*Review* **Liver Transplantation in Patients with Hepatocellular Carcinoma beyond the Milan Criteria: A Comprehensive Review**

**Pierluigi Toniutto \*, Elisa Fumolo, Ezio Fornasiere and Davide Bitetto**

Hepatology and Liver Transplantation Unit, Azienda Sanitaria Universitaria Integrata, 33100 Udine, Italy<EMAIL_ADDRESS>(E.F<EMAIL_ADDRESS>(E.F<EMAIL_ADDRESS>(D.B.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +39-0432-552636; Fax: +39-0432-559487

**Abstract:** The Milan criteria (MC) were developed more than 20 years ago and are still considered the benchmark for liver transplantation (LT) in patients with hepatocellular carcinoma (HCC). However, the strict application of MC might exclude some patients who may receive a clinical benefit of LT. Several expanded criteria have been proposed. Some of these consider pretransplant morphological and biological variables of the tumor, others consider post-LT variables such as the histology of the tumor, and others combine pre- and post-LT variables. More recently, the HCC response to locoregional treatments before transplantation emerged as a surrogate marker of the biological aggressiveness of the tumor to be used as a better selection criterion for LT in patients beyond the MC at presentation. This essential review aims to present the current data on the pretransplant selection criteria for LT in patients with HCC exceeding the MC at presentation based on morphological and histological characteristics of the tumor and to critically discuss those that have been validated in clinical practice. Moreover, the role of HCC biological markers and the tumor response to downstaging procedures as new tools for selecting patients with a tumor burden outside of the MC for LT is evaluated.

**Keywords:** hepatocellular carcinoma; liver transplantation; Milan criteria; alpha-fetoprotein


**Acknowledgements**

This research was funded by ERA-NET Manunet project Contract no. 28/2018 TexEMFiRe—"Manufacturing textiles with electromagnetic shielding and fireretardant properties by plasma based methods."


**4. Simulation results**

A Matlab/Simulink simulation environment has been designed for the VSI-fed asynchronous asymmetrical dual three-phase induction machine, and simulations have been done to prove the efficiency of the scheme proposed. Numerical integration using fourth order Runge-Kutta

3 12 active, corresponding to the largest vectors in the (*α* − *β*) subspace and the smallest ones in the (*x* − *y*) subspace plus a zero vector.

algorithm has been applied to compute the evolution of the state variables step by step in the time domain. Table 3 shows the electrical and mechanical parameters for the asymmetrical dual three-phase induction machine.

**Table 3.** Parameters of the asymmetrical dual three-phase induction machine

Computer simulations allow valuing the effectiveness of the proposed control system under unload and full-load conditions, with respect to the mean squared error (MSE) of the speed and stator current tracking. In all cases is considered a sampling frequency of 6.5 kHz, and that the initial conditions of the covariance matrix (*ϕ*(0)), and the process and measurement noise, are known. The Kalman Filter has been started with the following initial conditions; *ϕ*(0) = *diag* 1111 , in order to indicate that the initial uncertainty (rms) of the state variables is 1 A. Because *ϕ*(*k*) is time varying, the KF gain is sensitive to this initial condition estimate during the initial transient, but the steady final values are not affected [11]. The magnitudes of the process noise (*R�*) and measurement noise (*Rν*) are known and are generate using a Random Source block of the Simulink Signal Processing Blockset, assuming the following values, *R�* = 15 × 10−3 and *Rν* = 25 × 10−3, respectively.

### **4.1. Efficiency of current control loop**

10 Induction Motor

The predictive model should be used 64 times to consider all possible voltage vectors. However, the redundancy of the switching states results in only 49 different vectors (48 active and 1 null) as shown on Figure 2. This consideration is commonly known as the optimal solution. The number of voltage vectors to evaluate the predictive model can be further reduced if only the 12 outer vectors (the largest ones) are considered. This assumption is commonly used if sinusoidal output voltage is required and it is not necessary to synthesize (*x* − *y*) components. In this way, the optimizer can be implemented using only 13 possible stator voltage vectors3. This way of proceeding increases the speed at which the optimizer can be run, allowing decreasing the sampling time at the cost of losing optimality. A detailed study of the implications of considering the optimal solution can be found at [6]. For a generic multi-phase machine, where *f* is the number of phase and *ε* the search space (49 or 13 vectors), the control algorithm proposed produces the optimum gating signal combination

*3.2.2. Optimizer*

*Sopt* as follows:

**Algorithm 1** Proposed algorithm

**comment:** Optimization algorithm

**K***e*(*k*) = **Γ**(*k*) · **C***TRν*

**S***i* ← **S***i*,*j* ∀ *j* = 1, ..., *f*

*Jo* ← *J*, **S***opt* ← **S***i*

*Jo* := ∞, *i* := 1 **while** *i* ≤ *ε* **do**

*Uαβxys* =

**if** *J* < *Jo* **then**

**4. Simulation results**

plus a zero vector.

**end if** *i* := *i* + 1 **end while**

**comment:** Compute the covariance matrix. Equation 23 **Γ**(*k*) = *ϕ*(*k*) − *ϕ*(*k*) · **C***T*(**C** · *ϕ*(*k*) · **C***T* + *Rν*)−1 · **C** · *ϕ*(*k*) **comment:** Compute the KF gain matrix. Equation 22

**comment:** Compute stator voltages. Equation 12

**comment:** Compute the cost function. Equation 25

*T*

**comment:** Compute the correction of the covariance matrix. Equation 24

**comment:** Compute a prediction of the state. Equation 15

= *Vdc* · **T** · **M**

A Matlab/Simulink simulation environment has been designed for the VSI-fed asynchronous asymmetrical dual three-phase induction machine, and simulations have been done to prove the efficiency of the scheme proposed. Numerical integration using fourth order Runge-Kutta

3 12 active, corresponding to the largest vectors in the (*α* − *β*) subspace and the smallest ones in the (*x* − *y*) subspace

*uαs*, *uβs*, *uxs*, *uys*, 0, 0

**X**ˆ(*k* + 1|*k*) = **AX**(*k*) + **BU**(*k*) + **H***�*(*k*)

*J* =� *e*ˆ*iαs*(*k* + 1|*k*) + *e*ˆ*iβs*(*k* + 1|*k*) �2

*ϕ*(*k* + 1) = **A** · **Γ**(*k*) · **A***T* + **H** · *R�* · **H***T*

A series of simulation tests are performed in order to verify the efficiency of current control loop in three points of operation of the machine. Figure 5 shows the current tracking in stationary reference frame (*α* − *β*) and (*x* − *y*) subspaces considering sub-optimal solution in the optimization process (12 active and 1 null vectors). The predicted stator current in the *α* component is shown in the upper side (zoom graphs and green curves). For all cases of analysis efficiency is measured with respect to the MSE of the currents tracking in (*α* − *β*)-(*x* − *y*) subspaces and the total harmonic distortion (THD), defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency, obtained from the Powergui-Continuous Simulink block. A 2.5 A reference stator current at 12 Hz is established for the case of Figure 5 (a). Figure 5 (b) shows the current tracking in the (*α* − *β*) and (*x* − *y*) subspaces using a 2 A reference stator current at 18 Hz and Figure 5 (c) shows the current tracking in stationary reference frame using a 1.5 A reference stator current at 36 Hz. Table 4 summarizes the results of the three previous trials where are considered different amplitudes and angular frequencies for the reference current.

From the obtained results can be emphasized as follows:

c. As increases the frequency of the reference currents the switching frequency decreases, consequently there is a degradation in the THD of the stator currents as can be seen in

The Asymmetrical Dual Three-Phase Induction Machine and the MBPC in the Speed Control 397

The structure of the proposed speed control for the asymmetrical dual three-phase induction machine based on a KF is shown in Figure 6. The process of calculation of the slip frequency (*ωsl*) is performed in the same manner as the Indirect Field Orientation methods, from the

machine (*Rr*, *Lr*) [13, 14]. The inner loop of the current control, based on the MBPC selects control actions solving an optimization problem at each sampling period using a real system model to predict the outputs. As the rotor current can not be measured directly, it should be estimated using a reduced order estimator based on an optimal recursive estimation algorithm

**Figure 6.** Proposed speed control technique based on KF for the asymmetrical dual three-phase

Different cost functions (*J*) can be used, to express different control criteria. The absolute current error, in stationary reference frame (*α* − *β*) for the next sampling instant is normally used for computational simplicity. In this case, the cost function is defined as Equation

which is computationally obtained using the predictive model. However, other cost functions can be established, including harmonics minimization, switching stress or VSI losses [6]. Proportional integral (PI) controller is used in the speed control loop, based on the indirect vector control schema because of its simplicity. In the indirect vector control scheme, PI speed

reference used by the predictive model is obtained from the calculation of the electric angle used to convert the current reference, originally in dynamic reference frame (*d* − *q*), to static

*s* is the stator reference current and *iαβ*(*k* + 1|*k*) is the predicted stator current

∗

∗ *ds*, *i* ∗

*qs*) and the electrical parameters of the

*ds* in dynamic reference frame. The current

Table 4

from the Equations 21-24.

induction machine

∗

controller is used to generate the reference current *i*

reference frame (*α* − *β*) as shown in Figure 6.

25, where *i*

**4.2. Proposed speed control method**

reference currents in dynamic reference frame (*i*

**Table 4.** Simulation results obtained from Figure 5

**Figure 5.** Stator current in (*α* − *β*) component tracking and (*x* − *y*) current components. (a) 2.5 A (peak) current reference at 12 Hz. (b) 2 A current reference at 18 Hz and (c) 1.5 A current reference at 36 Hz

c. As increases the frequency of the reference currents the switching frequency decreases, consequently there is a degradation in the THD of the stator currents as can be seen in Table 4

### **4.2. Proposed speed control method**

12 Induction Motor

Method Test MSE*α*, MSE*β* MSE*x*, MSE*y* THD*α*, THD*β*

(a) (b) (c)

4 0.005 0.015 0.025 1.5 2 2.5

Time [s]

0 0.05 0.1 0.15 -4

Time [s]

0 0.05 0.1 0.15 -4

Time [s]

0 0.05 0.1 0.15 -4

**Figure 5.** Stator current in (*α* − *β*) component tracking and (*x* − *y*) current components. (a) 2.5 A (peak) current reference at 12 Hz. (b) 2 A current reference at 18 Hz and (c) 1.5 A current reference at 36 Hz

a. The MBPC is a flexible approach that, opposite to PWM based control methods, allows a straightforward generalization to different requirements only changing the cost function b. The MBPC method is discontinuous technique, so the switching frequency is unknown. This feature reduces the switching losses (compared to continuous techniques) at expense

**Table 4.** Simulation results obtained from Figure 5

Time [s]

0 0.05 0.1 0.15 -4

*ia, i\*a* [A]

*iß, i\*ß* [A]

0

2

4

0

2

4 0.01 0.02 0.03 2 2.5 3

*ix, iy* [A]

0

2

4

*i* \* *i*

 *i* \* *i i*

*yi xi*

of an increase in the harmonics of the stator current

*iß, i\*ß* [A]

0

2

4

*ia, i\*a* [A]

0

2

*ix, iy* [A]

0

2

4

Time [s]

0 0.05 0.1 0.15 -4

Time [s]

0 0.05 0.1 0.15 -4

(a) 0.2105, 0.2322 0.9298, 0.9304 7.1330,7.5969 MBPC (b) 0.1989, 0.2141 1.0957, 1.0885 10.3610, 11.8192

(c) 0.2287, 0.2348 1.2266, 1.3102 15.8951, 17.4362

 *i* \* *i i*

*i* \* *i*

*ia, i\*a* [A]

0

2

4 4 6 8 10 12

1 1.5 2

*iß, i\*ß* [A]

0

2

4

*ix, iy* [A]

0

2

4

Time [s]

0 0.05 0.1 0.15 -4

x 10-3

*i* \* *i*

 *i* \* *i i*

*y i xi*

Time [s]

0 0.05 0.1 0.15 -4

Time [s]

0 0.05 0.1 0.15 -4

*y i xi* The structure of the proposed speed control for the asymmetrical dual three-phase induction machine based on a KF is shown in Figure 6. The process of calculation of the slip frequency (*ωsl*) is performed in the same manner as the Indirect Field Orientation methods, from the reference currents in dynamic reference frame (*i* ∗ *ds*, *i* ∗ *qs*) and the electrical parameters of the machine (*Rr*, *Lr*) [13, 14]. The inner loop of the current control, based on the MBPC selects control actions solving an optimization problem at each sampling period using a real system model to predict the outputs. As the rotor current can not be measured directly, it should be estimated using a reduced order estimator based on an optimal recursive estimation algorithm from the Equations 21-24.

