Optimizing an FPR-based supplier-retailer integrated problem with an outsourcer, rework, expedited rate, and probabilistic breakdown

Internal supply chains exist in many global enterprises, where manufacturing tasks and sales jobs operate separately, but the management needs to integrate their financial performance reports. In addition, the fabrication planning must meet specific operational goals, such as meeting external clients’ requirements on quality and short order due dates, avoiding internal fabricating interruptions due to inevitable equipment breakdowns, and minimizing overall manufacturing and stock holding costs. Motivated by helping multinational corporations deal with the issues mentioned earlier, this study aims to optimize a finite production rate (FPR)-based supplier-retailer cooperative problem with multi-shipment, rework, subcontracting, probabilistic failure, and expedited rate. Wherein using an outsourcer and expedited-rate help shorten the needed batch producing time significantly; the rework of defects and corrective action on unanticipated breakdown assist in up-keeping the quality and avoiding fabricating delay. We develop an FPR- based model to cautiously represent the considered manufacturing features and activities involved in transporting end products and retailers’ stock holding. Model’s formulating and investigating assists us in gaining the function of operating costs. In addition, optimization procedures with a proposed algorithm help us verify its convexity and decide the model’s best fabricating runtime solution. Finally, we validate how this study works and what important information our model can disclose using a numerical example to facilitate management’s decision-making to end our work. issues of product defectives, rework, equipment failures, and various corrected actions on managing, planning, and controlling different manufacturing systems. This study incorporates an outsourcer and expediting in-house fabricating rate to reduce the batch production time and satisfy external customers’ needs of short order due dates. Antelo and Bru (2010) explored the influence of subcontracting strategy and restructuring the firm on operating in an uncertain environment. The researchers examined the option and role of outsourcing versus production cost and the potential timing and need for organizational restructuring to determine the optimal managerial decision in the firm’s future. Rivera-Gómez et al. (2018) intended to simultaneously implement subcontracting, fabrication, and maintenance in a manufacturing system featuring various progressive deterioration processes. They explored such deterioration effects on the quality and machine reliability. The study assumed minimal repair and preventive maintenance to restore a failed machine to an operating condition and planned a proper subcontracting amount to meet client demand. Their study aimed to minimize overall operating expenses comprising fabrication, outsourcing, stock holding, preventive maintenance, product defects, machine repair, and backlog costs. By building a stochastic control model and using numerical methodologies, the study defined the control policies’ structure and applied statistical analyses and optimization methods to decide their control policies’ optimality. Lastly, through numerical illustrations, the study highlighted the relationships among fabrication, maintenance, subcontracting, deterioration, quality, and reliability to justify their results. Kershaw et al. (2021) incorporated machine learning into the decisions of predicting welding quality and adjusting welding speed. The researchers used two cameras to collect required real-time data for this preliminary study to develop appropriate training for machine learning. In addition, the study used a convolutional neural network to analyze the correlations from the collected top-side and back-side welding data sets to predict the quality and control speed of the welding processes.

Internal supply chains exist in many global enterprises, where manufacturing tasks and sales jobs operate separately, but the management needs to integrate their financial performance reports. In addition, the fabrication planning must meet specific operational goals, such as meeting external clients' requirements on quality and short order due dates, avoiding internal fabricating interruptions due to inevitable equipment breakdowns, and minimizing overall manufacturing and stock holding costs. Motivated by helping multinational corporations deal with the issues mentioned earlier, this study aims to optimize a finite production rate (FPR)-based supplier-retailer cooperative problem with multi-shipment, rework, subcontracting, probabilistic failure, and expedited rate. Wherein using an outsourcer and expedited-rate help shorten the needed batch producing time significantly; the rework of defects and corrective action on unanticipated breakdown assist in up-keeping the quality and avoiding fabricating delay. We develop an FPRbased model to cautiously represent the considered manufacturing features and activities involved in transporting end products and retailers' stock holding. Model's formulating and investigating assists us in gaining the function of operating costs. In addition, optimization procedures with a proposed algorithm help us verify its convexity and decide the model's best fabricating runtime solution. Finally, we validate how this study works and what important information our model can disclose using a numerical example to facilitate management's decision-making to end our work.

