opportunities emerge with relevant challenges to deal with, as the complexity of managing efficiently closedloop systems significantly increases. One of the reasons behind that is the fact that closedloop archetypes should accommodate at the same time uncertainty in the volume of demand and in the returns, which implies that traditional models for controlling openloop systems must be reconsidered in this new closedloop setting [9].
In this sense, the new circular model creates the need for understanding the dynamic behaviour of closedloop production and distribution systems and developing knowledge equivalent to the one we have for traditional (openloop) systems. As such, a new line of enquiry has emerged in the literature: that of understanding how the main variables of these closedloop supply chains, mainly orders and inventories, behave over time. However, the literature in this field is still relatively limited.
Interestingly, Tang and Naim [18] observed that returns may positively impact on the operational performance of these systems through a significant decrease of order variability, even though their complexity is higher (as previously discussed). Later works confirmed these results [1, 3, 19, 22, 23], while we note that AdensoDíaz et al. [1] observed that for high values of the return yield, this parameter tended to increase the variability of the orders issued – hence suggesting a nonlinear relationship between order variability and return yield. In addition, several works showed that a higher return yield reduces inventory variability [3, 23]. However, Turrisi et al. [19] reported an increase of endproduct inventory variability when the return yield increases.
Overall, these works provide us with interesting insights on the dynamic response of closedloop supply chains. Nonetheless, they generally consider that a fixed percentage of the used products, namely the return yield, is collected after a consumption lead time [1, 3, 18, 19, 22, 23]. This assumption, which can be attributed to the complexity of the relevant analytical modelling, implies that returns variations are exclusively a consequence of variations in the product demand. Hence, it is reasonable to interpret these previous conclusions as the positive impact of the returns on the supply chain when these are highly correlated with the demand. Under these circumstances, we wonder how uncertainty in the volume of returns collected from the market would alter these conclusions. In this sense, we tackle what we name a ‘dual source uncertainty problem’ (demand uncertainty plus returns uncertainty), which is widely recognised by both managers and academics, but has been barely analysed in the literature.
Thus, this research work adds to the literature by exploring the impact of the uncertainty in the volume of returns on the dynamic behaviour of closedloop supply chains. To do so, we will consider a hybrid manufacturing/remanufacturing system (HMRS). Our study is concerned with the proportional orderupto (POUT) replenishment rule [8]. We selected this discretetime inventory policy since it is optimal to maximize the dynamic performance of supply chains when both order and inventory variabilities are considered [7]. Potter and Disney [17] illustrate how this rule can be easily employed in realworld supply chains to effectively cope with the wellknown Bullwhip Effect [13], which refers to the amplification of the variability of orders as one moves up a supply chain. Our methodological approach is based on modelling and simulation techniques, while we employ designed experiments and statistical analyses to derive realworld implications.
This research article has been structured as follows. After developing the problem statement in this section, we describe the supply chain model that has been considered for the purposes of this research. Then, we present and justify the experimental design, followed by the numerical results and their statistical analysis as well as discussion according to our research aim of investigating the effect of returns volume uncertainty. Finally, we conclude and suggest a future research agenda in this field.
Supply chain model
 (1)
RSF (reception, settling, and feeding) state. At the beginning of each time period, the endproduct inventory receives both new and remanufactured products, assuming the latter are asgoodasnew. If past backorders exist, they are also satisfied from the endproduct inventory. In addition, the rawmaterial inventory provides manufacturing with what is required to meet the orders issued, while all the returns that have been collected during the previous period are pushed into the remanufacturing process. This assumption is common in works in this field [1, 3, 18, 19, 22, 23], which will be the benchmark for our study.
 (2)
MSC (manufacturing, serving, and collection) state. During the course of the time period, consumer demand is received, and it is satisfied as long as inventory is available. If stockout occurs, unsatisfied demand is also recorded. Similarly, returns are collected and stored in the returns inventory. During this main part of the time period, both the manufacturing and remanufacturing processes are ongoing.
 (3)
UFS (updating, forecasting, and sourcing) state. At the end of each time period, the inventory onhand (or net stock) and workinprogress are updated. If necessary, a new backorder is generated. Then, product needs are forecasted by means of using a simple exponential smoothing (SES) method, and finally an order is issued to manufacture the new products required according to a POUT replenishment model.
