Wafer foundries face numerous challenges in localizing the semiconductor supply chain, necessitating various measures to overcome these challenges. Given their limited funding, time and resources, these measures require prioritization.
To prioritize these measures, this study proposes a dynamic fuzzy compromise planning (DFCP) approach, which dynamically allocates resources across a limited budget based on the priority of measures within each time period. The DFCP approach embeds a fuzzy technique for order preference by similarity to ideal solution mechanism into a fuzzy mixed binary-nonlinear programming model.
The DFCP approach has been applied to a real-world case. Experimental results demonstrated that the DFCP approach satisfied the three objectives of wafer foundries, while existing methods either over-concentrated resources on a few possible measures or produced discontinuous planning fragments.
Semiconductor supply chain localization is undoubtedly one of the most advanced manufacturing models in the semiconductor industry, yet it has received little discussion to date. The DFCP approach combines multi-criteria decision-making practices with fuzzy optimization models, which is quite different from most existing fuzzy compromise programming methods.
1. Introduction
Semiconductor supply chain localization refers to a trend in which wafer foundries move their wafer fabrication plants (wafer fabs) to the vicinity of chip design companies or build new wafer fabs near them [1]. The motivation stems from the urgent need of chip design companies or their governments to secure semiconductor manufacturing capabilities and mitigate geological risks [2]. International events such as the COVID-19 pandemic, the USA–China trade war and the Russia–Ukraine war have further reinforced this trend [3].
Semiconductor supply chain localization is undoubtedly one of the most advanced manufacturing models in the semiconductor manufacturing industry, yet it has been little discussed so far due to its novelty. So far, researchers have reached consensus that the regions (countries) in which new fabs are built to localize semiconductor supply chains were often predetermined based on customer demand and political pressure rather than optimized [4], which enhanced the sustainability of wafer foundries but was detrimental to their short-term competitiveness [1, 5]. In addition, wafer foundries faced several challenges that needed to be overcome in some way in semiconductor supply chain localization, such as unfamiliarity with the laws, cultural differences, insufficient local human resources, uncertain local government subsidies, competition from local rivals, higher wage levels, etc. [5–7]. Several possible measures are then conceived to overcome these challenges [8].
In the literature, Chiu and Chen [9] proposed a neutrosophic collaborative intelligence (NCI) method to mitigate the impact of cultural differences in semiconductor supply chain localization. Chen et al. [10] proposed an interpretable fuzzy collaborative intelligence (EFCI) method to prioritize feasible measures to address the challenges of localizing the semiconductor supply chain. Chen and Chiu [11] proposed the fuzzy arithmetic mean (FAM)–decomposition analytic hierarchy process (AHP)–the technique for order preference by similarity to ideal solution (TOPSIS) method to resolve the indeterminacy issue in planning semiconductor supply chain localization by considering multiple perspectives when formulating decisions. However, these methods are static methods, while semiconductor supply chain localization is a long-term process, which is a research gap and motivates us to propose a dynamic approach. In addition, given the limited budget and resources available for these possible measures and the high degree of uncertainty surrounding the localization of semiconductor supply chains, it is necessary to prioritize these possible measures.
To fill these gaps, the dynamic fuzzy compromise programming (DFCP) approach is proposed in this study, in which fuzzy technique for order preference by similarity to ideal solution (FTOPSIS) [12] is inserted into a dynamic programming (DP) model to evaluate the overall utilities of possible measures taken in each period. Fuzzy compromise programming methods have been widely used for multi-criteria decision-making (MCDM) or multi-objective mathematical programming (MOMP) in various fields [10, 13–17].
The proposed methodology has the following novelties:
Past fuzzy compromise programming research either applied fuzzy MCDM or fuzzy MOMP methods. Few combined both types of methods.
Most of the existing fuzzy compromise programming methods focus on static planning rather than dynamic planning.
In the DFCP approach, the limited budget in each time period is allocated among some selected possible measures based on the evaluation results in order to maximize the sum of overall utilities over the entire planning horizon. In contrast, the existing fuzzy compromise programming methods will spend most of the budget on possible measures with the highest overall utility. However, this possible measure does not necessarily come cheap. Spending part of the budget on possible measures that have lower overall utilities but are cheaper may provide greater returns.