Nomenclature
T'Z = cycle time in situation one, λ = annual demands, Q = production lot size, β = mean annual Poisson-distributed breakdowns, t = time to breakdown occurring, tr = equipment repair time, M = equipment repair cost, π = the outsourced portion of a batch (where 0 < π < 1), Kπ = fixed subcontracting cost, β1 = the linking factor between Kπ and K, Cπ = unit subcontracting cost, β2 = the linking factor between Cπ and C, P1A = annual adjustable production rate, P1 = standard production rate (i.e., without using the adjustable-rate), α1 = the linking factor between P1A and P1, CA = unit cost when adjustable-rate is used, C = standard unit cost, KA = setup cost with adjustable-rate implmented, K = standard setup cost, α2 = the linking factor between KA and K, x = annual uniform-distributed defective rate, d1A = defective item's production rate in t1Z, so, d1A = xP1A, P2A = annual adjustable reworking rate, P2 = standard reworking rate, CRA = unit rework cost when adjustable reworking rate is used, CR = rework cost with P2 implemented, α3 = the linking factor between CA and C, and CRA and CR, t1Z = production uptime, t'2Z = situation 1's rework time, t'3Z = stock distributing time in situation one, t'nZ = the time between two consecutive deliveries in situation one, h = unit holding cost, h1 = unit holding cost per reworked item, h3 = unit safety stock's holding cost, C1 = unit safety stock cost, h2 = unit holding cost at the buyer side, CT = unit distributing cost, K1 = fixed distributing cost, n = the number of shipments in a cycle, g = tr, machine repair time, H = stock level after receipt of the outsourced goods, H2 = stock level when rework time ends, H1 = stock level when uptime ends, H0 = situation 1's stock level, TZ = situation 2's cycle time, t 2Z = rework time in situation two, t3Z = stock distributing time in situation two, tnZ = the time between two consecutive deliveries in situation two, T = cycle time for a model without outsourcing, breakdown, nor adjustable-rate, t1 = uptime for a model without outsourcing, breakdown, nor adjustable-rate, t2 = the rework time for a system without outsourcing, breakdown, nor adjustable-rate, t3 = stock distributing time for a system without outsourcing, breakdown, nor adjustable-rate, d1 = defective items' producing rate for a model without outsourcing, breakdown, nor adjustable-rate, D = the amount of goods per delivery, I = the leftover goods when distributing interval ends, I(t) = stocks level at time t, Ic(t) = buyer's stock level at time t, Id(t) = defective stock level at time t, IF(t) = safety stock level at time t, TC(t1Z)