**Figure 6.** Proposed speed control technique based on KF for the asymmetrical dual three-phase induction machine

Different cost functions (*J*) can be used, to express different control criteria. The absolute current error, in stationary reference frame (*α* − *β*) for the next sampling instant is normally used for computational simplicity. In this case, the cost function is defined as Equation 25, where *i* ∗ *s* is the stator reference current and *iαβ*(*k* + 1|*k*) is the predicted stator current which is computationally obtained using the predictive model. However, other cost functions can be established, including harmonics minimization, switching stress or VSI losses [6]. Proportional integral (PI) controller is used in the speed control loop, based on the indirect vector control schema because of its simplicity. In the indirect vector control scheme, PI speed controller is used to generate the reference current *i* ∗ *ds* in dynamic reference frame. The current reference used by the predictive model is obtained from the calculation of the electric angle used to convert the current reference, originally in dynamic reference frame (*d* − *q*), to static reference frame (*α* − *β*) as shown in Figure 6.

performance of the proposed algorithm, based on a Kalman Filter. The estimated rotor current converges to real values for these test conditions as shown in figures, proving that the observer

The Asymmetrical Dual Three-Phase Induction Machine and the MBPC in the Speed Control 399

In this chapter a new approach for the speed control of the asymmetrical dual three-phase induction machine has been proposed and evaluated. The speed control scheme uses an inner loop predictive current control based on the model, where the main advantage is the absence of modulation techniques. The MBPC is described using a state-space representation, where the rotor and stator current are the states variables. The proposed algorithm provides an optimal estimation of the rotor current in each sampling time in a recursive manner, even when internal parameters of the drive are not precisely known, and the measurements of the state variables are perturbed by gaussian noise. The theoretical development based on a Kalman Filter has been validated by simulations results. The method has proven to be efficient

The author gratefully the Paraguay Government for the economical support provided by means of a Conacyt Grant (project 10INV01). Also, wishes to express his gratitude to the

[1] Levi, E. (2008). Multiphase electric machines for variable-speed applications. *IEEE Transactions on Industrial Electronics*, Vol. 55, No. 5, (May 2008) page numbers

[2] Bucknal R. & Ciaramella, K. (2010). On the Conceptual Design and Performance of a Matrix Converter for Marine Electric Propulsion. *IEEE Transactions on Power Electronics*,

[3] Zhao Y. & Lipo, T. (1995). Space vector PWM control of dual three-phase induction machine using vector space decomposition. *IEEE Transactions on Industry Applications*,

[4] Boglietti, A.; Bojoi, R.; Cavagnino, A.& Tenconi, A. (2008). Efficiency Analysis of PWM Inverter Fed Three-Phase and Dual Three-Phase High Frequency Induction Machines for Low/Medium Power Applications. *IEEE Transactions on Industrial Electronics*, Vol.

[5] Arahal, M.; Barrero, F.; Toral, S.; Durán, M.; & Gregor, R. (2008). Multi-phase current control using finite-state model-predictive control. *Control Engineering Practice*, Vol. 17,

Vol. 25, No. 6, (June 2010) page numbers (1497-1508), ISSN 0885-8993

55, No. 5, (May 2008) page numbers (2015-2023), ISSN 0278-0046

No. 5, (October 2008) page numbers (579-587), ISSN 0967-0661

Vol. 31, No. 5, (October 1995) page numbers (1100-1109), ISSN 0093-9994

even when considering that the machine is operating under varying load regimes.

anonymous reviewers for their helpful comments and suggestions.

*Engineering Faculty of the National University of Asunción Department of Power and Control Systems, Asunción-Paraguay*

performance is satisfactory.

**5. Conclusions**

**Acknowledgments**

**Author details**

**6. References**

Raúl Igmar Gregor Recalde

(1893-1909), ISSN 0278-0046

(a) Simulation results for a ±320 rpm step wave speed comand tracking (b) Simulation results for a ±2.5 A step in the reference current comand tracking

(c) Simulation results for a 50 Nm trapezoidal load

**Figure 7.** Simulation results for a proposed speed control. The predicted stator current in the *α* component is shown in the upper side (zoom graphs, red curves)

Figure 7 (a) shows simulation results for a 200 revolutions per minute (rpm) trapezoidal speed reference, if we consider a fixed current reference (*i* ∗ *ds* = 1 A). The subscripts (*α* − *β*) represent quantities in the stationary frame reference of the stator currents. The measurement speed is fed back in the closed loop for speed regulation and a PI controller is used in the speed regulation loop as shown in Figure 6. The predicted stator current in the *α* component is shown in the upper side (zoom graph, red curve). Under these test conditions, the MSE in the speed and current tracking are 0.75 rpm and 0.15 A, respectively. Figure 7 (b) shows the step response for the induction machine to a change of ±2.5 A in the current reference (*i* ∗ *ds* see Figure 6), if we consider a fixed speed reference (*ω*∗ *r* = 200 rpm). In these simulation results, the subscripts (*α* − *β*) represent the stator current in stationary reference frame. Under these test conditions, the MSE in the stator current tracking are 0.1 A for the reference current (*i* ∗ *ds*) and 0.18 A considering stationary reference frame. Finally, Figure 7 (c) shows a trapezoidal load application response, and the rotor current evolution (measured and observed) in stationary reference frame. These simulation results substantiate the expected performance of the proposed algorithm, based on a Kalman Filter. The estimated rotor current converges to real values for these test conditions as shown in figures, proving that the observer performance is satisfactory.


**Analytical Chemistry Today and Tomorrow**

## Miguel Valcárcel

92 Analytical Chemistry

ed. Belmont: Thomson 2004.

[40] Skoog DA, West DM, Holler EJ, Crouch SR. Fundamentals of Analytical Chemistry. 8

[41] The Merck Index, Merck Research Laboratories, New York, 1996.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50497

## **1. Introduction**

Dealing with Analytical Chemistry in isolation is a gross error [1]. In fact, real advances in Science and Technology —rather than redundancies with a low added value on similar topics— occur at interfaces, which are boundaries, crossroads —rather than barriers between scientific and technical disciplines mutually profiting from their particular approaches and synergistic effects. Figure 1 depicts various types of interfaces involving Analytical Chemistry.

**Figure 1.** Analytical Chemistry at various interfaces. (1) Internal and interdisciplinary interfaces in the realm of Chemistry. (2) Interfaces with norms and guides. For details, see text.

© 2012 Valcárcel, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Valcárcel, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Analytical Chemistry should in fact be present at a variety of interfaces such as those of Figure 1.1. Two belong to the realm of Chemistry (the framework of reference), namely:

Analytical Chemistry Today and Tomorrow 95

**Figure 2.** Analytical Chemistry is a discipline of Chemistry (C) inasmuch as it is responsible for "Analysis", an essential component of Chemistry in addition to theory, synthesis and applications in

These four general definitions have been used to formulate various more conventional

"*Analytical Chemistry is a scientific discipline that develops and applies methods, instruments and strategies to obtain information on the composition and nature of matter in space and time*" (Working Party on Analytical Chemistry of the European Federation of Chemical

"*Analytical Chemistry is a metrological discipline that develops, optimizes and applies measurement processes intended to produce quality (bio)chemical information of global and partial type from natural and artificial objects and systems in order to solve analytical problems*

The strategic significance of Analytical Chemistry arises from the fact that it is an information discipline and, as such, essential to modern society. Analytical Chemistry as a scientific discipline has its own foundations, which materialize in keywords such as information, metrology, traceability, analytical properties, analytical problems and analytical measurement processes. Also, it shares some foundations with other scientific and

To be coherent with the previous definitions, Analytical Chemistry should have the aims

technical areas such as Mathematics, Physics, Biology or Computer Science.

different fields (e.g. environmental science, agriculture, medicine).

definitions such as the following:

*derived from information needs*" [3].

Societies) [2].

**2.2. Aims and objectives**

and objectives depicted in Figure 3.

Also, if Analytical Chemistry is to be coherent with its foundations, aims and objectives (see Section 2.2. of this chapter), it should establish two-way relationships with a variety of international written standards (norms and guides) in order to contribute to the continuous improvement of human activities (see Figure 1.2). The classical relationship between Analytical Chemistry and quality has materialized in ISO 17025:2005, which is the reference for laboratory accreditation. This norm contains technical requirements and other, management-related specifications that are shared with those in ISO 9001:2008, which is concerned with quality in general. Also, written standards dealing with knowledge management and social responsibility are highly relevant to the foundations and applications of Analytical Chemistry, even though they have rarely been considered jointly to date. In addition, Analytical Chemistry is very important for effective environmental protection, and occupational health and safety, since the (bio)chemical information it provides is crucial with a view to making correct decisions in these two complementary fields.


**2.2 Description of intervention**

In 2015, the Catholic Relief Services (CRS) Lesotho, a partner with Ministry of Education and Training, the Early Childhood Care and Development (ECCD) Unit, started a project, *Whose Child is This?* The project was an intervention to address the deplorable condition of children in the daycare facilities at the Thetsane Area. In 2014, a child who had been seriously ill-treated by a caregiver in one of the day-care centres in the area prompted action of the community and ECCD stakeholders. The story had gone viral in local radio stations and newspapers. Due to that, the ECCD Unit visited the concerned facility and discovered there were many other daycare facilities that had mushroomed and were not known or "registered" with Ministry. The response to this situation resulted in more visits to the facility from ECCD stakeholders, partners and non-governmental organizations. The visits revealed the following concerns: "unsafe physical environments where children were cared for, unsanitary practices among facilitators/caregivers, overcrowding, inadequate and poor nutrition, and lack of activities to stimulate the development of children" [7]. The major challenge faced by caregivers in the daycare centres was lack of training and experience in the care of children aged below 3. Catholic Relief Services therefore designed the *WCiT* project to address the situation. Three strategic objectives of the project were:

One of the interventions made was the design of "one stop service delivery centres" that offered critical services needed by children and families and the services were provided by specialist agencies such as nutrition sector, immunization and health checks to detect any malfunctions and disabilities among the children, protection and education services. Activities days named *well-being days* (WBD) were designed by CRS and held once every quarter on a Sunday in the community affected. The WBDs were meant to sensitize parents and communities about the importance of child development. On such days, CRS in collaboration with the departments of health, social protection, nutrition and other critical partners, offered their specialized services of immunisations, deworming and others to ensure all children whose parents attended the activity, benefited from the services given. Additionally, there is training of caregivers in child care and stimulation that is provided, resulting in implementation of all the three strategic objectives of WCiT? project indicated above.

