Strategic reliable supply chain network design: determining tradeoffs between cost and risk

ABSTRACT The design of a supply chain network (SCN) should address two conflicting objectives, i.e. inexpensive yet reliable operation. This paper presents models to choose supply facilities and determine distribution options while considering the expected risk of not serving customers attributed to supply shortages. The goal is to design a reliable network with a lower cost under traditional cost objectives. We formulate a stochastic mixed-integer biobjective programming model considering the protection of facilities and solve this problem with a progressive hedging algorithm (PHA). We examine the tradeoff curve between the cost and risk through a case study involving Shanghai in China. The results indicate that substantial improvements in reliability can be reached with a limited increase in the total cost.


Introduction
The supply chain network (SCN) is critical in business activities today, and its stability and reliability are both of very high strategic importance for national economic and social security. However, external attacks or internal failures may result in facilities unable to satisfy demands, and one or more facilities may be disrupted periodically after establishment. Moreover, production demands are stochastic and may be confronted with a sudden increase or decline. This leads to excessive transportation, purchase or storage costs, as customers must obtain products from more distant facilities or accept alternative products. Hence, reliability can be understood as the system performance while facing various uncertain scenarios, which is vital to SCNs (Snyder and Daskin 2005).
In addition, the construction of SCN facilities requires a very high investment cost and long-term commitment. Once completed, facilities are not easily removed or rebuilt. Hence, their locations must be carefully chosen to minimise the total cost (Kang et al. 2016). Day-today operating and transportation costs are also important components of the total cost, which decision makers must consider when designing a whole network (Schmitt et al. 2015). Centralised production options with largescale facilities may result in low construction costs, CONTACT  Supplemental data for this article can be accessed here. https://doi.org/10. 1080/00207543.2021.1994163 while decentralised production options with small-scale facilities may result in low transportation costs (Kim and Moon 2008). Moreover, more reliable facilities with higher capacities usually require a larger budget. A network must be robust to changes in demand, which is another critical issue.
As an important technology that can effectively reduce the risk emerging from the tracking system and data management (Azzi, Chamoun, and Sokhn 2019), blockchain technology can revolutionise supply chain processes and increase the transparency and efficiency of complex supply chains (Sunny, Undralla, and Pillai 2020;Manupati et al. 2020). Blockchain technology resolves overpowering trust issues and facilitates secure and authenticated information exchange in SCNs (Saberi et al. 2019). Most studies on the application of blockchain technology to supply chain management have concentrated on the informational or operational level (Min 2019;Casado-Vara et al. 2018;Queiroz and Wamba 2019;Longo et al. 2019). However, the reliability of facilities hosting blockchain capabilities also deserves attention.
A large amount of literature on supply chain management has focused on reliability or disruption issues (Cui, Ouyang, and Shen 2010;Snyder et al. 2016). Most studies have considered disruption issues from a supply-side perspective, in which the production quantity delivered by a supplier is a random variable or the facility capacity is uncertain (Heckmann, Comes, and Nickel 2015). In this paper, we introduce a new parameter, the protection level. As stated in Church and Scaparra (2007), one example of protection is enhancement of the defense level of a given hub to withstand natural disasters or terrorist attacks, such as a relay protection system at a transformer substation of an electricity network. Different protection levels correspond to varying failure probabilities and handling capacities of a hub facility.
Network reliability models usually consider the cost of construction while ignoring the routing cost resulting from a certain disruption. However, in regard to SCNs, such as transportation networks, the operating cost is a major component of the total cost. The hypothesis that the supply capacity is infinite is unrealistic (Johansson, Hassel, and Zio 2013). For example, in a power network, the maximum supply capacity of electricity may not be able to satisfy the peak demand (Kang et al. 2013). The network design problem, which determines various parameters, including the location, capacity, and type of facilities, is one of the most comprehensive strategic decision problems that should be optimally solved to accomplish long-term efficient operations (Wang, Lai, and Shi 2011;Meng et al. 2013;Tian et al. 2016;Hu et al. 2019). The various formulations of the network design problem include linear deterministic models and complex nonlinear stochastic models, one-and two-objective models, and one-and two-stage models (Huang and Goetschalckx 2014;Peng et al. 2011;Scaparra and Church 2008;Qi, Shen, and Snyder 2010;Tian, Ren, and Zhou 2016;Hou et al. 2015). Models with fortifications to overcome facility disruptions have been developed (Liberatore, Scaparra, and Daskin 2011;Bhattacharya et al. 2013). The focus of these studies is often directed at the identification of those key facilities the enemy may most likely damage and aims to fortify nodes or arcs to maximise the total cost or minimise the network flow capacity (Israeli and Wood 2002;Zhang, Sun, and Wang 2016). The connection is the greatest concern of these models, while the capacity and cost are often neglected. Our work adopts a scenario planning approach to determine the tradeoffs between the total cost and risk. The uncertainty in the demand is represented by several scenarios for which an occurrence probability is specified. A twostage stochastic mixed-integer biobjective programming model is proposed to simultaneously determine the setup cost and protection investment of hubs, total transportation cost, and total handling cost to minimise the total cost and risk.