Mathematical model
Conceptually, the first term models the variability in returns due to variations in the demand, while the second term models the intrinsic variability of returns. We will use the noise ratio m = λ/σ to express the relationship between the standard deviation of both errors.
To implement the previously described operation of the closedloop supply chain, we have built on the model by Tang and Naim [18] for HMRSs with fixed return yield, which in turn was developed as an extension of the widely studied APIOBPCS model [11] for traditional supply chains. Specifically, our study is based on Tang and Naim‘s [18] type 3 system where the closedloop supply chain makes the best use of the information shared.
Performance metrics
It should be highlighted that productionrelated costs are related to the BW ratio, while inventoryrelated costs tend to increase as the NSAmp ratio grows increase [7]. This underscores the need for finding an appropriate balance between both sources of internal variability, where it is commonly possible to reduce one of them at the expense of increasing the other [16].
Experimental design

Average return yield (β), which allows us to compare the traditional system, when β = 0, versus the closedloop system. With the aim of capturing nonlinear effects if they exist, we consider five scenarios defined by different levels for this variable: 0, 0.25, 0.50, 0.75, and 1.

Noise ratio (m), which allows us to analyse the impact of the returns volume uncertainty in the closedloop supply chain. For the same previous reason, we consider five scenarios defined by levels for this variable: 0 (case of no uncertainty in returns volume, as they only vary according to the demand), 0.5, 1, 2, and 4 (case of very high uncertainty in volume of returns).
In this research work, we have chosen T_{m} = T_{r} = 4, hence illustrating a practical setting where the manufacturing and remanufacturing lead times are equal. Setting the equality T_{m} = T_{r} is aligned with prior works, who showed that this yields ‘optimum’ dynamics. For example, Hosoda and Disney [10] underlined the benefits of making equal the manufacturing and remanufacturing lead times. Interestingly, they observed that shortening remanufacturing lead times may not have desirable consequences if manufacturing lead times are fixed (a ‘leadtime paradox’). Tang and Naim [18] also showed that the equality yields tradeoffs in overall dynamic performance. From Eq. (8), given that T_{m} = T_{r} = 4, the estimated pipeline lead time that minimizes the longterm inventory drift in the inventory is easily given by T_{p} = 4. Since the consumption time tends to be significantly higher than the manufacturing and remanufacturing lead times, we have selected T_{c} = 16. For the consumer demand, we have assumed μ = 100 and σ = 20, whose coefficient of variation (20%) is within the common range of variation of retail series: 15%  50% [5].
Regarding the value of the control parameters, Disney [6] recommends, for T_{m} = 4, the setting T_{a} = 4, T_{i} = 7, T_{w} = 28 with the aim of balancing the Bullwhip phenomenon and inventory holding requirements. We have employed this combination, as it represents a ‘good design’ of a traditional supply chain. Finally, we have fixed SS = 50, which represents a practical setting where the safety stock equals to 50% of the mean demand.
We selected T_{h} = 10,000 time periods as the horizon of the simulation runs, where the first 100 time periods, a warmup area, are not considered to minimize the impact of the initial conditions of the HMRS. We have verified the stability of the response and the consistency of the results under these conditions according to common practices [21]. We note that this discretetime simulation model has been implemented via MatLab R2014b. Given the low experimental effort of each simulation run, of less than 1 second per run, we have used a full factorial design of experiments composed of 5^{2} = 25 scenarios, which has been replicated five times for a total of 125 simulation runs.