### **2.3 Achievements**

Achievements were realized due to the intervention. First, the training of caregivers including their willingness to participate in the project was realized. In the particular daycare centre, the caregiver went further to enroll for a 2-year training programme in early childhood education with the Lesotho College of Education. She reported that she completed her studies and now holds a certificate in early childhood education (CECE). She further explained that she took the decision to enroll because she felt it was important for the children to receive proper care provided by a knowledgeable person. She alluded that she was aware that children had the right to *good and loving care* provided by knowledgeable and trained adults.

Secondly, the project was successful in introducing well-being days (WBDs) since the services that were offered attracted a lot of parents who under normal circumstances rarely had time to take their children to access some of the services, particularly in the health centres. In her words, the caregiver said, "*Now I understand the importance of good nutrition in the early years of a child's life, therefore I cook for them so that I can introduce different foods and menus. That has made me happy."*

Lastly, the project has helped to improve child development outcomes through parents' better understanding of child nutrition, health, protection and stimulation by parents and families. In this regard, parents provide children with adequate and proper nutrition.

## **3. Lessons learned**

In discussing the lessons learned by the caregiver, the Nurturing Care Framework (NCF) is used to form the basis of the discussion. The Framework [8] promotes a holistic approach in early childhood development. It asserts that for a child to grow up well it must be healthy, have good nutrition, responsive care, stimulation, safety and security. There are five components of the NFC. However, in this paper, specific focus is on components 1, 2 and 3. Components 4 and 5 were not specifically highlighted in the study because issues of safety and security including early learning surfaced in the care practices discussed in the three components researched on. The components are presented as individual themes that guide the discussion and are accompanied by questions that were posed to the caregiver and the observations that were made. In that regard, it is hoped that the study would inform how the caregiver's care practices linked with the Framework.

#### **3.1 Component 1: good health**

The nurture and care surrounding this component relates to monitoring of children's physical and emotional condition; giving affectionate and appropriate responses to child's daily needs, protecting child from household and environmental hazards, practicing hygiene which minimizes infections, use promotive and preventive health services and seeking appropriate treatment for children's illnesses.

In **Table 1** below, the caregiver commented on good health and related health matters of babies in her centre.

*Child Care for the under 3 Year Old Children: Experiences from Lesotho DOI: http://dx.doi.org/10.5772/intechopen.93918*

#### **Table 1.** *Good health and health matters of babies.*

### **3.2 Component 2: adequate nutrition**

The component relates to a baby's nutrition right from when a mother is pregnant and eats well in order to supply micronutrients and supplements that help baby to develop. Brain development is critical in the first three years of a child's birth hence breastfeeding, particularly exclusive breastfeeding, is critical from immediately after baby's birth. Complementary feeding must be introduced from 6 months hence food safety and family food security are essential for adequate nutrition.

Below in **Table 2**, the caregiver commented on the issue of nutrition of the babies in her centre.

**Table 2.** *Nutrition of babies.*

#### **3.3 Component 3: responsive caregiving**

Responsive caregiving entails observing and responding to babies' and children's needs and their movements. This caregiving practice is the basis for protection of baby against injury; recognition of baby's illness or discomfort, learning and building of social relationships and trust.

The caregiver was surveyed on how she provided responsive caregiving to babies and toddlers in her centre (**Table 3**).

*Child Care for the under 3 Year Old Children: Experiences from Lesotho DOI: http://dx.doi.org/10.5772/intechopen.93918*

#### **Table 3.**

*Responsive caregiving to children's needs.*

#### **4. Discussion**

The Nurturing Care Framework provides the importance of why care and nurture must be accorded the children in order that they can "survive and thrive". The critical attention we need to pay to the earliest moments of a child's life cannot be understated. A child's foundation to survive and thrive is nested in the nurturing environment in order for a child to develop socially, physically, cognitively, emotionally and spiritually [9]. The role of nutrition, good health, early stimulation, protection and safety of both the mother and child can ensure that children have a chance to develop holistically.

In the case study centre, the caregiver seems to be familiar with some of the critical actions and requirements for child development and wellbeing. She further applies some of the knowledge she had when she was bringing up her own children and she applies that appropriately. However, being unsure of the immunization schedule and proper injections children require at a specific time might compromise the health of the child and put children at risk. Nonetheless, she seems to rely on the services she gets from scheduled visits of clinic nurses in the area to undertake

health checks of the children. One critical finding from the daycare centre was that the caregiver had no knowledge of the pregnancy history of the mother. That lack of knowledge would possibly deny the baby proper attention it required in the event the mother herself had had a difficult pregnancy period that might have affected the baby's healthy development. It would seem the caregiver needs to conduct one-to-one interviews with the mothers of the babies in her care in order to learn more about the history of the baby from conception. Such additional information would then be documented in the baby's health book and when necessary it would be shared with the health facility when need arose.

On the other hand, some serious challenge the caregiver had was that of parents who did not provide balanced and nutritious food for the children's meals. The fact that some children had only starch-based foods compromised their nutrition. Nevertheless, the caregiver with consent from the parents introduced feeding at the centre and parents had to pay increased fees and that practice allowed children to be provided with good nutrition. Through the CRS training that the caregiver had attended, she was able to design an appropriate menu for the children. Adequate nutrition throughout the early years from pre-natal to eight years cannot be over-emphasized. Inadequate nutrition before birth and in the first years of life can seriously interfere with brain development and lead to such neurological and behavioral disorders as learning disabilities and mental disorders [10]. Therefore, when children do not feed well, they become vulnerable to diseases that could otherwise have been curbed through good nutrition.

At the beginning, Retšepile Jesu Day Care centre was neither registered nor formally known to the Ministry of Education and Training. Resultantly, the daycare centre was not receiving any support in terms of training of the caregiver and advice or guidance on baby care. After the Day Care centre and others in the area were known to the Ministry and other partners in ECCD, the caregivers in the area were exposed to basic training on child development and care. The caregiver's enthusiasm and desire to provide improved and quality child care service, prompted her later to enroll for a Certificate in Early Childhood Education (CECE) course at the Lesotho College of Education. She qualified in 2018 and currently she strives to improve her practice at the centre. In a study conducted in Kenya in 2000, mothers of children below 3 years of age reported that they ensured their babies were happy by singing lullabies to them or feeding them (p. 132, [11]). On the other hand, Dodge and Phinney [12] highlight the importance of play in early childhood. They inform that "play provides the foundation for academic or "school learning". It is the preparation children need before they learn…play is the work of young children", (p. 3). The issue of care and nurture is one of the critical ingredients to a healthy start for young children and where parents engage in such care practices, as stimulation and play, the children are likely to benefit.

### **5. Conclusions and recommendations**

As mentioned earlier, this study was undertaken to establish how far the care practices offered by the caregiver were aligned to some of the components of the Nurturing Care Framework. The Framework is relatively a new innovation and as such, had never been introduced to the caregiver, let alone to a number of ECCD stakeholders in the country. The extent of the quality of care and nurture that the caregiver has been sensitized about may be sufficient to ensure children benefit extensively from how she interacts and handles them. If the caregiver had been knowledgeable about the Framework, it would be expected that her care and nurture practices would be adequate. It is therefore concluded that

some aspects of components 1, 2 and 3 of the NCF are practiced by the caregiver although the quality of care and nurture may still remain inadequate given that the caregiver is still learning how to implement some of the practices in the Framework.


**2.11 Clear cell**

Clear cell UC is a very rare variant of UC characterized by tumour cells with glycogen-rich cytoplasm (**Figure 10**). It is crucial to do the correct differential diagnosis among clear cell UC, clear cell adenocarcinoma of the bladder, metastatic clear cell renal cell carcinoma or clear cell carcinoma of the female genital tract [28].

Only a few case reports are available for this rare histologic variant. The evidence suggests a high progression rate to muscle-invasive and metastatic BC, and although treatment strategy is poorly defined, an aggressive approach with early RC is advocated [40].

#### **Figure 9.**

*It contains both carcinoma as well as sarcomatous areas usually with high-grade urothelial carcinoma on the surface and a high-grade undifferentiated sarcoma underneath in the lamina propria (HE × 100).*

#### **Figure 10.**

*Clear cell variant of urothelial carcinoma consists of abundant clear cytoplasm due to glycogen content and it is characterized by large nests of tumour cells with high- grade nuclear atypia and clear cytoplasm (HE* **×** *200).*


**1. Introduction**

Wines, like many other natural food products, contain varying amounts of different nitrogenous substances, the most important of which are proteins [1]. Proteins found in wine are mostly derived from grape berries. Using immunological methods, the specific polyclonal antibodies raised against the total proteins of a Portuguese Malvasia Fina monovarietal wine have been applied to analyse the origin of the wine proteins [2] which are entirely from the berry pulp. Three years later, a similar immune detection study was conducted [3] and three various polyclonal antibodies raised against must, yeast, and bacteria proteins were applied to analyse the origin of proteins in Chardonnay wine. The results indicated that most of the wine proteins came from grapes and many of them were glycoproteins, but there were also some proteins from the yeast. Yeast may affect the wine protein composition in two ways: by transferring proteins to the wine during the process of yeast autolysis and/or hydrolysing the must proteins via the exocellular protease present in the yeasts [1]. Furthermore, the analysis of a Sauvignon Blanc wine using nano-high performance liquid chromatography (HPLC)/tandem mass spectrometry showed that within the 20 identified proteins there were two proteins from bacteria and one from fungi, which could be attributed to sources in the vineyard including natural infections and improper handling during harvest [4].

#### **Table 1.**

*Proteins reported in grapes and wines from different grape varieties: molecular weight (MW) and isoelectric point (pI).*

In previous studies, proteins from grapes and wines have been reported with molecular weight (MW) in the range 6–200 kDa and isoelectric points (pI) in a range 3–9 kDa, as shown in **Table 1** [4–9]. However, the majority of wine proteins have MW and pI in a low range (20–30 and 4.1–5.8 kDa, respectively) and possess a net positive charge at the pH of the wine [2, 5, 10]. Studies on fractions of wine proteins using denaturing polyacrylamide gel electrophoresis have shown that the wine protein fraction is mainly composed of only a few polypeptides with MW ranging from 15 to 30 kDa, but a more detailed examination of whole protein fraction indicates a very large number of distinct polypeptides, exhibiting similar MW but subtle differences in electrical charges [11]. In that study, the authors also revealed via highly specific antibodies and N-terminal sequencing analysis that most wine polypeptides were structurally similar, suggesting the existence of a common precursor to most or all of the wine proteins which could generate all of the detected polypeptides by limited proteolysis.

In a study on Muscat of Alexandria wine [12], two major proteins with MW of 24 and 32 kDa, respectively, by SDS-PAGE are found with significant contribution to protein haze, and the 24 kDa protein produced about 50% more haze than the 32 kDa protein. The N-terminal sequence of the protein with MW of 24 kDa showed homology to thaumatin and to a number of plant thaumatin-like proteins, and the N-terminal sequence of enzyme digested peptides of the protein with MW of 32 kDa showed homology to plant chitinases [13]. Another study analysed the two main wine proteins present in sodium dodecyl sulphate capillary gel electrophoresis (SDS-CGE), which were determined with MW at 22 and 26 kDa, respectively, being concluded as corresponding to thaumatin-like proteins (TLPs) and chitinases [14]. Both thaumatin-like proteins and chitinases in wine are pathogenesis-related (PR) proteins derived from grapes.