The DFCP approach seeks compromises between various criteria and time periods, showing its dynamic nature, while most existing fuzzy compromise planning methods sought a compromise between various criteria or objective functions.
Traditional non-artificial intelligence methods for similar purposes include stochastic methods [18], structure dynamics control methods [19], etc. However, these methods are either computationally intensive or difficult for planners to understand.
In the DFCP approach, a fuzzy mixed binary-nonlinear programming (FMBNLP) model [9] is constructed to assist a wafer foundry in dynamically allocating the limited budget in each time period among some selected possible measures, considering the high degree of uncertainty surrounding the localization of semiconductor supply chains. The objective function is to maximize the sum of overall utilities over the entire planning horizon. However, the FMBNLP model is intractable to be solved using existing optimization software. To address this issue, the FMBNLP model is converted into a crisp MBNLP problem to facilitate the problem solving.
The remaining of this study is organized as follows. Section 2 identifies the various forces driving the localization of semiconductor supply chains. Section 3 lists challenges in semiconductor supply chain localization. To overcome these challenges, possible measures that can be taken by semiconductor manufacturers are also put forth. Considering the limited budget and resources available for these possible measures and the high degree of uncertainty surrounding the localization of semiconductor supply chains, the DFCP approach is proposed to dynamically prioritize these measures in Section 4. In Section 5, a real case based on the initial implementation experiences and phased results of three semiconductor manufacturers is analyzed using the DFCP approach. The experimental results are then discussed in Section 6, and Section 7 gives conclusions and future research prospects.
2. Literature review
2.1 Semiconductor supply chain resilience
Xiong et al. [20] reviewed the relevant literature on semiconductor supply chain disruptions to analyze the vulnerabilities of semiconductor supply chains, so as to formulate resilience strategies. They focused on geopolitical security issues and public health events, thereby identifying challenges faced by supply chain participants and formulating possible mitigation strategies that could be adopted. According to their analysis results, innovative supply chain management practices and decentralized networks for necessary redundancy were imperative.
Ramirez and Le [21] asserted that semiconductor supply chains were increasingly vulnerable to disruptions from geopolitical conflicts, natural disasters and intellectual property theft. To address this issue, supply chain resilience was considered critical to integrate information, concerns and approaches across supply networks. To this end, they reviewed the relevant literature and utilized bibliometric network visualization to identify relationships between industry-specific concerns and resilience-boosting methodologies.
In the view of Moktadir and Ren [22], the COVID-19 pandemic, Ukrainian–Russian conflict, China–USA trade war and environmental concerns regarding carbon emissions have made semiconductor supply chains more vulnerable. To help overcome such vulnerability, they integrated decomposed fuzzy set-based Delphi method, weighted influence nonlinear gauge system and quality function deployment to identify and assess the strength–interaction relationships between resilience challenges and mitigation strategies.
In another study, Chen [5], considered six factors – USA–China trade war, geopolitics, the COVID-19 pandemic, Ukrainian–Russian war, the rise of environmental awareness and the need for semiconductor supply chain transparency as influencing factors on semiconductor supply chain resilience. To mitigate the impact of such factors, semiconductor supply chain localization was considered an effective strategy. To this end, they applied decision trees, strength, weakness, opportunity and threat analysis, AHP and TOPSIS to overcome the challenges faced by wafer foundries during semiconductor supply chain localization.
2.2 Fuzzy compromise planning
Some relevant recent literature on fuzzy compromise planning is reviewed as follows. One mainstream of fuzzy compromise planning incorporates fuzzy MP for planning purposes. For example, a fuzzy multi-objective, multi-echelon, multi-product mixed integer-linear programming (FMILP) model with varying importance and priorities was formulated in Subulan et al. [16] to select the locations of multiple distribution, collection and recycling facilities. The objective function was to minimize the total closed-loop supply chain cost. Fuzzy goals were set for some key variables, and then the FMILP model was converted into an equivalent linear programming (LP) model and solved with an objective function that maximized the sum of the satisfaction degrees of the fuzzy goals.