Introduction
This study examined a FPR-based supplier-retailer cooperative problem with multi-shipment, subcontracting, probabilistic failure, expedited rate, and rework. Optimizing an FPR-based supplier-retailer integrated type of system helps global firms' intra-supply chains minimize their overall operating expenditures. Nachiappan and Jawahar (2007) explored the operational issues of a vendor-managed inventory (VMI) supply chain involving one vendor and the multi-buyer. The researchers focused on the supply chain's profit relating to the selling quantity and the contractual agreement price. To reach the agreement price, partners share their revenues. In addition, the study built a math model and formulation to explore the influence of different acceptable contractual prices to derive the optimal sales amount for each buyer. A heuristic using the genetic algorithm helped the study to resolve this integer programming model with nonlinear nature. Lastly, the researchers evaluated the quality of their obtained solution with sensitivity analyses. Hajej et al. (2015) explored the optimal production plan considering stochastic demand, system deterioration, service level requirement, maintenance, product returns, and shipment tasks. The customer's return items are assumed to be still new and re-saleable. The researchers formulated the studied problem as a quadratic model representing the relevant stock, shipment, fabrication, and maintenance. Lastly, they provided simulation outcomes to expose the shipping time impact on the planning of fabrication, maintenance, and shipment tasks. Sazvar et al.
(2021) used a multi-objective capacity planning technique to explore a supply chain featuring sustainable-resilient for making strategic and tactical decisions. Wherein researchers focused on planning optimally for meeting clients' demands with weak operations and high disruption risks. The researchers developed a mathematical model with a resilient demand-side framework. They applied an actual case study of the influenza vaccine supply chain to validate their model and investigate the tradeoff between sustainability and resilience. In addition, the researchers used a vigorous fuzzy optimization method to cope with uncertainties, and they solved their multi-objective model by using goal programming with utility functions. Finally, after exploring the influences of the quantitative results of the problem's structural variables, the study suggested specific managerial insights into the situation. Other works (Cetinkaya & Lee, 2000;Sucky, 2005;Garcĺa & de las Morenas, 2012;Sahebi et al., 2019;Brahmi et al., 2020;Pham & Doan, 2020;Pourmohammadi et al., 2020;Toncovich et al., 2020;Farmand et al., 2021;Nguyen et al., 2021) studied the impact of different shipping strategies on controlling and managing various types of supply chains.
Additionally, the fabrication planning must meet various operational goals, e.g., satisfying external clients' requirements on product quality and short order due dates, avoiding in-house fabricating interruptions due to inevitable equipment breakdowns, and minimizing total manufacturing and inventory holding expenses. Hence, implementing the screening and rework processes for random defects and instantly correcting the inevitable machine failures are critical for production managers. Kenne and Gharbi (2001) explored the optimal fabricating rate for a multiproduct parallel-machine manufacturing system subject to stochastic failure and repair rates. The researchers used an experimental design, Markov chain, discrete event simulation, and response surface techniques to handle their cost-minimization-oriented problem. Both exponential and nonexponential failure/repair times under constant demand rates are investigated using a simulation approach to estimate the optimal control and fabricating rate policy. Maggio et al. (2009) used a decomposition analytical approach to evaluate mean throughputs and buffers for an unreliable three-machine fabrication system. Their model considered deterministic machine processing times and geometric-distribution breakdown and repair rates. The researchers used simulation techniques to verify their model's results and discussed potential extensions to their model. Singh et al. (2014) studied a time-dependent demand economic production model considering multiple setups and rework. Their proposed green supply chain features a reverse logistic, i.e., considering one rework setup dealing with defects from multiple regular batch processes. Lastly, they offered a numerical illustration for their model with sensitivity analysis. Sharma and Rai (2021) explored failure modes for repairable systems using censored data analysis. In addition to conventional criteria in predicting failure modes (e.g., the time between machine failures), the researchers considered the virtual age models treating preventive and corrective maintenance as imperfect in their future reliability censored data analysis. Wherein their proposed models also offered a likelihood function for estimating system parameters. To help demonstrate the applicability of their methods and models, the researchers provided an aviation case study. Other works (Flapper et al., 2002;Öztürk et al., 2015;Chiu et al., 2018;Mallick et al., 2019;Pham & Doan, 2020;Gera, 2021;Hani, 2021;Shekhar et al., 2021) examined the effects of dissimilar issues of product defectives, rework, equipment failures, and various corrected actions on managing, planning, and controlling different manufacturing systems.
This study incorporates an outsourcer and expediting in-house fabricating rate to reduce the batch production time and satisfy external customers' needs of short order due dates. Antelo and Bru (2010) explored the influence of subcontracting strategy and restructuring the firm on operating in an uncertain environment. The researchers examined the option and role of outsourcing versus production cost and the potential timing and need for organizational restructuring to determine the optimal managerial decision in the firm's future. Rivera-Gómez et al. (2018) intended to simultaneously implement subcontracting, fabrication, and maintenance in a manufacturing system featuring various progressive deterioration processes. They explored such deterioration effects on the quality and machine reliability. The study assumed minimal repair and preventive maintenance to restore a failed machine to an operating condition and planned a proper subcontracting amount to meet client demand. Their study aimed to minimize overall operating expenses comprising fabrication, outsourcing, stock holding, preventive maintenance, product defects, machine repair, and backlog costs. By building a stochastic control model and using numerical methodologies, the study defined the control policies' structure and applied statistical analyses and optimization methods to decide their control policies' optimality. Lastly, through numerical illustrations, the study highlighted the relationships among fabrication, maintenance, subcontracting, deterioration, quality, and reliability to justify their results. Kershaw et al. (2021) incorporated machine learning into the decisions of predicting welding quality and adjusting welding speed. The researchers used two cameras to collect required real-time data for this preliminary study to develop appropriate training for machine learning. In addition, the study used a convolutional neural network to analyze the correlations from the collected top-side and back-side welding data sets to predict the quality and control speed of the welding processes. Furthermore, the researchers used varying-speed experimental trials to explore the feasibility of applying bead-width welding speed in multi-layer perceptrons and provided an efficient algorithm with extra computational efforts to achieve an optimal/ideal bead-width rate for the welding process. Other works (Khouja, 2000;Bardhan et al., 2007;Jauhari and Pujawan, 2014;El-khalek et al., 2019;Mallick et al., 2019;Chiu et al., 2020;Gupta and Ivanov, 2020;Chiu et al., 2021;Hermawan, 2021) examined the influence of different controllable manufacturing rates and outsourcing options on planning, operating, and optimizing various global supply chains and production systems. Little works have explored optimizing an FPR-based supplier-retailer integrated problem with an outsourcer, rework, expedited rate, and probabilistic breakdown; we aim to fill this gap.