**Author details**

Majda Breida1 \*, Saad Alami Younssi1 , Mohamed Ouammou1 , Mohamed Bouhria1 and Mahmoud Hafsi2

1 Laboratory of Materials, Membranes and Environment, Faculty of Sciences and Technologies of Mohammedia, University Hassan II, Casablanca, Morocco

2 International Institute for Water and Sanitation, National Office for Electricity and Drinking Water, Rabat, Morocco

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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*Article* **Using a Product Life Cycle Cost Model to Solve Supplier Selection Problems in a Sustainable, Resilient Supply Chain**

**Yu-Jwo Tao 1,2,3, Yi-Shyuan Lin 1, Hsuan-Shih Lee 4,5, Guo-Ya Gan 6 and Chang-Shu Tu 7,\***

**Abstract:** Supplier selection constitutes a crucial component of manufacturing procurement. We developed a product life cycle cost (PLCC) model to support Taiwanese light-emitting diode (LED) manufacturers in capacity planning for sustainable and resilient supply chain (SC) management. For firms, supply chain PLCC (SCPLCC) is a key consideration, but relevant evidence is scarce. We applied two types of goal programming, namely multiobjective linear programming and revised multichoice goal programming (RMCGP), to develop a PLCC-based model that minimizes net costs, rejections, and late deliveries. Moreover, we constructed a decision-making tool for application to a case of SC sustainable procurement management in a high-tech Taiwanese LED company. Managers can resolve relevant problems by employing the two approaches of the SCPLCC model with various parameters. The implementation of RMCGP with weighted linear goal programming sensitivity analysis produced sufficient findings, according to a study of five models for practical implications. The primary findings of the current model assist business decision-makers in minimizing PLCC, reducing PLCC cost, minimizing net cost, number of rejections, number of late deliveries, achieving PLCC goals, and selecting the best supplier in the context of sustainable SC development.

**Keywords:** supplier selection; product life cycle cost; geometric mean weighting; penalty weighting; multiobjective linear programming; revised multichoice goal programming

#### **1. Introduction**

Because of the globalization of commercial markets and improvements in information technology, a well-constructed supply chain management (SCM) system is an instrumental tool for gaining competitive advantage [1,2]. In higher SC levels, supplier selection constitutes an integral component of manufacturing procurement and a pivotal industrial activity [3–5]. With the growing globalization of industry, SCM has become an increasingly multifaceted undertaking. SCM is an essential element of most businesses and is critical to corporate success and customer satisfaction. SCs represent the pathway between suppliers and buyers, customers, or consumers [6].

The primary goal of a manufacturing company is to make the correct product in the correct amount for the correct customer in a timely manner. Purchasing companies demand advanced buyer interactions with their suppliers for a respectful relationship between the two parties.

**Citation:** Tao, Y.-J.; Lin, Y.-S.; Lee, H.-S.; Gan, G.-Y.; Tu, C.-S. Using a Product Life Cycle Cost Model to Solve Supplier Selection Problems in a Sustainable, Resilient Supply Chain. *Sustainability* **2022**, *14*, 2423. https://doi.org/10.3390/su14042423

Academic Editor: Shervin Hashemi

Received: 31 December 2021 Accepted: 16 February 2022 Published: 20 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Sustainability in industry has emerged as a crucial strategy that expands beyond organizational boundaries to include the entire SC. Concerns regarding SC resilience have also arisen. Research on the intersection between the sustainability and resilience of SCs is nascent and is a consequence of their mutual effects. However, confusion regarding concepts, measurements, and implementation methods of sustainable and resilient SCs remains.

Some life cycle studies have compared the environmental sustainability of organic and nonorganic pork SCs. The present study investigated how overall food SC performance depends on the performance of partners in a sustainable and energy-efficient SC [7–9].

A light-emitting diode (LED) is a semiconductor device that emits light through the recombination of electrons with electron holes within the apparatus. LEDs are a green technology with high potential for reducing global CO2 emissions. McKinsey stated that the overall market share of LED manufacturers was likely to increase after 2012, with global annual revenues projected to reach €37 billion by 2016 and €64 billion by 2020. Fortune Business Insights reported that the value of the global lighting market reached an estimated US\$118.33 billion in 2019 and is projected to reach US\$163.72 billion by 2027 [10,11]. Using white LED lighting technology, according to the optoelectronics industry development organization (OIDA), may cut CO2 emissions by 2.5 billion tons per year globally.

The LED industry is a prominent example of sustainability and resilience concepts in SCM. Although the industry is highly competitive and dynamic, its products are resource and emission intensive in both the production and use phases. In the context of climate change, the growing focus placed on sustainability represents a response to demands for carbon emission reductions. Resilience constitutes a response to climate adaptation challenges. Sustainable SCM (SSCM) has been employed for objectives concerning climaterelated adaptation. The basic concepts of resilience SCM (RSCM) are derived from the characteristic elements of resilience theory. Despite the increasing relevance of SSCM and RSCM to enterprises with respect to addressing climate change concerns, studies have largely neglected the need for the systematic integration of the two paradigms [12–16].

Resilience is key to the ability of organizations to effect positive change and overcome various challenges, even in crisis situations. The extent of an organization's ability to respond to various disturbances depends on that organization's objectives and level of maturity in crisis management. In human resource management, organizational resilience is acknowledged as a multidisciplinary, multidimensional quality. Suryaningtyas et al. [7] reported a positive association between organizational resilience and organizational performance. For general managers, this suggests that organizational resilience should be continually applied both operationally and strategically to maintain a company's sustainability.

To choose suppliers and distribute resources in the food industry, Kaviani et al. [17] develop a combined intuitionistic fuzzy analytic hierarchy process and fuzzy multi-objective optimization approach. Noppasorn et al. [18] provided a Fuzzy Programming approach for optimizing multi-objective Aggregate Production Planning problems in uncertain situations.

We developed a product life cycle cost (PLCC) model to support Taiwanese LED manufacturers in capacity planning for sustainable and resilient SCM. Taiwan has a unique political and economic environment. The present PLCC-based model integrates SSCM and RSCM, thus allowing for high degrees of flexibility and efficiency. In applying this model, LED firms can employ technologies that provide decision-makers with strategic guidance with regard to examining and comparing various alternative sustainability strategies.

Although SCPLCC is a vital corporate consideration, relevant evidence is limited. SCPLCC has become associated with deciding how one supplier should be selected from various alternatives.

The supplier base must be optimized to identify high-performing suppliers in SCs. Approaches for solving SCPLCC-related problems have been discussed. Details are provided as follows.

Few attempts have been made to incorporate information vagueness into the SCPLCC problem. The multiobjective linear programming (MOLP) model can account for the variation in or imprecision of a decision-maker's aspiration level (intermediate control variables), thus establishing a more certain key point for decision-making policy [17,19]. Herein, we implemented a fuzzy MOLP model and a revised multichoice goal programming (RMCGP) model. The application of weighted linear goal programming (WLGP) to the RMCGP model produced adequate results in a scenario involving the PLCC of a high-tech company.

We extended the work of Amid et al. [19] and referenced a study by Wang [5] to solve the PLCC problem. To solve the SCPLCC problem, we modified a sample data set of auto part manufacturers from a study by Kumar et al. [20]. For sustainable buying, we used real-world data from LED companies [21].

Third, to solve the SCPLCC problem, we incorporated geometric mean weighting into the MOLP and RMCGP models such that the decision-maker can understand differences between assigning and not assigning all objectives and constraints in an SC decision of equal importance [22]. Our SCPLCC model can help decision-makers optimize supplier selection and prioritization; moreover, it can enable purchasing managers to enhance SC performance through the fulfilment of PLCC goals and minimization of net costs, rejections, and late deliveries. Managers can resolve relevant problems by employing the two approaches of the SCPLCC model with various parameters [22].

To close the theory–practice gap, we integrated experiential information and the opinions of practitioners in considering industrial SCs. By proposing a novel PLCC framework encompassing aspects of both resilience and sustainability, we extended existing conceptual frameworks on SSCM and RSCM. We considered climate change the most critical environmental concern that warrants SCM responses in terms of both sustainability and resilience through climate change mitigation and adaptation measures, respectively. We selected the LED industry as the study subject because it contributes substantially to climate change and is vulnerable to its adverse effects (because of the globalized and highly complex SC).

The first goal programming was developed by Charnes and Cooper [1]. Most goal programming methods rely on mapping one goal to a single scalar aspiration level. However, one goal may map multiple choice aspiration levels [2]. Chang conceived multichoice goal programming (MCGP) to address such scenarios [2]. The two main characteristics of MCGP are as follows. First, the aspiration levels used in goal programming need not be scalars; they can be vectors. Second, in the problem formulation stage, the aspiration level should not be underestimated. Acknowledging the complexity of the multiplicative mixed binary terms employed in MCGP, Chang [4] devised an MCGP approach that obviates the need for such terms altogether. MCGP methods can be implemented to solve real-world decision-making problems.

Nasr et al. [23] demonstrated the applicability of a fuzzy goal programming technique in the garment manufacturing and distribution business through a case study. Beiki et al. [24] used a real-world case study of automotive manufacturing to apply the linguistic entropy weight approach and the multi-objective programming (MOP) method to the applicability of a sustainable supplier selection and order allocation issue.

The remainder of this paper is organized as follows: Section 2 presents a review of the literature on quantitative decision-making techniques concerning SCs. Section 3 introduces the explanation of the solution of the SCPLCC problem under the two present approaches. In Section 4, considering a Taiwanese LED firm, the problem-solving process of the two goal programming approaches based on a sample data set of auto part manufacturers from a study by Kumar et al. [20] is described. In Section 5, conclusions are drawn regarding the SCCM-related advantages provided by these two approaches.

#### **2. Literature Review**

Criteria concerning SC selection and supplier ratings have been a research focus since the 1960s. In a review article, Dickson [25] compiled a list of more than 50 distinct factors meaningful to SCM. Various methods have been used in SC research, including linear weighting methods and mathematical programming models. For example, linear programming and goal programming, as multicriteria decision-making techniques, aim to facilitate decision-making by minimizing undesirable deviations in goal-related values.

In the present study, we classified studies on SCs according to whether they employed the qualitative factor approach or the integrated factor approach. Table 1 provides information on SC studies in which mathematical programming models were applied. SC models involve the use of diverse approaches, such as simple weighted scoring methods and compound mathematical programming techniques. The incorporation of multiple elements in the selection criteria is desirable and is often associated with high subjectivity in the decision-making process [26].

Few studies have considered fuzziness in the analysis of SCPLCC data. Kumar et al. [39] presented a fuzzy goal programming model that minimizes the total tolerable weight variations of variables. In the present study, we employed two fuzzy programming approaches.

#### **3. Methods**

Zimmermann [40] used the approach of Bellman and Zadeh [41] and reformulated a linear programming problem with a fuzzy goal and fuzzy restrictions such that it could be solved as a conventional linear programming problem. Indexes, decision variables, and parameters were accounted for in the construction of an enriched multiobjective linear programming model in compliance with a set of assumptions, which are listed as follows.

The lead time and demand of the item are constant and known with confidence. The indexes, parameters, and decision variables of the SCPLCC model are defined in

Table 2.

**Table 2.** Definitions of indexes, parameters, and decision variables.

**Table 2.** *Cont.*

Note: Fuzzy parameters are indicated by a tilde.