Results and discussion
Average of the performance metrics from the simulation runs
β  m  BW  NSAmp  AB  ANS 

0  0  0.448  8.231  6.094  56.10 
0  0.5  0.470  9.555  7.303  57.50 
0  1  0.532  13.26  10.64  60.57 
0  2  0.825  29.89  22.19  74.71 
0  4  1.931  95.30  54.84  106.6 
0.25  0  0.364  7.816  5.614  55.62 
0.25  0.5  0.386  9.085  6.904  56.96 
0.25  1  0.459  13.23  10.56  61.35 
0.25  2  0.747  29.54  22.48  73.64 
0.25  4  1.856  92.87  52.56  102.4 
0.5  0  0.296  8.241  5.923  55.87 
0.5  0.5  0.325  9.765  7.510  57.48 
0.5  1  0.380  13.34  10.71  60.61 
0.5  2  0.648  28.96  21.83  73.93 
0.5  4  1.786  94.36  54.12  106.0 
0.75  0  0.255  9.734  7.462  57.57 
0.75  0.5  0.273  10.82  8.847  58.39 
0.75  1  0.334  14.51  11.71  62.20 
0.75  2  0.631  31.31  24.34  74.11 
0.75  4  1.702  93.74  54.76  104.8 
1  0  0.234  12.02  9.478  59.43 
1  0.5  0.252  13.07  10.46  60.62 
1  1  0.332  17.63  14.06  65.05 
1  2  0.604  33.44  25.77  75.09 
1  4  1.731  98.31  57.74  104.3 
Results of the ANOVA
Source  DF  Adj SS  Adj MS  FV  PV 

(a) Bullwhip (BW) ratio  
Model  28  40.0801  1.43143  1464.6  0.000 
Blocks  4  0.0025  0.00063  0.65  0.630 
Linear  8  40.0702  5.00852  5124.57  0.000 
Average return yield (β)  4  0.7972  0.19931  203.93  0.000 
Noise ratio (m)  4  39.2710  9.81774  10,045.22  0.000 
TwoWay Interactions  16  0.0094  0.00059  0.6  0.876 
Average return yield (β) * Noise ratio (m)  16  0.0094  0.00059  0.6  0.876 
Error  96  0.0938  0.00098  
Total  124  40.1739  
Rsq  99.70%  Rsq (adj)  99.60%  
(b) Net Stock Amplification (NSAmp) ratio  
Model  28  131,692  4703.3  2318.34  0.000 
Blocks  4  4  1.0  0.51  0.731 
Linear  8  131,660  16,457.5  8112.25  0.000 
Average return yield (β)  4  307  76.7  37.80  0.000 
Noise ratio (m)  4  131,354  32,838.4  16,186.70  0.000 
TwoWay Interactions  16  27  1.7  0.84  0.641 
Average return yield (β) * Noise ratio (m)  16  27  1.7  0.84  0.641 
Error  96  195  2.0  
Total  124  131,886  
Rsq  99.85%  Rsq (adj)  99.81%  
(c) Average Backlog (AB)  
Model  28  40,282.8  1438.7  624.32  0.000 
Blocks  4  18.2  4.5  1.97  0.105 
Linear  8  40,247.6  5030.9  2183.23  0.000 
Average return yield (β)  4  247.7  61.9  26.87  0.000 
Noise ratio (m)  4  39,999.9  10,000.0  4339.58  0.000 
TwoWay Interactions  16  17.0  1.1  0.46  0.960 
Average return yield (β) * Noise ratio (m)  16  17.0  1.1  0.46  0.960 
Error  96  221.2  2.3  
Total  124  40,504.0  
Rsq  99.45%  Rsq (adj)  99.29%  
(d) Average Net Stock (ANS)  
Model  28  40,296.4  1439.2  253.82  0.000 
Blocks  4  25.3  6.3  1.11  0.354 
Linear  8  40,162.4  5020.3  885.42  0.000 
Average return yield (β)  4  114.6  28.6  5.05  0.001 
Noise ratio (m)  4  40,047.9  10,012.0  1765.79  0.000 
TwoWay Interactions  16  108.7  6.8  1.20  0.284 
Average return yield (β) * Noise ratio (m)  16  108.7  6.8  1.20  0.284 
Error  96  544.3  5.7  
Total  124  40,840.7  
Rsq  98.67%  Rsq (adj)  98.28% 
Under these circumstances, and according to the framework defined in Fig. 2, we observe that increasing the return yield has a significant potential for reducing productionrelated costs in the HMRS. However, if closing the loop also translates into a relevant increase in the returns volume uncertainty, the reverse material flow could enormously complicate the efficient control of inventories up to the extent of provoking an undesired surge in production costs.
Figure 4 shows an interesting Ushaped relationship between the NSAmp and the average return yield. That is, for low values of the yield, the variability of inventories is decreasing in β, which has been observed in previous works [3, 23]; however, for high values of this parameter, the variability of inventories is increasing in β, an effect that has also been observed in the literature [19]. This striking relationship requires further investigation. Given that the slope of the BW ratio is decreasing in β, we conclude that the improvement of the dynamics in the closedloop system is more significant in the first stages of the implementation of the circular model (i.e. when β is increasing but it is still low).