CPLEX is not feasible for large instances of stochastic programming models because of memory and space limitations (Cui et al. 2012;Xuan et al. 2012;Cai et al. 2014;Xue et al. 2015). A progressive hedging algorithm (PHA) has been widely employed to solve various problems (Nedjah and Mourelle 2015;Rockafellar and Wets 1991). Gul, Denton, and Fowler (2015) proposed a multistage stochastic mixed-integer programming formulation for the assignment of surgeries to operating rooms during a finite planning period and implemented a PHA to obtain near-optimal surgery schedules. Kim, Wu, and Huang (2015) presented a multiperiod news vendor model, which was formulated as a multistage stochastic programming model with integer recourse decisions and extended the PHA to solve efficiently the model. Veliz et al. (2015) proposed medium-term forest planning with an integrated approach considering both harvesting and road construction decisions in the presence of uncertainty modelled as a multistage problem and demonstrated that a scenario-based PHA performed competitively. The PHA is adopted to solve the proposed two-stage stochastic programming model in our work.
A typical SCN comprises several distinct components. Suppliers generate products, and hubs reprocess these products and distribute them to customers. The design of reliable SCNs can be accomplished via both network formulation and location-allocation decisions considering the total cost and risk. Our work features the following contributions to the literature.
(1) We provide a multiobjective mixed-integer formulation of the SCN design problem considering disruption. The model determines hub facility locations, protection level of each facility, and distribution routes for products. The cost includes construction, protection, handling and transportation costs, while the risk includes facility disruption and production shortage costs. The objectives aim to minimise the total cost and total risk. Compared to the traditional one-objective model, our model is more reasonable and more practical in terms of actual applications. In particular, we introduce a new parameter, namely, the protection level, which could link cost and risk decisions well during the planning phase of SCNs.
(2) The PHA is applied in our work to efficiently solve the proposed problem. This algorithm decomposes the problem into a number of scenario subproblems and quickly solves each scenario. An optimal solution can be easily obtained within an acceptable amount of time, which is very important in practical applications.
(3) We conduct a case study involving districts in Shanghai, China. Numerical results and their sensitivity to various parameters are presented. Additionally, the tradeoff curve between the cost and risk is provided, and useful managerial insights are proposed.
The rest of the paper is organised as follows: in the next section, we define the problem and propose a corresponding stochastic biobjective programming model. In Section 3, we introduce the PHA to solve the above problem. In Section 4, a case study involving select districts in Shanghai, China, is presented. In the last section, we conclude this work with a summary and provide suggestions for future research.

Problem definition and mathematical formulation
In a typical SCN, there are always three distinct components, i.e. supply facilities (suppliers), storage facilities (hubs), and demand facilities (customers) as shown in Figure 1. The arcs in the network represent the connections among the nodes and the transportation costs. A supplier manufactures a certain product, a hub processes and delivers this product, and a customer consumes the product. For example, in an electricity network, a power plant is the supplier, a transformer substation is the hub, and a factory or resident is the customer. This paper proposes a new mathematical model to minimise two conflicting objectives (the total cost and total risk). The main function of critical infrastructures is to satisfy the demand. Hence, our model is a demand-driven model. The model aims to choose potential suppliers and hubs from a node set and considers product distribution routes to satisfy the given demand while determining the protection level of each hub to minimise the total risk.
It is supposed that suppliers are established in advance, which is reasonable for SCNs. Therefore, our model is primarily designed to address the following issues: (1) where to establish a hub; (2) how to decide the protection level to reduce the risk; (3) which suppliers should be selected for each facility; and (4) how products are transported.