A fuzzy goal programming method based on multi-objective compromise was proposed in He et al. [14], selecting from 31 assets in the Financial Times Stock Exchange (FTSE) stock market based on their return rates, covariances and turnover rates, in which goals were established for the three objective functions, and then the absolute deviations from these goals were aggregated using the geometric mean.
A fuzzy multi-objective compromise method was proposed in Alizadeh et al. [13] to manage groundwater resources. Their study considered objectives such as minimizing the sum of deviations between groundwater demand and supply, minimizing the sum of groundwater level drawdowns, minimizing the sum of total dissolved solid concentrations, etc. The constraints contained a multi-layer perceptron to estimate state variables, so it could not be solved directly. To address this issue, possible solutions were first fed into the multilayer perceptron to derive state variables to construct complete constraints and verify the feasibility of the solutions. The non-dominated sorting genetic algorithm II (NSGA-II) was then applied to select diverse Pareto-optimal solutions.
To plan the cost-emission operation of heat and power hubs for an industrial consumer, a bi-objective nonlinear programming model was formulated in Khodaei et al. [23]. By establishing goals for the objective functions, the bi-objective nonlinear programming model was converted into a fuzzy compromise goal programming problem to be solved.
Another mainstream of fuzzy compromise planning is the application of fuzzy MCDM in planning. For example, fuzzy vlsekriterijumska optimizacija i kompromisno resenje (FVIKOR) was applied by Vinodh et al. [24] to select the most suitable conceptual design of automotive parts in a group fuzzy MCDM environment. As many as 20 criteria were considered to evaluate the performances of these designs, so compromises had to be made between so many criteria. There were five decision-makers comparing four alternatives. However, the weights of criteria were only assigned subjectively and might be prone to high inconsistencies.
An intuitionistic fuzzy gray model was proposed by Mousavi et al. [15] to select the optimal design of an automotive component in the entire oil pump. Three attributes of five alternatives were considered and compromised. The weights of the criteria were subjectively assigned as intuitionistic fuzzy numbers. The performances in optimizing these attributes were also given in intuitionistic fuzzy numbers, and on this basis, the positive ideal separation matrix and the negative ideal separation matrix were constructed. After measuring the deviations of each alternative from the positive ideal separation matrix and the negative ideal separation matrix, the gray correlation coefficient was used to evaluate the overall performance of the alternative [25].
To select a subset of projects (i.e., a portfolio) and allocate limited resources among favored projects, the elimination and choice expressing reality method (ELECTRE III) was applied by Rivera et al. [24], where fuzzy outranking relations were used to compare various portfolios to select the best portfolio as a non-strict outranked and non-dominated solution.
Fuzzy analytic hierarchy process and FVIKOR was combined in Wang et al. [17] to select the most suitable third-party logistics (3PL), in which 10 experts compared 10 alternatives based on their performances on 15 criteria. First, fuzzy geometric mean (FGM) was applied to derive the fuzzy weights of criteria from the fuzzy pairwise comparison matrix. The results were then fed into FVIKOR to evaluate and/or compare the overall performances (i.e. the worst group scores) of the 3PLs.
Given the constraints of budget, time and resources [26], wafer foundries needed to prioritize feasible measures to address the challenges of localizing the semiconductor supply chain, which constituted a novel fuzzy MCDM problem that has not been solved before. To fill this gap, an EFCI method was proposed in Chen et al. [10], in which improved fuzzy weighted intersection was designed to a posteriori aggregate the evaluation results of decision makers using various fuzzy MCDM methods into a type-2 fuzzy approximation.
To mitigate the impact of cultural differences on the localization of the semiconductor supply chain, an NCI method was proposed in Chiu and Chen [27], in which expert judgments were aggregated and the indeterminacy of these judgments was retained until the last step, thus making a flexible decision, which differed from previous studies. In the NCI method, the calibrated neutrosophic geometric mean was applied by each expert to derive the neutrosophic weights of each criterion. Then, the suitability of each measure was evaluated using the neutrosophic technique for order of preference by similarity to the ideal solution. Finally, the neutrosophic weighted intersection operator was devised to aggregate the evaluation results of all experts.