Model description
First, we provide a Nomenclature to ease the reading before describing the proposed FPR-based manufacturer-retailer collaboration system. Consider a batch manufacturing plan established to satisfy a λ demand rate of a specific product. The studied system is not reliable. It randomly fabricates x proportion of defective goods. In each cycle, right after the standard manufacturing process, a rework process can repair all faulty items made in this cycle. Further, the equipment is subject to Poisson-distributed failures with β as its annual mean. Hence, time t before a breakdown occurs adheres to an Exponential distribution with βe -βt as its density function. Upon occurrence of a failure, our study adopts an abort/resume policy, which puts the machine under repair at once and assuming a fixed repair time tr. The production of the unfinished/interrupted lot resumes as soon as the machine is restored. This study uses dual uptime-reduced strategies. One is to subcontract a π portion of lot-size Q to the external suppliers, and the other is to accelerate the in-house manufacturing rate. A fixed setup cost Kπ and unit cost Cπ accompany this subcontracting policy, and another fixed setup cost KA and unit cost CA link to the adjusted-rate plan. Eq. (1) to Eq. (7) denote the relationships between each strategically-relevant parameter and its corresponding standard variable.
( ) where α1 denotes the proportion of speed P1A is faster than the standard manufacturing rate P1; βi (for i = 1, 2) and αi (for i = 2, 3) are the linking factors between cost-relevant parameters; P2A stands for the accelerate reworking rate. The study allows no stock-out condition, i.e., (P1A -d1A -λ) > 0 must hold. The external supplier guarantees the outsourced products' quality. The scheduled receipt time for the outsourced goods is at the end of the in-house rework time (i.e., at the beginning of distributing time). Upon gathering the entire lot, n fixed-quantity shipments are distributed at t'nZ (i.e., a constant time interval) during t'3Z to the customer side. We build the following models to study different situations of stochastic breakdown occurrences explicitly:

Situation 1: A breakdown happens in uptime t1Z
In situation one, the time to a breakdown occurs t < t1Z. We adopt an A/R controlling policy to correct the failure and continue the production when the correction action is done. Figure 1 depicts the stock level of the proposed FPR-based problem (in thicker lines) compared to a problem with only rework (in thinner lines). Fig. 1 indicates stock level reaches H0 when a failure occurs. It remains at H0 during correction/repair time tr. Once the device is restored, its level rises to H1 when t1Z ends. It arrives at H 2 when the rework time t' 2Z ends. By receiving the outsourced goods, the stock level increases to H, right before the beginning of stock distribution time t'3Z. Finally, during t'3Z, n equal-quantity shipments deplete the inventory level to zero (see Fig. 1 for details).  The inventory level of defective products made is as follows: Total stocks of finished items during t'3Z are as follows (Chiu et al., 2020):  Situation one's total operating expenses per cycle TC(t1Z)1 consists of below: the variable and fixed subcontracting costs and in-house production cost, the variable and fixed distributing costs, machine repair cost, safety stock relating cost, rework related costs, and stock holding costs (comprising the defective, finished, and reworked products, and buyer side's stocks) during T'Z as displayed in Eq. (19).
By substituting Eqs.

Situation 2: No breakdown happens in uptime
In situation two, the time before a breakdown occurs t > t1Z. Fig. 5 displays situation two's stock level (in thicker lines) compared to a system with rework only (in thinner lines). It specifies that when the uptime ends, the level rises to H1, and it further reaches H2.when the rework finishes. By receiving the outsourced items, the inventory level arrives at H, before the beginning of product distributing time t3Z. Fig. 6 exhibits the safety stock's level in situation two. Safety stock stays the same at all time. The inventory level of defective products in situation 2 is the same as Fig. 3, excluding tr. Similar to subsection 2.1., we observe straightforward formulas as follows: Total finished stocks in t3Z for situation 2 are (Chiu et al., 2020): Total buyer side's stocks in TZ for situation 2 are (Chiu et al., 2020): Total operating expenses per cycle TC(t1Z)2 in situation two consists of below: the variable and fixed subcontracting expense s and in-house production cost, the variable and fixed distributing costs (see Fig. 5), safety stock holding cost (see Fig. 6), re work related expenses, and total stock holding expenses (comprising the defective, finished, and reworked items, and buyer' s inventories) in TZ as exhibited in Eq. (30).

Numerical illustration
To demonstrate the proposed model's capability and applicability, this section provides the following numerical example with the assumption of system variables, as shown in Table 1. Table 1 The assumption of system variables  TCU(t1Z)] is convex, one knows that the optimal t1Z* exists. A broader βvalue range is applied to test for convexity of E[TCU(t1Z)], and these results prove our proposed model's more general applicability (see Table 2). For E [TCU(t1Z)] is convexity, we apply the solution procedure mentioned earlier for finding the optimal solution. First, by assume initially e -βt1Z = 0 and e -βt1Z = 1, and apply Eq. (39) to obtain t1ZL = 0.0687 and t1ZU = 0.1961. Then, utilizing the present t1ZU and t1ZL values to recalculate e -βt1ZU and e -βt1ZL . Then, by re-applying Eq. (39) with the current e -βt1ZU and e -βt1ZL to update the t1ZU and t1ZL values. If (t1ZL = t1ZU) is true, then t1Z* arrives (i.e., t1Z* = t1ZL = t1ZU); otherwise, repeat the steps mentioned above until (t1ZL = t1ZU) is true. Table 3 shows the step-by-step iterative outcomes for locating t1Z*. It discloses the initial t1Z's upper and lower bounds, t1Z*, and the convexity of E[TCU(t1Z)] concerning to t1Z. Fig. 7 illustrates the E[TCU(t1Z)]'s behavior relating to t1Z, and it indicates that t1Z* = 0.0838 and E[TCU(t1Z*)] = $12,870.75.