Let G = (N, A) represent an SCN, where N is the set of nodes and A is the set of directed arcs. Let S represent the set of suppliers, H the set of hubs, and C the set of customers. Note that N = S ∪ H ∪ C. The directed arcs only extend from S to H and from H to C. Each customer i ∈ C exhibits an uncertain demand d ξ i , which is modelled through the application of a set of discrete scenarios indexed with ξ , and each scenario is assigned a certain probability of occurrence, i.e. p ξ . The setup cost of hub j is f j and the handling capacity of hub j is u j . The supply of supplier k ∈ S is denoted as s k . The transportation cost from any node pair (i, j) is c ij . Let λ j represent the cost of product handling.
Any risk could result in an economic loss. Therefore, we quantify the risk with the cost, including facility protection and production shortage costs. These two cost components are common in practice. The electricity system of a city is chosen as an example. The facility protection cost could be regarded as the cost to protect and repair any damaged transformer substations (hubs) periodically. The production shortage cost could be regarded as the production loss (customers) attributed to a power shortage. In this paper, we concentrate on the protection of hubs because the protection cost associated with the above arcs may be included in the hub protection cost. In addition, we do not consider the setup cost of the suppliers, material cost, and inventory but concentrate on the cost and risk tradeoff of the whole network. There are three sets of decision variables in the model, namely, hub variables (y j ), flow variables (x ξ (ij) ), and protection variables (z j ). In detail, the following applies: where x ξ (ij) is the flow of products from nodes i to j and z j is the protection level of facility j.
Let z j ∈ {0, 1, . . . , Q} represent the protection level. A higher z j value suggests advanced equipment or technology or a lower risk at a higher cost. We assume that regarding hub j, the investment to execute protection measures g j (z j ) is a monotonically increasing function of z j , and the risk factor of hubs w j (z j ) is a monotonically decreasing function of z j , namely, a higher investment suggests a lower risk. Alternatively, the higher the investment is, the higher the resilience. Moreover, we assume that u j = u j (z j ), where u j is also a monotonic increasing function of z j . With a higher protection level, a hub maintains a higher capacity. The protection cost is related to the product amount and risk factor of hubs under all scenarios. Let θ i represent the risk factor of not serving customer i. In practice, θ i could be considered the importance of customer i. A higher θ i value suggests more important customers. For example, from an economic perspective, developed areas are more important than are developing areas. When power shortages occur, a higher cost is incurred if the power supply is cut off in developed areas than that incurred when the power supply is cut off in developing areas. The production shortage cost is related to products whose demands are not satisfied and the risk factor of not serving customers under all scenarios.
We formulate this problem as a stochastic multiobjective problem. The objectives are as follows: Objective ω 1 computes the total cost, where the first part describes the setup cost of the hubs, the second part describes the protection investment of the hubs, the third part denotes the total transportation cost, and the last part denotes the total handling cost. Objective ω 2 computes the total risk of the hubs and the production shortage risk.
The reliability network design problem (RNDP) is formulated as follows: The objective function (4) is straightforward. Our model minimises the weighted sum αω 1 + (1 − α)ω 2 of the two objectives, where ω 1 denotes the total cost, ω 2 denotes the total risk, and 0 < α < 1. By solving the problem considering various values of α, we can generate a tradeoff curve between these two objectives. Then, the decision maker can formulate decisions according to his or her risk or cost preference. Furthermore, the tradeoff curve can indicate the degree to which one objective must be sacrificed to improve the other objective. Constraint (5) ensures that the flow in and out of a hub remains balanced under all scenarios. Constraint (6) requires that the demand is entirely satisfied. Constraint (7) insists that the flow originating from a supplier should not exceed its supply. Constraint (8) safeguards that product handling at a hub does not exceed its capacity and ensures that product manufacturing does not occur when the hub is inactive. Constraint (9) ensures that only active hubs are protected and that the protection level does not exceed the highest level. Constraint (10) guarantees that no negative flows occur. Constraint (11) states that y j is a binary number. Constraint (12) ensures that the protection level adheres to its defined range. Note that the model is a stochastic nonlinear model. We intend to transform this model into a stochastic mixed-integer programming model to solve the problem. For a given hub, one and only one protection level can be selected. Hence, we define a new variable as follows: We can obtain the following lemma.