#### Model: SCPLCC problem.

We formulate the multiobjective SCPLCC problem with four fuzzy objectives and fuzzy crisp constraints as follows.

$$\text{Minimize } \mathbf{Z}\_1 \widetilde{=} \sum\_{i=1}^{n} \mathbf{P}\_i \mathbf{x}\_i \tag{1}$$

$$\text{Minimize } \mathbf{Z}\_2 \widetilde{=} \sum\_{i=1}^n \mathbf{R}\_i \mathbf{x}\_i \tag{2}$$

$$\text{Minimize Z}\_3 \widetilde{=} \sum\_{i=1}^n \mathbf{L}\_i \mathbf{x}\_i \tag{3}$$

$$\text{Minimize } \mathbf{Z}\_4 \widetilde{=} \sum\_{i=1}^n \mathbf{C}\_i \mathbf{x}\_i \tag{4}$$

The problem is subject to the following constraints:

$$\sum\_{i=1}^{n} x\_i \ge \overset{\sim}{\mathbf{D}} \text{ (aggregate demand constraint)}\tag{5}$$

$$\mathbf{x}\_{i} \le \widetilde{\mathbf{U}}\_{i} \; \forall \; i \; ; \; i = 1 \; \; 2, \ldots, \; n \; \text{(capacity constraint)}\tag{6}$$

$$\sum\_{i=1}^{n} r\_i(\mathbf{x}\_i) \ge \mathbf{P}, \ i = 1, 2, \dots, n \text{ (total items purchased constraint for superficial } i) \tag{7}$$

$$\sum\_{i=1}^{n} f\_i(\mathbf{x}\_i) \le \mathbf{F}\_\prime \text{ } i = 1, 2, \dots, n \text{ (Supplier quota flexibility) for supplier } i \text{)} \tag{8}$$

$$\mathbf{P}\_{i}\mathbf{x}\_{i} \le \mathbf{B}\_{i}, \ i = 1, 2, \dots, n \text{ (budget constraint)}\tag{9}$$

$$\mathbf{x}\_{i} \ge \mathbf{0}, \ i = 1, \ 2, \ldots, \ n \text{ (non-negative constraint)}\tag{10}$$

#### *3.1. Key Elements of Objectives or Constraints of the SCPLCC Model*

This model has four main fuzzy objectives: minimizing the total net cost, minimizing rejected items, minimizing late deliveries, and realizing the supplier's goal regarding the PLCC. The aggregate demand constraint ensures that the item is available in the required quantity over a fixed planning period. The supplier production capacity constraint limits the supply on the basis of the uncertain aggregate demand being set at 10% of the deterministic model. The budget constraint means that no one supplier can exceed its budget. The nonnegativity constraint prohibits negative orders. In general, the tilde (~) indicates that a situation is fuzzy. In the present model, both the objective functions and demand constraints are fuzzy parameters [15,22].

Depending on the objectives and restrictions and on whether the weights are equal or unequal, the fuzzy decision is either symmetric or asymmetric, respectively [22,40]. This problem is defined as the following membership function:

$$
\mu\_d(\mathfrak{x}) = \min(\mu\_{\mathcal{S}}(\mathfrak{x}), \mu\_{\mathfrak{c}}(\mathfrak{x})) .
$$

A general linear MOLP model for supplier selection involving the minimization (*Z*1, *Z*2, *Z*3, *Z*4) and maximization (*Z*2) of the fuzzy and crisp constraints of the objective function is expressed as follows [22]:

*Z*1 = *Z*3 = *Z*4 = *n* ∑ *i*=1 *ckixi*, *k* = 1, 2, 3, 4 *Z*2 = *n* ∑ *i*=1 *ctixi*, *t* = 2, for maximization of the fuzzy and crisp constraints of the objective function. such that *n* ∑ *i*=1 *arixi* ≥ *dr*, *r* = 1, 2, . . . , *m* for fuzzy restrictions (capacity constraints 1–4),

*n* ∑ *i*=1 *bsixi* ≥ *ds*, *s* = 1, 2, . . . , *m* for crisp restrictions (budget constraints 1–4), and *xi* ≥ 0, where *i* = 1, 2, . . . , *n*.

In fuzzy linear programming, objectives and restrictions are treated the same because they are defined through an individual membership function. Figure 1 presents the fuzzy objective functions and constraints of the SCPLCC problem.

The membership function (*Zk*) and maximization goals (*Zl*) are expressed as

$$\mu\_{zk}(\mathbf{x}) = \begin{cases} 1 & \text{for } \qquad \mathbf{Z}\_k \le \mathbf{Z}\_k^- \\\ f\_{\mu\_{zk}} = \frac{(\mathbf{Z}\_k^+ - \mathbf{Z}\_k(\mathbf{x}))}{(\mathbf{Z}\_k^+ - \mathbf{Z}\_k^-)} & \text{for } \qquad \mathbf{Z}\_k^- \le \mathbf{Z}\_k(\mathbf{x}) \le \mathbf{Z}\_k^+ \\\ 0 & (k = 1, 2, \dots, p) \end{cases} \tag{11}$$

$$\mu\_{\mathcal{Z}l}(\mathbf{x}) = \begin{cases} 1 & \text{for } \qquad \mathbf{Z}\_l \ge \mathbf{Z}\_l^+ \\\ f\_{\|\mathbf{z}\_{\mathcal{I}l} - \mathbf{(}\mathbf{Z}\_l^- - \mathbf{(}\mathbf{I}\_l^-) \mathbf{K}\_l^-\|} & \text{for } \qquad \mathbf{Z}\_l^- \le \mathbf{Z}\_l(\mathbf{x}) \le \mathbf{Z}\_l^+ \\\ 0 & (l = p+1, \ p+2, \dots, q) \end{cases} \tag{12}$$

where *Z*− *k* and *Z*+ *l* can be obtained by solving the multiobjective problem by considering only one objective at a time; *Z*+ *k* is the maximum value (i.e., the least optimal solution) of the negative objective *Z*− *k* , and *Z*− *l* is the minimum value (i.e., the least optimal solution) of the positive objective function *Z*+ *l* [20,42,43].

#### *3.2. Solving the SCPLCC Problem through the Weighted Additive Approach*

The weighted additive (WA) model, which is convex, enables decision-makers to select different weights according to specific purposes.

When the SCPLCC problem is solved, the weights of the membership functions of the objectives and constraints are calculated according to a supertransitive approximation; thus, these weights are assigned separately. In Equations (13)–(19), *αj* is the weighting coefficient that indicates the relative importance of the fuzzy goals and fuzzy restrictions.

**Figure 1.** Presentation of the objective function as a fuzzy number: (**a**) minimum *Z*− *k* and (**b**) maximum *Z*− *l* .

The following crisp simplex objective programming function is the same as that of the fuzzy model.

$$\text{Max}\sum\_{j=1}^{S} \alpha\_{j}\lambda^{\*}\tag{13}$$

$$
\lambda\_j \le \mu\_{zj}(\mathbf{x}), \ j = 1, \ 2, \ \dots, \ q, \text{ for all objective functions} \tag{14}
$$

*γr* ≤ *μhr*(*x*), *r* = 1, 2, . . . , *h*, for all constraints (15)

$$\log\_m(\infty) \le b\_{m\prime} \ m = 1, \ldots, p,\tag{16}$$

$$
\lambda \in [0.1] \tag{17}
$$

$$\sum\_{j=1}^{S} \alpha\_{j} = 1, \alpha\_{j} \ge 0,\tag{18}$$

$$\infty\_i \ge 0, \ i = 1, \ 2, \ \dots, n. \tag{19}$$

Refer to the study by Amid et al. [19] for a more detailed discussion of this model.

#### Weighted Max–Min Approach

Lin [44] devised and provided a proof for a weighted max–min approach that can capture an ideal resolution within a feasible area such that the ratio of the achievement level is as close to the ratio of the weight as possible. Lin noted that the WA model of Tiwari et al. [45] yields objectives involving heavy weights with relatively greater achievement values. However, the proportion of the achievement levels is not essentially the same as that of the objective weights [20,44,46]. To solve the present SCPLCC problem, the following equations corresponding to Lin's weighted max–min model were employed [20]:

$$\text{Max } \lambda \tag{20}$$

subject to

$$w\_j \lambda \le \mu\_{zj}(\mathbf{x}) \; j = 1, \; 2, \; \dots, q\_{\prime} \text{ for all object functions} \tag{21}$$

$$
\gamma\_r \le \mu\_{lr}(\mathbf{x}) \; r = 1, \; \mathbf{2}, \; \dots, h \; \text{for all constraints} \tag{22}
$$

$$g\_m(\mathbf{x}) \le b\_{m\nu} \ m = 1, \ldots, p,\tag{23}$$

$$
\lambda \in [0.1] \tag{24}
$$

$$\sum\_{j=1}^{S} \alpha\_j = 1, \; \alpha\_j \ge 0,\tag{25}$$

$$\forall x\_i \ge 0, \ i = 1, \ 2, \ \dots, n. \tag{26}$$

See Amid et al. [20] for a more detailed description of this model.

#### *3.3. Revised MCGP Approach for Solving the SCPLCC Problem*

We employed the RMCGP achievement function model developed by Chang [47]. Two RMCGP achievement function models were implemented. Details are presented as follows.

Specifically, the type I model is used for the scenario in which "more is better" (i.e., where achievement is the upper bound):

$$\begin{aligned} \text{Minimize } & \sum\_{i=1}^{n} \left[ w\_i (d\_i^+ + d\_i^-) + a\_i (e\_i^+ + e\_i^-) \right] \\ \text{Subject to } & \begin{aligned} f\_i(X)h\_i - d^+ + d^- &= h \cdot u \cdot i = 1 \cdot 2 \qquad n \end{aligned} \tag{77} \end{aligned} \tag{78}$$

$$\text{if } f\_i(X)b\_i - d\_i^+ + d\_i^- = b\_i y\_i \text{ i = 1, 2, \dots, n, \text{ } n, \tag{27}$$

$$\mathbf{e}\_{i}\mathbf{y}\_{i} - \mathbf{e}\_{i}^{+} + \mathbf{e}\_{i}^{-} = \mathbf{g}\_{i,\text{max}}\text{ i } = 1,\text{ 2, ..., \text{ }n\text{.} \tag{28}$$

$$\mathcal{G}i, \text{min} \le \mathcal{Y}i \le \mathcal{G}i, \text{max} \tag{29}$$

$$d\_{\mathbf{i}}^{+}, d\_{\mathbf{i}}^{-}, e\_{\mathbf{i}}^{+}, e\_{\mathbf{i}}^{-} \ge 0, \mathbf{i} = 1, \, \mathbf{2}, \, \dots \,, n,\tag{30}$$

Here, *X* ∈ *F*, where *F* is a feasible set and *X* is unrestricted in sign.

Note that *bi* ∈ {0, 1} is a control variable attached to | *fi*(*X*) − *yi*|, which can be either achieved or released in Equation (27). In terms of real conditions, *bi* is subject to some constraints in guiding the relationships between the objectives of the SCPLCC model.

The type II model is used in the scenario in which "less is better" (i.e., where achievement is the lower bound):

$$\begin{aligned} \text{Minimize } & \sum\_{i=1}^{n} \left[ w\_i (d\_i^+ + d\_i^-) + a\_i (e\_i^+ + e\_i^-) \right] \\ \text{Subject to } & \\ & f\_i(X)b\_i - d\_i^+ + d\_i^- = b\_i y\_i \text{ i = 1, 2, \dots, n, } \end{aligned} \tag{31}$$

$$y\_i - e\_i^+ + e\_i^- = g\_{i, \text{min}} \; i = 1, \; 2, \; \dots \; \; n,\tag{32}$$

$$\mathcal{G}i, \text{min} \le \mathcal{Y}i \le \mathcal{G}i, \text{max} \tag{33}$$

$$d\_{\mathbf{i}}^{+}, d\_{\mathbf{i}}^{-}, e\_{\mathbf{i}}^{+}, e\_{\mathbf{i}}^{-} \ge 0, \mathbf{i} = 1, \, 2, \, \dots, \, \mathbf{n}, \tag{34}$$

Here, *X* ∈ *F*, where *F* is a feasible set and *X* is unrestricted in sign.