Table 3
The step-by-step iterative outcomes for locating t1Z** Step t1ZU

Joint effect of key features on the proposed study
The joint effect of differences in (CRA / C) ratio and π on E[TCU(t1Z*)] are demonstrated in Fig. 8. It reveals that E[TCU(t1Z*)] significantly upsurges when both (CRA / C) and π increase.

Fig. 9 displays the joint influence of changes in α1 and n on E[TCU(t1Z)]. It shows E[TCU(t1Z)]
surges considerably as both n and α1 rise. Fig. 10 illustrates the joint influence of differences in α1 of the production rate and n on the t1Z*. It indicates that t1Z* considerably declines as α1 rises, and t1Z* increases significantly as n increases. Fig. 10. Joint influence of changes in α1 and n on t1Z* Fig. 11 shows the collective effect of differences in 1/β and π on runtime t1Z*. It discloses that t1Z* exceedingly drops as π rises. When π ≤ 0.4, the optimal t1Z* declines noticeably as 1/β surges; and when π > 0.4, t1Z* slightly drops as 1/β rises. Fig. 11. Collective effect of differences in 1/β and π on t1Z* Fig. 12. Combined effect of changes in α1 and π on t1Z*

Fig. 9. Joint influence of variations in α1 and n on E[TCU(t1Z)]
The combined effect of changes in α1 and π on TZ* is depicted in Fig. 12. It reveals that TZ* noticeably increases as α1 rises; TZ* surges considerably as π upsurges. Fig. 13 exhibits the joint influence of difference in α1 and π on utilization. It specifies that utilization exceedingly declines as π rises. When π ≤ 0.4, the machine utilization considerably drops as α1 increases; and when π > 0.4, utilization reduces marginally as α1 increases. 14 displays the impact of differences in π on utilization. It exposes that utilization greatly declines as π rises. In our example, for π = 0.4, it shows that utilization drops from 0.3186 to 0.1915, a 39.90% decline due to our outsourcing strategy. Analytical results regarding the critical π value is depicted in Fig. 15. It discloses that the critical π = 0.7621. In other words, once the outsourcing portion rises to 0.7621 and beyond, it is more beneficial to utilize a pure 'buy' strategy.  16 depicts variations in the ratio of adjustable portion of production rate (P1A / P1) on machine utilization. It indicates that machine utilization radically drops as (P1A / P1) increases. In our example, for (P1A / P1) = 1.5, utilization reduces from 0.2868 to 0.1915, a 33.25% decrease due to our adjustable-rate strategy. Fig. 17 compares our utilization with other similar systems. Since our model considers dual utilization-reduction strategies (i.e., both outsourcing and adjustable-rate options), our utilization declines to 0.1915, or 33.2% lower than that in a similar system with outsourcing strategy only (see Fig. 17). Moreover, our utilization is 39.9% lower than that in a similar study with an adjustable-rate approach only (Chiu et al., 2020), or 59.8% less machine utilization than a similar system without implementing neither outsourcing nor adjustable-rate strategies (Chiu et al., 2018). For utilization reduction, as mentioned above, the prices we pay are 2.04%, 6.54%, and 10.35% increase in E[TCU(t1Z*)], respectively.
A further explorative outcome reveals the impact of individual utilization-reduction strategy on utilization and E[TCU(t1Z*)], as demonstrated in Fig. 18. It reveals that in our example, to reduce the utilization, a more cost-effective approach is to implement α1 = 0.5 along with increasing π. It also confirms that in our example, π = 0.4 and α1 = 0.5, utilization = 0.1915 and E[TCU(t1Z*)] = $12,871. Moreover, this study can offer managerial decision-support information concerning how to efficiently implement the utilization-reduction strategy, as demonstrated in Fig. 19. For our example, it exposes that the most beneficial approach to reducing utilization starts with the following steps.
(1) Initially, use the adjustable-rate strategy only, then continue to increase α1 to 1.114. At this point, utilization declines to 0.2263, and E[TCU(t1Z*)] rises to $12,877 (see the dash red-line in Fig. 19); (2) then, to further reduce utilization, the explorative result suggests to switch to the combined strategies; and starting with π = 0.527 and α1 = 0. By keeping π at 0.527 and increasing α1 (see the dash blue-line in Fig. 19). The suggestive steps mentioned above offer the most cost-effective approach to reduce utilization.