Lemma 2.1: z j = q∈Q z jq q, q∈Q z jq = y j , and ∀j ∈ H.
Next, we define a sequence of variables such that the following applies: Via these transformations, the protection investment and risk and capacity of hubs become fixed constants, and the case in which two variables are multiplied in the objective is avoided. We now define a new variable, namely, f jq = g jq + f j , ∀j ∈ H, ∀q ∈ Q. Then, y j is eliminated.
The objectives of the model are transformed into: Note that Equation (18) We then rewrite ω 2 as: Through this transformation, ω 2 becomes linear. A two-stage stochastic mixed-integer programming model (the above-mentioned RNDP) is proposed as follows: subject to constraints (5), (6), (7), (10), and (19), and the following is obtained: L ξ kjq ≥ 0 ∀k ∈ S, ∀j ∈ H, ∀q ∈ Q, ∀ξ ∈ The first part of Equation (21) encompasses the setup and protection costs (ω 1 1 ), the second part is the transportation cost (ω 2 1 ), the third part is the handling cost (ω 3 1 ), the fourth part is the risk of the hubs (ω 1 2 ), and the last part is the product shortage risk (ω 2 2 ). The meaning of Equation (22) is the same as that of Equation (8). Constraint (23) ensures that one hub can choose one and only one protection level. Constraints (24) and (25) define the range and type of the variables.

Solution approach
For small-size stochastic programming problems, it is conceptually possible to convert the SP into an equivalent deterministic program and solve it (i.e. in extensive form) using commercial software (e.g. CPLEX). However, their computation time is increase exponentially as the size of the problem grows. Decomposition algorithms, such as stage-based (e.g. L-shaped method) and scenario-based (e.g. progressive hedging), can avoid this challenge by decomposing the original problem into a series of subproblems. They are thus usually often applied for solving large-scale problems.
We introduce an adaptation of the PHA to solve the proposed RNDP. The PHA was first proposed by Rockafellar and Wets (1991) based on scenario decomposition, which is not limited to problems with convexity and can be applied to stochastic mixed-integer programs. For various scenarios, the PHA decomposes a given problem into a number of scenario subproblems and separately solves each scenario. The method moves the nonanticipativity constraints to the objective function as penalty terms with Lagrange multipliers and penalty parameters. All scenario subproblems are independently solved until the nonanticipativity constraints are satisfied within a prespecified termination threshold (Kim, Wu, and Huang 2015).
To facilitate the generation of a separable stochastic program, we define a new decision variable z ξη jq = 1, which represents hub j with protection level q under scenario ξ in iteration η. z ξη jq denotes the solutions of all scenario subproblems. To ensure that the solutions of the scenario subproblems are also solutions of the RNDP, nonanticipativity constraints must be considered, as expressed in constraint (26), wherez The augmented Lagrangian relaxation technique is usually applied to relax the nonanticipativity constraints, which are moved into the objective function as penalty terms with Lagrangian multipliers and penalty parameters (Hu et al. 2019). The objective function of the RNDP is transformed as follows: Because the first-stage variable z ξη jq is a binary variable, the quadratic term in step 4 can be avoided. We know that ||z  (27) can be rewritten as follows: To accelerate the PHA, we propose a strategy to update coefficient f (the setup cost of the hub), which is described in Equation (29), where δ ∈ (0, 1) is the threshold value and β > 1 is a parameter to adjust the value of f over successive iterations.
For hub j with protection level q, a small value ofz η−1 jq indicates that hub j is selected only in a small number of scenarios, while a large value ofz η−1 jq indicates that hub j is selected in the majority of all scenarios. Therefore, we increase the setup cost f so that the subproblems tend to avoid the selection of hub j when the value ofz η−1 jq is lower than the given threshold. In contrast, we decrease the setup cost f to ensure that hub j is more likely to be selected in the subproblems when the value ofz η−1 jq is higher than the given threshold. The values of δ min , δ max and β are obtained in the next section.
To avoid quick PHA convergence (a good solution may not be obtained). We usually define large δ max and small δ min values, e.g. δ max = 0.8 and δ min = 0.2, respectively. Although the PHA can eventually force z ξη jq andz η jq to be equal, many iterations are required (which is a very timeconsuming task) for complex stochastic integer programming problems. We thus introduce the following strategy to accelerate the PHA. The meaning is similar to that of Equation (28). However, Equation (29) is implemented whenz η jq continuously satisfies a certain condition (i.e. within a given threshold interval) over several PHA iterations. For instance, let f The implementation process of the PHA is explained below.