The definitions given in the definition of the type I model apply to the variables. All mixed-integer terms in Equations (27) and (29) can be easily linearized through the approach developed by Chang [47]. As presented in Equations (27), (29) and (30), no selection limitations were imposed on a specific objective, but some dependent relationships were observable between goals. Thus, we can add the auxiliary constraint *bi* ≤ *bi*+1 + *bi*+2 to the RMCGP achievement function model, where *bi*, *bi*+1, and *bi*+2 are binary variables. Therefore, if *bi* = 1, *bi*+1 or *bi*+2 must also equal 1. In other words, if goal 1 has been accomplished, then either goal 2 or goal 3 must have also been accomplished. Chang [47] presented a case regarding the managerial implications of these restrictions.

#### *3.4. Process of SCPLCC Problem Resolution*

A comprehensive solution to the SCPLCC problem was obtained through the following steps. Step 1: Construct the model of the SCPLCC problem.

Step 2: Solve the MOLP problem through geometric mean weighting and obtain the lower and upper bounds (i.e., the max and min) of the ideal value of the four objectives, respectively.

Step 3: Replicate the procedure for each remaining objective. Define the lower and upper bounds of the optimal values for each objective according to the set of constraints.

Step 4: Process these values as the lower and upper bounds of the ideal values for the crisp construction of the SCPLCC problem.

Step 5: For each objective function, find a lower bound and an upper bound matching the established resolutions for each goal. Let *Z*− *j* and *Z*+ *j* denote the lower and upper bounds of the *j*th objective goal Z*j*, respectively [20].

Step 6: For each objective function, find the membership function in relation to Equations (11) and (12).

Step 7: Subject the criteria to geometric mean weighting.

Step 8: Establish and solve the corresponding WA model for the SCPLCC problem in relation to Equations (13)–(19).

Step 9: Establish and solve the corresponding max–min model for the SCPLCC problem in relation to Equations (20)–(25).

Step 10: Implement RMCGP through the geometric-mean-weighted and no-penalty-weighted construction of the fuzzy optimization problem, as expressed in Equations (27) and (30).

Step 11: Implement RMCGP through the geometric-mean-weighted and penalty-weighted construction of the fuzzy optimization problem, as presented in Equations (27) and (34).

Step 12: Solve the RMCGP model through the geometric-mean-weighted and penaltyweighted goal programming construction of the fuzzy optimization SCPLCC problem. Subsequently, compare the results obtained under the two goal programming approaches. Figure 2 shows a schematic representation of the entire methodology (MOLP and RMCGP) used to address the SCPLCC procurement challenge.

**Figure 2.** Graphic representation of the whole process.

#### **4. Practical Example**

The company on which the SCPLCC model was tested is part of a multinational group in the LED research and development sector. Specifically, the firm manufactures parts for made-to-order electric lights. External purchases accounted for more than 75% of the total annual costs of the company. The manager of the LED firm formed a team to propose three prospective providers. This group included managers from buying, marketing, quality control, manufacturing, engineering, and research and development.

Members of the team convened multiple sessions to develop profiles for competing providers and assembled a preliminary list of three companies for evaluation purposes [21]. The management is concerned with improving the efficiency of the purchasing process and optimizing the company's sourcing strategies. The managers believe that evaluating and certifying their vendors is essential for achieving inventory reduction and shortening the time to market. They had been instructed to develop longer-term trust-based relationships with a smaller group of vendors. In response, a team was formed to recommend three or four suitable vendors. The team consisted of managers from the purchasing, marketing, quality control, production, engineering, and research and development departments. The team convened several meetings to create profiles for the evaluation of three initial candidate vendors. An SCPLCC problem model was developed for vendor selection and quota allocation under the consideration of uncertain environmental conditions. Four main objective functions were investigated: (1) minimizing net cost, (2) minimizing net rejections, (3) minimizing late deliveries, and (4) minimizing PLCC. All four functions were under practical constraints regarding item demand, vendor capacity limitations, and vendor budgets, among other factors. The price quoted *Pi*, percentage of rejections *Ri* on a scale from 0 to 1, percentage of late deliveries *Li*, the PLCC (designated as *Ci*), suppliers' cost capacity *Ui*, suppliers' quota flexibility *Fi* on a scale from 0 to 1, the vendors' ratings *ri*, on a scale from 0 to 1, and suppliers' budget allocation *Bi* were considered. Profiles of the three suppliers are presented in Table 3.

**Table 3.** Profiles of the three suppliers.

In this case demonstration, the linear membership function was employed to fuzzify the right-hand side of the restrictions in the preceding SCPLCC model. The net cost, rejections, late deliveries, and supplier capacity at the lowest and highest levels of the membership function must be defined according to Equations (11) and (12). The fuzzy parameters' uncertainty level was assumed to be 10% of that of the deterministic model. The values corresponding to the lowest and highest aspiration levels of the membership functions are listed in Table 4.

**Table 4.** Limiting values in the membership functions of net cost, rejections, late deliveries, PLCC, vendor capacities, and budget information.

#### *4.1. Application of the WA Approach to a Numerical Example*

We examined a numerical example through the WA approach employed by Tiwari et al. [45]. Before solving the problem, we first determined the weights of four goals and six restrictions through supertransitive approximation. The following binary comparison matrix was assumed to consist of the obtained net cost, rejections, late deliveries, PLCC, supplier 1 constraints, supplier 2 constraints, and supplier 3 constraints:

Supertransitive approximation [48] was conducted to generate the comparison matrix, and the following weights were obtained [9]: *w*1 = 0.2958, *w*2 = 0.0579, *w*3 = 0.0863, *w*4 = 0.0365, *w*5 = 0.1291, *w*6 = 0.1254, *w*7 = 0.0392, *w*8 = 0.0199, *w*9 = 0.0151, and *w*10 = 0.1949.

#### 4.1.1. Solving the SCPLCC Problem through the WA Approach

For this SCPLCC example, the optimal quota allocations (i.e., the purchasing orders), production capacity limitations, and budget restrictions were obtained through Zimmermann's WA method [49], as shown in Equations (13)–(19). This SCPLCC problem can now be reformulated as the following program:

Maximize 0.2958*λ*∗ 1 +0.0579*λ*∗ 2 +0.0863*λ*∗ 3 +0.0365*λ*∗ 4 +0.1291*λ*∗ 5+0.1254*λ*∗ 6 +0.0392*λ*∗ 7 +0.0199*λ*∗ 8 + 0.0151*λ*∗ 9 + 0.1949*λ*∗ 10

Subject to

$$
\lambda\_1^\* \le (71833 - (3x\_1 + 2x\_2 + 6x\_3)) / (71833 - 57000)
$$

$$
\lambda\_2^\* \le (521 - (0.05x\_1 + 0.03x\_2 + 0.01x\_3)) / (521 - 413)
$$

$$
\lambda\_3^\* \le (816 - (0.04x\_1 + 0.02x\_2 + 0.08x\_3)) / (816 - 604)
$$

$$
\lambda\_4^\* \le (90000 - (1.92x\_1 + 1.04x\_2 + 3.94x\_3)) / (90000 - 10000)
$$

$$
\mu\_1^\* \le (71833 - (3x\_1 + 2x\_2 + 6x\_3)) / (71833 - 57000)
$$

*μ*∗ 2 ≤ (521 − (0.05*x*1 + 0.03*x*2 + 0.01*x*3))/(521 − 413) *μ*∗ 3 ≤ (816 − (0.04*x*1 + 0.02*x*2 + 0.08*x*3)/(816 − 604) *μ*∗ 4 ≤ (90000 − (1.92*x*1 + 1.04*x*2 + 3.94*x*3))/(90000 − 10000) *Z*1 = 3*x*1 + 2*x*2 + 6*x*3 *Z*2 = 0.05*x*1 + 0.03*x*2 + 0.01*x*3 *Z*3 = 0.04*x*1 + 0.02*x*2 + 0.08*x*3 *Z*4 = 1.92*x*1 + 1.04*x*2 + 3.94*x*3 *x*1 + *x*2 + *x*3 = 20000 *λ*∗ 5 ≤ (5500 − *x*1)/(5500 − 5000) *λ*∗ 6 ≤ (16500 − *x*2)/(16500 − 15000) *λ*∗ 7 ≤ (6600 − *x*3)/(6600 − 6000) *μ*∗ 5 ≤ (5500 − *x*1)/(5500 − 5000) *μ*∗ 6 ≤ (16500 − *x*2)/(16500 − 15000) *μ*∗ 7 ≤ (6600 − *x*3)/(6600 − 6000) 0.88*x*1 + 0.91*x*2 + 0.97*x*3 ≥ 18400 0.02*x*1 + 0.01*x*2 + 0.06*x*3 ≤ 600 *λ*∗ 8 ≤ (27500 − 3*x*1)/(27500 − 25000) *λ*∗ 9 ≤ (110000 − 2*x*2)/(110000 − 100000) *λ*∗ 10 ≤ (38500 − 7*x*3)/(38500 − 35000) *xi* ≥ 0 and integer, *i* = 1, 2, 3.

The numerical example of the SCPLCC problem was solved using LINGO software (2002) Chicago, IL, USA [50]:

*x*1 = 240 *x*2 = 15,570 *x*3 = 4190 *μ*1 = 0 *μ*2 = 0 *μ*3 = 0 *μ*4 = 0 *μ*5 = 0 *μ*6 = 0 *μ*7 = 0.3066 *μ*8 = 1 *μ*9 = 1 *μ*10 = 0.0011 *z*1 = 57,000 *z*2 = 521 *z*3 = 656.20 *z*4 = 33,162.20.

4.1.2. Solving the SCPLCC Example through the Weighted Max–Min Approach

The optimal quota allocations (i.e., the purchasing orders), production capacity limitations, and budget constraints were obtained using the weighted max–min approach developed by Lin [44], as expressed in Equations (20)–(26). This SCPLCC problem can now be reformulated as the following program:

Maximize *λ* Subject to

> 0.2958*λ* ≤ (71833 − (3*x*1 + 2*x*2 + 6*x*3))/(71833 − 57000) 0.0579*λ* ≤ (521 − (0.05*x*1 + 0.03*x*2 + 0.01*x*3))/(521 − 413) 0.0863*λ* ≤ (816 − (0.04*x*1 + 0.02*x*2 + 0.08*x*3))/(816 − 604) 0.0363*λ* ≤ (90000 − (1.92*x*1 + 1.04*x*2 + 3.94*x*3))/(90000 − 10000) 0.2958*μ* ≤ (71833 − (3*x*1 + 2*x*2 + 6*x*3))/(71833 − 57000) 0.0579*μ* ≤ (521 − (0.05*x*1 + 0.03*x*2 + 0.01*x*3))/(521 − 413)

```
0.0863μ ≤ (816 − (0.04x1 + 0.02x2 + 0.08x3))/(816 − 604)
0.0363μ ≤ (90000 − (1.92x1 + 1.04x2 + 3.94x3))/(90000 − 10000)
                     Z1 = 3x1 + 2x2 + 6x3
                 Z2 = 0.05x1 + 0.03x2 + 0.01x3
                 Z3 = 0.04x1 + 0.02x2 + 0.08x3
                 Z4 = 1.92x1 + 1.04x2 + 3.94x3
                     x1 + x2 + x3 = 20000
             0.1291λ ≤ (5500 − x1)/(5500 − 5000)
           0.1254λ ≤ (16500 − x2)/(16500 − 15000)
             0.0392λ ≤ (6600 − x3)/(6600 − 6000)
               0.88x1 + 0.91x2 + 0.97x3 ≥ 18400
                0.02x1 + 0.01x2 + 0.06x3 ≤ 600
           0.0199λ ≤ (27500 − 3x1)/(27500 − 25000)
         0.0151λ ≤ (110000 − 2x2)/(110000 − 100000)
           0.1949λ ≤ (38500 − 6x3)/(38500 − 35000)
               where xi ≥ 0 and i = 1, 2, and 3
```
The numerical example of the SCPLCC problem was solved using LINGO software (2002):

*x*1 = 0 *x*2 = 15,750 *x*3 = 4250 *λ* = 0.9595 *μ*1 = 0 *μ*2 = 0 *μ*3 = 0 *μ*4 = 0 *μ*5 = 0 *μ*6 = 0 *μ*7 = 0.3066 *μ*8 = 1 *μ*9 = 1 *μ*10 = 0.0011 *z*1 = 57,000 *z*2 = 515 *z*3 = 655 *z*4 = 33,125.