To minimize the cost and error in placing microphasor measurement units in power delivery networks, a multi-objective optimization problem was solved in Maji et al. [28], for which the particle swarm optimization technique was applied to evolve the currently feasible solutions to a near-optimal solution. Considering the multi-objective nature, Pareto optimal solutions were ultimately identified.
The past fuzzy compromise planning studies reviewed above belonged to either the fuzzy MP category or the fuzzy MCDM category. Different from past fuzzy compromise planning research, the DFCP method proposed in this study belongs to both categories by embedding FTOPSIS (a fuzzy MCDM method) into the FMBNLP model (a fuzzy MP method). Few studies have made similar attempts in the past. For example, the weights of criteria using analytic network process were derived by Tolga et al. [29] and then fed the results into a fuzzy compromise goal programming but did not merge the two methods into one as in this study. In addition, the weights of the criteria were kept fixed during the optimization process of Tolga et al. [29], while they may change from time to time in this study. Furthermore, most past research in this field has made a compromise between various criteria or objective functions, while the DFCP approach also makes a compromise between actions taken at different time periods. The differences between the DFCP approach and some existing methods are summarized in Table 1.
Differences between the DFCP approach and some existing methods
| Method | Problem | Model/method | Category | Type | Compromise between |
|---|---|---|---|---|---|
| Vinodh et al. [24] | Conceptual design selection | FVIKOR | Fuzzy MCDM | Static | Criteria |
| Subulan et al. [16] | Distribution, collection, and recycling facility location selection | FMILP | Fuzzy MP | Static | Objective functions |
| He et al. [14] | Asset selection | Multi-objective fuzzy goal programming | Fuzzy MP | Static | Objective functions |
| Mousavi et al. [15] | Optimal design selection | Intuitionistic fuzzy gray TOPSIS | Fuzzy MCDM | Static | Criteria |
| Alizadeh et al. [13] | Groundwater resource management | Fuzzy multi-objective nonlinear programming, multi-layer perceptron and NSGA-II | Fuzzy MP | Static | Objective functions |
| Khodaei et al. [23] | Cost-emission operation planning of industrial consumers | Bi-objective nonlinear programming + fuzzy compromise goal programming | Fuzzy MP | Static | Objective functions |
| Liu et al. [30] | Supplier selection | Multi-objective linear programming + fuzzy compromise goal programming | Fuzzy MP | Static | Objective functions and alternatives |
| Rivera et al. [24] | Portfolio analysis | ELECTRE III + fuzzy outranking | Fuzzy MCDM | Static | Criteria |
| Wang et al. [17] | 3PL selection | FGM + FVIKOR | Fuzzy MCDM | Static | Criteria |
| DFCP approach | Semiconductor supply chain localization | FTOPSIS and FMBNLP | Fuzzy MCDM, fuzzy MP | Dynamic | Criteria and time periods |
The past fuzzy compromise planning studies reviewed above either apply fuzzy MP or fuzzy MCDM methods. Unlike these past fuzzy compromise planning studies, the DFCP approach proposed in this study combined the two types of methods by embedding FTOPSIS (a fuzzy MCDM method) into a FMBNLP model (a fuzzy MP method). In addition, in most past studies in this field make compromise between various criteria or objective functions, while the DFCP approach also seeks a compromise between the actions taken in various time periods.
3. Gaps and objectives
After reviewing relevant literature, it is clear that existing methods in this field have the following gaps that need to be filled:
There is a lack of dynamic planning methods for semiconductor supply chain localization in the long term and
There is a need to dynamically prioritize possible measures to overcome the challenges of semiconductor supply chain localization.
The research objectives of this study include.
Objective #1: Multiple (but not all) possible measures should be taken simultaneously;
Objective #2: These possible measures must be completed gradually and
Objective #3: More budget and resources should be allocated to possible measures with higher priorities.