Step Description 1: Algorithm terminates = false is set, the iteration index is η = 0, the penalty parameter is ρ η = 0.01, and the termination parameter is ε = 0.001.

Case study
To illustrate the capabilities of the proposed model, we solve the problem of reliable SCN design with a case study involving districts in Shanghai, China. We assume that there are four suppliers (nodes 1, 4, 7, and 14), seven hubs (1, 3, 4, 7, 9, 11, and 14), seventeen customers (nodes 1-17), four protection levels (A, B, C, and D, from low to high costs) and five scenarios (VL, L, N, H, and VH, with the demand in ascending order). The population density of the districts is adopted as the demand under the baseline scenario. We define demand levels of 60%, 80%, 120%, and 140% of the baseline demand under the other four scenarios. Intuitively, severe emergency events cause a very demand with low probabilities. We thus set a high probability under the scenarios with lower demands and define a low probability under the scenarios with higher demands. The probabilities of the scenarios are 0.3, 0.3, 0.2, 0.1, and 0.1. The case area is shown in Figure 2, where all 17 districts are customers. The production needed is proportional to the population density of the districts, and the setup cost is proportional to the per capita gross domestic product (GDP). The transportation cost between any pair of nodes is proportional to the shortest distance between these nodes. The 17 districts and the corresponding population density and per capita GDP values are given in Table A1. The shortest distance matrix between the districts is summarised in Table A2. Districts with a higher per capita GDP exhibit a lower economic level and can build hubs with a higher capacity. In other words, the hub capacity is negatively proportional to the per capita GDP. Enough production is provided by the suppliers. Detailed information is listed in a supplementary file. Solutions are obtained with the PHA approach and optimisation software CPLEX 12.5. The software is run on an Intel Core i7-5500U 2.4-GHz processor with 4.0 GB of RAM in a Windows 10 environment.

Numerical analysis
The risk-related weight (α) exerts a major impact on the cost and risk. Let α occur in (0, 0.05, 0.1, . . . , 0.95, 1), and we can analyse the relationship between α and the objectives, as shown in Figure 3. It is obvious that the results are sensitive to the risk acceptability level. With increasing α, ω 1 decreases and ω 2 increases in a stepwise manner. We divide the risk approval level into 4 intervals, i.e. [0,0.4], [0.4,0.6], [0.6,0.8], and [0.8,1]. Decision makers can determine the appropriate risk level according to their budget constraints, because the essence of risk is still cost, and the difference is decision makers value the cost of prevention beforehand or the cost of remediation afterwards. For the SCN, prevention is far better than remedy, so more of the budget may be spent on prevention.  We construct a tradeoff curve in this case, and the results are shown in Figure 4. The horizontal axis indicates the total cost (ω 1 ), while the vertical axis indicates the total risk (ω 2 ). The steepness of the curve indicates that large improvements in reliability can be attained with small increases in the total cost when α is relatively small. As α decreases from 1 to 0, the cost increases from 0 to 280,539, thus contributing to a decrease of 95.8% in the risk. However, decision makers may show little interest in solutions when α is larger than 0.5 because more hubs with high protection levels are active for these values. The network is more reliable but is too expensive to implement. For example, for α = 0.2, the selected hubs (protection level) are 7(D), 11(D), and 14(D), and the risk of product shortage is just 8,495. A high total cost of 108,951 yields a low total risk of 15,739. In contrast, for α = 0.8, only 7(A) is selected as a hub (protection level), and the product shortage risk reaches 108,838. A relatively low total cost of 17,630 leads to a high total risk of 113,223. The model tends to select more hubs and reinforces the corresponding protection levels with a higher risk-related weight, thus resulting in a lower risk for these hubs and unsatisfied demands.
The results for the different risk acceptance levels and scenario combinations are shown in Figure 5, where missing nodes indicate no supply. Under the determined scenario N, with increasing α, fewer hubs are set up, and fewer customers are satisfied to reduce the cost. We could consider that for α = 0.3, production is essential and important to customers, and decision makers would rather pay higher costs to satisfy the demands, and vice versa. Based on Figure 5(c,d), we find that considering the cost, the hubs set up in the central area and near the customer demands can more easily satisfy these demands. Moreover, node 7 is a very important node in the entire network, and the protection level is also higher than in other scenarios.