#### 4.1.3. Solving the SCPLCC Example by Using the RMCGP Approach

We now consider an RMCGP problem with goals and constraints that cannot be solved under current goal programming methods. The optimal quota allocations (i.e., the purchasing orders), supplier production capacity, and financial budget constraints were considered. This SCPLCC problem was then formulated as follows:

Main goals (with each goal designated as *G*):

Capacity constraints:

Budget constraints:

(*G*8) 3*x*1 = 25, 000 (*G*8, MIN.) or 27,500 (*G*8, MAX.) (X1, budget constraint of vendor 1)

Through an RMCGP approach involving no penalty weighting [47] combined with geometric mean weighting [22,47], this SCPLCC problem was rewritten as the following program:

Min = 0.2958(*d*− 1 + *e*− 1 ) + 0.0579(*d*− 2 + *e*− 2 ) + 0.0863(*d*− 3 + *e*− 3 ) + 0.0365(*d*− 4 + *e*− 4 ) +0.1291(*d*− 5 + *e*− 5 ) + 0.1254(*d*− 6 + *e*− 6 ) + 0.0392(*d*− 7 + *e*− 7 )

$$+0.0199(d\_8^- + e\_8^-) + 0.0151(d\_9^- + e\_9^-) + 0.1949(d\_{10}^- + e\_{10}^-)$$

$$\text{s.t.}$$

(3.1*x*1 + 2*x*2 + 7*x*3)*b*1 − *d*+ + *d*− = *y*1*b*1 for the net cost goal, with a lower value being more desirable

*y*1 − *e*+ + *e*− = 57000 represents |*y*1 − *g*1,min|,

where 57000 ≤ *y*1 ≤ 71833

(0.05*x*1 + 0.03*x*2 + 0.01*x*3)*b*2 − *d*+ + *d*− = *y*2*b*2 represents the rejection goal, with a lower value being more desirable; *y*2 − *e*+ + *e*− = 413 represents |*y*2 − *g*2,min|, where

$$413 \le y\_2 \le 521$$

(0.04*x*1 + 0.02*x*2 + 0.08*x*3)*b*3 − *d*+ + *d*− = *y*3*b*3 corresponds to the goal of minimizing late deliveries goal, with a lower value being more desirable.

*y*3 − *e*+ + *e*− = 604 represents |*y*3 − *g*3,min|, where

$$604 \le y\_3 \le 816$$

(1.92*x*1 + 1.04*x*2 + 3.94*x*3)*b*4 − *d*+ + *d*− = *y*4*b*4 corresponds to the PLCC goal, with a lower value being more desirable.

*y*4 − *e*+ + *e*− = 10000 represents |*y*4 − *g*4,min|, where

$$1000 \le y\_4 \le 90000$$

*x*1*b*5 − *d*+ + *d*− = *y*5*b*5 is the capacity constraint goal of supplier 1, with a lower value being more desirable.

*y*5 − *e*+ + *e*− = 5000 represents |*y*5 − *g*5,min|, where

$$5000 \le y\_5 \le 5500$$

*x*2*b*6 − *d*+ + *d*− = *y*6*b*6 is the capacity constraint goal of supplier 2, with a lower value being more desirable.

*y*6 − *e*+ + *e*− = 15000 represents |*y*6 − *g*6,min|, where

$$15000 \le y\_6 \le 16500$$

*x*3*b*7 − *d*+ + *d*− = *y*7*b*7 is the capacity constraint goal of supplier 3, with a lower value being more desirable.

*y*7 − *e*+ + *e*− = 6000 represents |*y*7 − *g*7,min|, where

≤ *y*7 ≤ 6600

*x*1*b*8 − *d*+ + *d*− = *y*8*b*8 is the budget constraint goal of supplier 1, with a lower value being more desirable.

*y*8 − *e*+ + *e*− = 25000 represents |*y*8 − *g*8,min|, where

$$25000 \le y\_8 \le 27500$$

*x*2*b*9 − *d*+ + *d*− = *y*9*b*9 is the budget constraint goal of supplier 1, with a lower value being more desirable.

*y*9 − *e*+ + *e*− = 100000 represents |*y*9 − *g*9,min|, where

$$100000 \le y\_9 \le 110000$$

*x*3*b*10 − *d*+ + *d*− = *y*10*b*10 is the budget constraint goal of supplier 1, with a lower value being more desirable.

*y*10 − *e*+ + *e*− = 35000 represents |*y*10 − *g*10,min|, where

$$\mathbf{35000} \le y\_{\theta} \le \mathbf{38500}$$

In this program, *b*1 = *b*2 + *b*3 + *b*4 + *b*5 + *b*6 + *b*7 + *b*8 + *b*9 + *b*10 so that the net cost, rejection, and late delivery goals, as well as zero, are achieved.

Moreover, *b*2 + *b*3 + *b*4 + *b*5 + *b*6 + *b*7 + *b*8 + *b*9 + *b*10 = 1; this addition of auxiliary constraints can force the net cost goal such that the lower-bound goal is achieved and either the rejection goal or the late delivery goal is achieved.

*Z*1 = 3*x*1 + 2*x*2 + 6*x*3 *Z*2 = 0.05*x*1 + 0.03*x*2 + 0.01*x*3 *Z*3 = 0.04*x*1 + 0.02*x*2 + 0.08*x*3 *Z*4 = 1.92*x*1 + 1.04*x*2 + 3.94*x*3 *x*1 + *x*2 + *x*3 = 20000 0.88*x*1 + 0.91*x*2 + 0.97*x*3 ≥ 18400 0.02*x*1 + 0.01*x*2 + 0.06*x*3 ≤ 600 *xi* ≥ 0 and *I* = 1, 2, 3. *d*+ *i* , *d*− *i* ,*e*+ *i* ,*e*− *i* ≥ 0 (*i* = 1, 2, . . . , 10) *bi* ≥ 0 (*i* = 1, 2, . . . , 10) are binary variable.

The numerical example of the SCPLCC problem was solved using LINGO software [50]:

*x*1 = 5000 *x*2 = 9166.67 *x*3 = 5833.33

y1 = 57,000 y2 = 410 y3 = 604 y4 = 10,000 y5 = 5000 y6 = 15,000 y7 = 6000 y8 = 25,000 y9 = 100,000 y10 = 35,000 *b*1 = 1 *b*2 = 0 *b*3 = 0 *b*4 = 0 *b*5 = 1 *b*6 = 0 *b*8 = 0 *b*9 = 0 *b*10 = 0

*z*1 = 68,383.33 *z*2 = 583.33 *z*3 = 850 *z*4 = 42,116.67

In sum, the RMCGP method involving geometric mean weighting and no penalty weighting solved the SCPLCC problem.

4.1.4. Solving the SCPLCC Example through RMCGP, Geometric Mean Weighting, and Penalty Weighting

In this SCPLCC example, the optimal quota allocations (i.e., purchasing order), production capacity limitations, and budget constraints of the suppliers were determined through RMCGP with a penalty-weighted approach, as expressed in Equations (27) and (30). This SCPLCC problem can now be reformulated as the following program:

Min = 0.2958(5*d*+ 1 + *d*− 1 + *e*− 1 ) + 0.0579(4*d*+ 2 + *d*− 2 + *e*− 2 ) + 0.0863(3*d*+ 3 + *d*− 3 + *e*− 3 ) +0.0365(2*d*+ 4 + *d*− 4 + *e*− 4 ) + 0.1291(*d*− 5 + *e*− 5 ) + 0.1254(*d*− 6 + *e*− 6 ) +0.0392(*d*− 7 + *e*− 7 ) + 0.0199(*d*− 8 + *e*− 8 ) + 0.0151(*d*− 9 + *e*− 9 ) + 0.1949(*d*− 10 + *e*− 10) s.t. (3.1*x*1 + 2*x*2 + 7*x*3)*b*1 − *d*+ 1 + *d*− 1 = *y*1*b*1 *y*1 − *e*+ 1 + *e*− 1 = 57000 57000 ≤ *y*1 ≤ 71833 (0.05*x*1 + 0.03*x*2 + 0.01*x*3)*b*2 − *d*+ 2 + *d*− 2 = *y*2*b*2 *y*2 − *e*+ 2 + *e*− 2 = 413 413 ≤ *y*2 ≤ 521 (0.04*x*1 + 0.02*x*2 + 0.08*x*3)*b*3 − *d*+ 3 + *d*− 3 = *y*3*b*3 *y*3 − *e*+ 3 + *e*− 3 = 604 604 ≤ *y*3 ≤ 816 (1.92*x*1 + 1.04*x*2 + 3.94*x*3)*b*4 − *d*+ 4 + *d*− 4 = *y*4*b*4 *y*4 − *e*+ 4 + *e*− 4 = 10000 10000 ≤ *y*4 ≤ 90000 *y*5 − *e*+ 5 + *e*− 5 = 15000 *x*1*b*5 − *d*+ 5 + *d*− 5 = *y*5*b*5 *y*6 − *e*+ 6 + *e*− 6 = 15000 *x*2*b*6 − *d*+ 6 + *d*− 6 = *y*6*b*6 15000 ≤ *y*6 ≤ 16500

*y*7 − *e*+ 7 + *e*− 7 = 6000 *x*3*b*7 − *d*+ 7 + *d*− 7 = *y*7*b*7 6000 ≤ *y*7 ≤ 6600 *y*8 − *e*+ 8 + *e*− 8 = 25000 3*x*1*b*8 − *d*+ 8 + *d*− 8 = *y*8*b*8 25000 ≤ *y*8 ≤ 27500 *y*9 − *e*+ 9 + *e*− 9 = 100000 2*x*2*b*9 − *d*+ 9 + *d*− 9 = *y*9*b*9 100000 ≤ *y*9 ≤ 110000 *y*10 − *e*+ 10 + *e*− 10 = 35000 6*x*3*b*10 − *d*+ 10 + *d*− 10 = *y*10*b*10 35000 ≤ *y*9 ≤ 38500 *b*1 = *b*2 + *b*3 + *b*4 + *b*5 + *b*6 + *b*7 + *b*8 + *b*9 + *b*10 *b*2 + *b*3 + *b*4 + *b*5 + *b*6 + *b*7 + *b*8 + *b*9 + *b*10 = 1 *Z*1 = 3*x*1 + 2*x*2 + 6*x*3 *Z*2 = 0.05*x*1 + 0.03*x*2 + 0.01*x*3 *Z*3 = 0.04*x*1 + 0.02*x*2 + 0.08*x*3 *Z*4 = 1.92*x*1 + 1.04*x*2 + 3.94*x*3 *x*1 + *x*2 + *x*3 = 20000 0.88*x*1 + 0.91*x*2 + 0.97*x*3 ≥ 18400 0.02*x*1 + 0.01*x*2 + 0.06*x*3 ≤ 600 *xi* ≥ 0 and *i* = 1, 2, 3. (*i* = 1, 2, . . . , 10) *bi* ≥ 0 (*i* = 1, 2, . . . , 10) are binary variables.