Conclusions
This work derives an optimal batch fabricating time for an FPR-based supplier-retailer integrated problem with an outsourcer, rework, expedited-rate, and breakdown to assist the management of transnational enterprises in minimizing operating costs of their internal supply chains. The specific operational goals of the studied problem include satisfying external clients' requirements on quality and short order due dates, avoiding internal fabricating interruptions due to inevitable breakdowns, and minimizing overall manufacturing and stock holding costs. First, we build an FPR-based model featuring: (1) The rework of defects and corrective action on the unanticipated breakdown to upkeep the quality and avoid fabricating delay; (2) An outsourcer and expedited rate to significantly shorten the producing time; and (3) Activities involved transporting end products and retailers' stock holding. Through the model's formulating and investigating, we gain the function of operating costs. Then, we utilize optimization procedures with a proposed algorithm to verify its convexity and derive the model's best fabricating time solution. Finally, we validate how this study works and what important information our model can disclose using a numerical example (see the following) to facilitate management's decision-making: (1) Table 2 verifies the convexity of operating costs against different βs, Table 3 exhibits the step-by-step iterating results for finding the optimal batch fabricating time, and Figure 7 depicts the operating cost's convexity; (2) Fig. 8 to Fig. 13 demonstrates the joint impact of main system features (including the ratio of (CRA / C), n, α1, 1/β, and π) on the system operating costs, optimal runtime and batch cycle length, and utilization; (3) Fig. 14 to Fig. 16 illustrates the impact of individual system feature (including the ratio of (P1A / P1) and π) on utilization, optimal operating costs, and make-or-buy choices; (4) Fig. 17 shows how our utilization outperforms that of existing studies; (5) Fig. 18 and Fig.19 reveal the impact of individual utilization-reduction strategy on optimal operating costs and utilization and disclose crucial decision-support insights concerning the efficient and economical ways to reduce utilization. Considering an uncertain annual product demand in the present problem and investigating its impact on the research outcomes is worth exploring for future work. Pham, T.H., & Doan, T.D.U. (2020). Supply chain relationship quality, environmental uncertainty, supply chain performance and financial performance of high-tech agribusinesses in Vietnam. Uncertain Supply Chain Management, 8(4), 663-674. Pourmohammadi, F., Teimoury, E., & Gholamian, M.R. (2020). A scenario-based stochastic programming approach for designing and planning wheat supply chain (A case study). Decision Science Letters, 9(4), 537-546. Rivera-Gómez, H., Gharbi, A., Kenné, J.-P., Montaño-Arango, O., & Hernández-Gress, E.S. (2018). Subcontracting strategies with production and maintenance policies for a manufacturing system subject to progressive deterioration. International Journal of Production Economics, 200, 103-118. Sahebi, I.G., Masoomi, B., Ghorbani, S., & Uslu, T. (2019). Scenario-based designing of closed-loop supply chain with uncertainty in returned products. Decision Science Letters, 8(4), 505-518. Sazvar, Z., Tafakkori, K., Oladzad, N., & Nayeri, S. (2021). A capacity planning approach for sustainable-resilient supply chain network design under uncertainty: A case study of vaccine supply chain. Computers and Industrial Engineering, 159, Art. No. 107406. Sharma, G., & Rai, R.N. (2021). Failure modes based censored data analysis for repairable systems and its industrial perspective. Computers and Industrial Engineering, 158, Art. No. 107439. Shekhar, C., Deora, P., Varshney, S., Singh, K.P., & Sharma, D.C. (2021).