The tradeoff between the average backlog and the average net stock is highly related with the NSAmp ratio, as we discussed in Section 2.2. Consistently with this notion, we can also observe here the previously highlighted Ushaped relationship. Thus, for low values of the return yield, the HMRS is capable of achieving a higher customer service level (that is, it operates with a lower backlog) with less stock. However, for high values of the average return yield, the decrease in production costs occurs at the expense of an increased stockout size and holding costs.
Nonetheless, Fig. 5 suggests that the NSAmp ratio, the average backlog, and the average net stock are much more sensitive to the noise ratio m. That is, we again observe that although the dynamic behaviour of the HMRS may benefit from collecting products, returns volume uncertainty strongly and negatively impacts on the operational performance of closedloop supply chains. In this sense, we see by observing Fig. 5 that when the intrinsic variability of returns increases, the actual service level significantly decreases even though the supply chain is operating with a higher level of average inventory. For this reason, returns volume uncertainty also tends to increase significantly the inventoryrelated costs of the HMRS under consideration.
Conclusions
It is widely accepted that reverse logistics represent, together with a clear environmental opportunity for societies that are embracing them, a relevant financial opportunity for businesses derived from retaining the value of products. Several prior works have observed that, in addition, closedloop supply chains can benefit from decreased production and inventory related costs through a smoothed dynamic behaviour. We show that, at the same time, uncertainty in the returns volume significantly threatens the operational performance of such supply chains, which may make that realworld supply chains struggle to materialise the said benefits of closedloop contexts. In this sense, closedloop supply chain managers face new challenges that must be overcome in order to strengthen the current transformation from a linear to a circular economic model.
The main results of this research can be interpreted as follows: (1) closedloop supply chains experience a considerable reduction of variability, and hence of production and inventoryrelated costs, when returns volume can be accurately estimated; while (2) closedloop supply chains may suffer from a dramatic increase in instability, and hence of costs, when the uncertainty in the volume of returns is very high. This puts special emphasis on managers to invest in forecasting the volume of returns. Previous research on both openloop and closedloop supply chains have highlighted the benefit of information transparency of workinprocess or goodintransit pipelines in the supply chain. Utopianly, this would be achieved in a closedloop setting by tracking products that are consumed and ascertaining volume of goods that are returned. In a practical setting, establishing forecasting techniques that can estimate such returns is a realistic substitute. In addition, such forecasting approaches will need to be appropriately integrated into the inventory policies of HMRSs to ensure ‘optimum’ stock control and ordering.
Alternatively, closedloop supply chains can be proactive in establishing a returns policy to encourage and regulate the volume of returns. This may be done via incentive schemes and establishing a collection network as a way of capturing the positive impact of a high yield and alleviating the negative impact of returns volume uncertainty.
An interesting contribution of our research to the literature on closedloop supply chain dynamics is the fact that we observed a Ushaped relationship between the return yield and the inventory performance of the HMRS. That is, when the return yield is high, the increase in the production stability in the closedloop system may occur at the expense of increasing at the same time the average backlog and the average inventory. In this sense, productionrelated costs are minimized when the average return yield is maximum and returns volume uncertainty is null, while inventoryrelated costs are minimized for an intermediate value of the return yield and also when the intrinsic variations of returns are null. Managers would therefore be required to determine the Ushape of their specific operation in order to better control their systems.
As with other previous studies, our model as described in Section 2, assumes a push policy, that is, returns are remanufactured as soon as possible in maketostock manner. While such a policy works well in the reverse flow of materials in some practical settings, other strategies for regulating the returns inventory may help to decrease the impact of returns volume uncertainty on closedloop supply chains. This research avenue is highlighted as an essential step in the exploration of the dynamic behaviour of closedloop supply chains.
Notes
Acknowledgements
This research was supported by UK’s Engineering and Physical Sciences Research Council (EPSRC) under the project Resilient Remanufacturing Networks (ReRuN): Forecasting, Informatics, and Holons (grant no. EP/P008925/1).
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