The numerical example of the SCPLCC problem was solved using LINGO software [50]:

*x*1 = 0 *x*2 = 15,750 *x*3 = 4250 y1 = 57,000 y2 = 410 y3 = 604 y4 = 10,000 y5 = 5000 y6 = 15,000 y7 = 6000 y8 = 25,000 y9 = 100,000 y10 = 35,000 *b*1 = 1 *b*2 = 0 *b*3 = 0 *b*4 = 0 *b*5 = 0 *b*6 = 1 *b*8 = 0 *b*9 = 0 *b*10 = 0 *z*1 = 57,000 *z*2 = 515 *z*3 = 655 *z*4 = 33,125.

The results demonstrated that RMCGP with geometric mean weighting and penalty weighting was a suitable approach for solving the SCPLCC problem.

#### 4.1.5. RMCGP with Mean Weighting, Penalty Weighting, and WLGP

To verify the RMCGP SCPLCC model problem, we modified the model through mean-weighted–penalty-weighted linear goal programming. The objective function was expressed as an equation presented in a study [13]:

$$\text{MIN} = \frac{\theta\_1}{T\_1}dn\_1^- + \frac{\theta\_2}{T\_2}dp\_2^+ + \frac{\theta\_3}{T\_3}dn\_3^- + \frac{\theta\_4}{T\_4}dn\_4^- + \frac{\theta\_5}{T\_5}dp\_5^+ + \frac{\theta\_6}{T\_6}dp\_6^+ + \frac{\theta\_7}{T\_7}dn\_7^- + \frac{\theta\_8}{T\_8}dn\_8^+ + \frac{\theta\_9}{T\_9}dn\_9^- + \frac{\theta\_{10}}{T\_{10}}dn\_{10}^- $$

where

*θi* = *i th* the *i*th weighted geometric mean; *i* = 1, 2, 3, . . . , 10 *θ*1 = 0.2958; *θ*2 = 0.0579; *θ*3 = 0.0863; *θ*4 = 0.0365; *θ*5 = 0.1291; *θ*6 = 0.1254; *θ*7 = 0.0392; *θ*8 = 0.0199; *θ*9 = 0.0151; and *θ*10 = 0.1949. *Ti* = normalization constant of the *i*th goal; *i* = 1, 2, 3, . . . , 10 *T*1 = 57,000 (total net cost goal) *T*2 = 515 (total rejection goal) *T*3 = 655 (total late delivery goal) *T*4 = 33,125 (total PLCC goal) *T*5 = 5000 (total capacity constraint goal of supplier 1) *T*6 = 15,000 (total capacity constraint goal of supplier 2)

*T*9 = 100,000 (total budget constraint goal of supplier 2)

*T*10 = 35,000 (total budget constraint goal of supplier 3)

Subsequently, the numerical example of the SCPLCC problem was solved using LINGO software [50]:

*x1* = 1034, *x2* = 15,000, *x3* = 3965, *y1* = 57,000, *y2* = 410, *y3* = 604, *y4* = 10,000, *y5* = 5000, *y6* = 15,000, *y7* = 6000, *y8* = 25,000, *y9* = 100,000, *y10* = 35,000, *z1* = 56,896.55, *z2* = 541.37, *z3* = 658.62, *z4* = 332,107.

An RMCGP SCPLCC model to which WLGP was applied should yield similar results to an RMCGP SCPLCC model to which WLGP was applied. The results indicated that supplier 2 is the most suitable.

#### *4.2. Summary of Results Obtained under All Approaches*

Table 5 presents a summary of the results obtained under all goal programming approaches.

**Table 5.** Results obtained through all goal programming approaches.

*4.3. Discussion of Results Obtained under the Two Approaches*

Notably, the weighted max–min method developed by Lin [39] 44 yielded the same solution to the SCPLCC problem as did the RMCGP method involving geometric mean weighting and penalty weighting.

RMCGP involving geometric mean weighting and no penalty weighting revealed that the lower-bound order quantity of supplier 1 was 5000. This is attributable to the lack of penalty-weighted constraints. Moreover, *b*1 = 1 and *b*5 = 1 (Table 5).

RMCGP involving mean weighting and penalty weighting yielded *b*1 = 1 and *b*6 = 1, and the upper bound of the order quantity of supplier 1 exceeded 15,000; specifically, *x*2 = 15,750. To ensure that the net cost rejection or late delivery goal is met, zero should be obtained (e.g., *b*1 = 1 and *b*6 = 1), and the auxiliary constraints of *bi* should be applied to the order quantity adjustment (Table 5).

To compare the results of the two verification approaches and increase the accuracy, we applied RMCGP with geometric mean weighting and penalty weighting. We also implemented a WLGP model. Figure 3 shows that the order quantity, net cost, rejections, late deliveries, PLCC, production capacity, and budget under the MCGP model approach were lower than those under the MOLP model approach. In sum, the RMCGP SCPLCC model yielded the same results as did the RMCGP with geometric mean weighting and penalty weighting and the WLGP model (refer to the results for the fifth model in Table 5).

**Figure 3.** Results obtained using revised multichoice goal programming (RMCGP), multiobjective linear programming (MOLP) model approaches.

#### *4.4. Sensitivity Analysis*

To test the RMCGP and the WLGP models using geometric mean weighting and penalty weighting, we employed a method presented by Ho [51]. Table 6 and Figure 4 demonstrate that if managers wish to diversify the supplier selection risk, decision-makers can set λ to 0 or 0.2 to divide low order quantities among the three suppliers. Otherwise, they can set λ to 0.8 or 1 to obtain relatively higher achievement levels.

**Table 6.** Sensitivity analysis results of the mean-weighted–penalty-weighted linear goal programming model.

**Figure 4.** Sensitivity analysis results of the WLGP model.

#### *4.5. Discussion*

A short review of the key results from the study is as follows. For the SCPLCC sustainable procurement challenge, the WLGP approach model and RMCGP with geometric mean weighting and penalty weighting are appropriate (from Table 6, we can discover *x*2 order quantity value 15,750 is acceptable).

The two approaches to tackling the SCPLCC problem provided here can assist decisionmakers in improving supplier selection and provide real-world consequences for the LED sector in terms of lowering PLCC costs, minimizing net costs, reducing rejections, and meeting PLCC objectives.

#### **5. Conclusions and Managerial Implications**

#### *5.1. Conclusions*

Because high-tech companies consider numerous factors (e.g., net cost, rejections, late deliveries, PLCC strategies), achieving only one objective is insufficient for PLCC reduction. SC models for solving this SCPLCC problem have seldom been investigated. In the present study, we solved the SCPLCC problem through two approaches, both of which employed geometric mean weighting. The results serve as a managerial reference for the examined company—specifically, for determining vendor quotas in SCM when the capacities and budget constraints of each vendor are uncertain (given a lower or upper bound). The first approach, which considered the uncertainty of the fuzzy model, used a linear membership function, and the entire formulation was solved through a fuzzy multiobjective programming approach. The SCPLCC problem was then transformed through a weighted max–min method, as well as through the application of an AW MOLP model and a corresponding crisp, single-objective linear programming approach. The second approach, which involved RMCGP with geometric mean weighting and penalty weighting, emphasized the supply of a high-quality product and PLCC reduction. Furthermore, this approach guided the relationships between goals in the multiobjective problem.

#### *5.2. Managerial Implications*

Our study has the following managerial implications.

First, the SCPLCC problem can easily be solved using commercially available linear programming software such as LINDO and LINGO.

Second, our solution to the SCPLCC problem is more comprehensive than that achieved through linear programming, conventional goal programming, and other deterministic methods applied when information vagueness is a concern. We transformed the SCPLCC problem into a weighted max–min fuzzy programming model with lower computational complexity, thus simplifying the application of fuzzy methodology [20].

Third, in real-world SCM scenarios, the provision of deterministic values of system parameters (e.g., production capacity and constraints) is unnecessary.

Fourth, our findings can assist managers of LED manufacturers in identifying associations between SSCM and RSCM, thereby facilitating informed decision-making in terms of both sustainability and resilience. We assert that transparency, as well as the consideration of the PLCC model in SCM and stakeholder engagement, can help firms gain competitive advantage. Our findings revealed several complementary and conflicting relationships among the formative elements of SSCM and RSCM. For example, flexibility enables sustainability in SCs but is at least partially discordant with long-term firm–supplier relationships. Our examination of a real-world case adds to the empirical evidence on the implementation of SSCM and RSCM. However, the generalizability of these results to other industries or regions is questionable given potential differences in managerial practices and other features.

Fifth, under the RMCGP approach [47], auxiliary constraints can inform betweengoal relationships in multiobjective problems. Regarding the example of the SCPLCC problem, auxiliary constraints *b*i facilitated goal realization (e.g., through the adjustment of order quota allocation). RMCGP is relevant to managerial decision-making problems. We modified an RMCGP approach proposed by Chang [47] involving weighted goal programming to solve the SCPLCC problem, accounting for multiple target levels by employing the multiplicative terms of binary variables. Regarding the mapping of one goal to numerous aspiration levels, under certain conditions, decision-makers may base their decisions on a goal that can be achieved on various aspiration level [52]. According to Little [53], operational models are only useful if they are simple, robust, easily controllable, adaptive, easily communicated, and address essential SCPLCC issues. In particular, our SCPLCC model satisfies the first four criteria [27].

We tested our SCPLCC model on a Taiwanese LED company. Because having precise knowledge of all parameters is not required, high-tech companies can easily use our two goal-programming approaches to select suppliers in a fuzzy environment. The two present methods for solving the SCPLCC problem can help decision-makers optimize supplier selection. They also enable managers (including purchasing managers) to manage SC performance and SSCM goals on the basis of factors such as the net cost, number of rejections, number of late deliveries, and overarching PLCC goals.

#### *5.3. Limitations*

To validate the SCPLCC problem, overcome the shortcomings of the two goal programming approaches, and ensure accurate outcomes, we compared the models with the RMCGP and weighted goal programming approaches. However, should decision-makers employ a hybrid RMCGP method with a multicriteria decision-making approach, they may obtain unexpected or confusing results.

#### *5.4. Future Directions*

To solve SCPLCC problems in scenarios involving multiple suppliers, our SCPLCC models can be integrated with other goal programming approaches, including multicriteria decision-making approaches such as de novo programming, the rough set approach [54,55], or the neutrosophic set approach [56].

**Author Contributions:** Conceptualization, Y.-J.T.; formal analysis, G.-Y.G.; C.-S.T. and Y.-J.T.; writing—original draft preparation, Y.-J.T. and C.-S.T.; writing—review and editing, C.-S.T. and Y.-J.T.; planning all works in the study, H.-S.L.; supervision, Y.-S.L. and H.-S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The study did not report any data.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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**3. Botanical description of mulberry plant**

Before any sort of investigations of a plant it is extremely urgent to go through its overall botanical details. Mulberry is a perennial, fast growing, woody, deciduous, deep and wide rooted plant [21]. Generally the height of Mulberry plant is approximately 5-6 feet from the ground level [22]. Stem of mulberry is cylindrical in shape with milky sap and fissured bark [23]. Mulberry leaves are generally 5-7.5 cm long and 6-10 cm wide, but they vary widely in their size and shape. Leaves are mostly deeply lobed or having serrate margins; leaf apex is mostly acute with cordate or truncate base. Basal nerves are generally 3; near the margins lateral nerves are forked. Flowers are yellowish green in color with chromosome number 2n = 28. There are differentiations between female and male spikes shape and size in mulberry. Male spikes (catkins) are cylindrical and broad where as female spikes (catkins) are ovoid and stalked, and female spikes (catkins) shorter than male spikes (catkins). Mulberry fruits are arranged longitudinally around the central axis in cluster of small fruits similar with blackberry or loganberries. Mulberry fruits are white to pinkish white in color and during the time of ripening it becomes purple or black in color. Fruits contain many drupes which are enclosed in a fleshy perianth, upto 5 cm long, sub-globose or ovoid in shape. Ovary of mulberry is unicellular with presence of a bifid stigma [2].