The model is tremendously impacted when variety is important to customers. Let α be 0.5, and the sensitivity analysis results for θ i are listed in Table 1. The penalty induced by unsatisfied demands tends to increase at a lower level of customer importance. This occurs because fewer hubs are selected, while active hubs are associated with a lower protection level, resulting in fewer products delivered. While increasing the importance of customers, the penalties induced by any unsatisfied demands are reduced. In this sense, customer information has a great impact on the design of SCN. The blockchain technology can realise real-time information update and break the information asymmetry among participants, that will benefit decision makers greatly and make the SCN be more flexible and customer-oriented. The geography and long-term relationships are going to become less important, and supply chain management will be more efficient.
In the case study problem, there are 4 suppliers, 7 hubs, 17 customers, 4 protection levels, and 5 scenarios.  The optimal solution with an objective function value of 53,279 yen can be obtained with CPLEX 12.5 software within 1 s, and the same optimal solution and objective function value can be obtained with the PHA within 10 s. Obviously, it is easier to solve a relatively small problem with CPLEX software than with the PHA. However, with increasing problem size (i.e. an increasing number of suppliers, hubs, customers, protection levels, and scenarios), the use of CPLEX software is not feasible because of memory and space limitations. For example, given a problem with 15 suppliers, 30 hubs, 100 customers, 10 protection levels, and 100 scenarios, which involves more than 1 million variables and 500,000 constraints, CPLEX software is not feasible due to memory limitations, while the PHA could yield a near-optimal solution within 3,000 s, and each scenario subproblem can be solved within 1 s.

Performance of the solution approach
This subsection evaluates the efficiency of the adopted PHA. All experiments were conducted on a PC in Windows 10 with an Intel 3.10-GHz dual-core processor CPU and 32 GB of memory. The PHA was coded in MATLAB and CPLEX 12.5 was called to solve the scenario subproblems. We also used CPLEX 12.5 to solve the RNDP with a maximum running time of 3,600 s, i.e. the best solution is obtained within 3,600 s. Table 2 presents the performance of CPLEX software and the PHA for the different The results indicate that for CPLEX, with increasing problem size, the computing time increases exponentially. Regarding the PHA, the computing time linearly varies with increasing problem size. This occurs because a single scenario subproblem can be solved in less than 1 s, and time is only consumed to repeatedly solve the scenario subproblems. Except for an experiment involving 30 hubs, 100 customers and 100 scenarios, the optimal solutions of the other experiments can be obtained in CPLEX. Compared to CPLEX, the PHA can generate a good solution for large problems in less time (e.g. the experiments encompassing 100 customers). In particular, for an experiment involving 30 hubs, 100 customers, and 100 scenarios, the PHA even obtains a better upper bound than does CPLEX. In summary, it is easier to solve small problems in CPLEX, while the PHA performs better than does CPLEX for large problems.

Conclusions
In this paper, we propose a new stochastic mixed-integer programming model that incorporates reliability issues into classical network design problems. The starting point of the model is the realisation that disruption and production shortage risks should be considered despite a certain cost and problem complexity increase. We introduce the concept of protection. Different protection levels correspond to varying disruption probabilities and handling capacities of hubs. Tradeoffs should be determined between the total cost and risk. We adopt the PHA to solve the established model. The case study demonstrates that a statistically insignificant increase in cost may yield a significant reduction in the risk. This is critical for decision makers associated with SCNs, as different types of cost indicators (CIs) should be treated according to distinct risk acceptance levels to hedge against uncertain demands.
The proposed approach could be of interest when modelling and solving more general network design problems under uncertainty. The main drawback of our model is the assumption that we only consider node disruption and protection while ignoring arc disruption and protection. This becomes reasonable only when arc disruption can be transformed into node disruption. However, if budget constraints apply, this assumption is not always realistic when arc disruptions occur more frequently. Moreover, the consideration of two conflicting objectives remains an important issue to be examined. An evolutionary multiobjective optimisation method could determine the Pareto optimal front and consider more parameters in practice. The aforementioned topic is the subject of our ongoing research.
Junliang He is an Associate Professor at