4. Methodology
In the DFCP approach, the FTOPSIS mechanism must be specifically embedded in the FMBNLP model rather than in other simpler optimization frameworks, because DFCP is a long-term planning process where early results set constraints for later periods. Furthermore, some alternatives are completed early on and no longer considered later, necessitating a DP approach. Moreover, the remaining alternatives compete with each other by considering multiple criteria, and the FTOPSIS mechanism can better account for these criteria.
4.1 Fuzzy mixed binary-nonlinear programming (FMBNLP) model
Semiconductor manufacturers apply the DFCP approach to take multiple (but not all) possible measures simultaneously and gradually, during which more budget and resources are allocated to possible measures with higher priorities, as illustrated in Figure 1. In each time period, the alternatives compared using FTOPSIS vary. Therefore, ideal and anti-ideal solutions also dynamically change over time periods, which is distinct from existing FTOPSIS methods.
A bar graph compares burden over time with different measures. The horizontal axis is labeled t with values 1, 2, 3, and 4. The vertical axis is labeled Burden. There are four vertical bars, each representing a different time point. The bars are grouped and some are stacked. The first bar has three segments: the bottom segment is white, the middle segment is light blue, and the top segment is dark blue. The second bar has four segments: the bottom three segments are white and the top segment is dark blue. The third bar has three segments: the bottom two segments are white and the top segment is dark blue. The fourth bar is entirely white. A legend on the right side indicates that the dark blue segment represents Possible measure number 3. The graph shows a trend of decreasing burden over time, with the dark blue segment appearing in the second and third bars.DFCP approach. Source: Author's composition
A bar graph compares burden over time with different measures. The horizontal axis is labeled t with values 1, 2, 3, and 4. The vertical axis is labeled Burden. There are four vertical bars, each representing a different time point. The bars are grouped and some are stacked. The first bar has three segments: the bottom segment is white, the middle segment is light blue, and the top segment is dark blue. The second bar has four segments: the bottom three segments are white and the top segment is dark blue. The third bar has three segments: the bottom two segments are white and the top segment is dark blue. The fourth bar is entirely white. A legend on the right side indicates that the dark blue segment represents Possible measure number 3. The graph shows a trend of decreasing burden over time, with the dark blue segment appearing in the second and third bars.DFCP approach. Source: Author's composition
The variables and parameters required for the DFCP approach are defined as follows.
: the normalized performance of possible measure q in optimizing criterion i during time period t; q = 1 ∼ Q; t = 1 ∼ T; i = 1 ∼n;
: ideal (zenith) solution in time period t; t = 1 ∼ T;
: anti-ideal (nadir) solution in time period t; t = 1 ∼ T;
: possible measure q; q = 1 ∼ Q;
B: budget;
: total cost of possible measure q, which is an estimate and therefore expressed as a fuzzy value; q = 1 ∼ Q;
: distance from possible measure q to the anti-ideal solution in time period t. q = 1 ∼ Q; t = 1 ∼ T;
: distance from possible measure q to the ideal solution in time period t. q = 1 ∼ Q; t = 1 ∼ T;
: if possible measure q is taken in time period t; if otherwise. q = 1 ∼ Q; t = 1 ∼ T;
q: possible measure index; q = 1 ∼ Q;
: percentage of possible measure q competed during time period t; q = 1 ∼ Q; t = 1 ∼ T;
: weighted score of possible measure q with respect to criterion i in time period t; q = 1 ∼ Q; t = 1 ∼ T; i = 1 ∼n.
t: time index; t = 1 ∼ T;
T: planning horizon;
: overall utility of possible measure q in time period t; q = 1 ∼ Q; t = 1 ∼ T and
: weight of criterion i; i = 1 ∼n.
All fuzzy parameters and variables in the DFCP approach are given in or approximated by triangular fuzzy numbers (TFNs).
The objective is to maximize the sum of overall utilities over the entire planning horizon:
The first constraint is that the total cost over the entire project horizon should not exceed the budget:
In addition, the sum of the percentages of each possible measure completed within the planning scope should not exceed 1, i.e. fully or partially completed:
If a possible measure has already been completed, the measure will not be executed during the next time period. In addition, it is best to complete a possible measure within continuous time periods. After considering these requirements,
Subsequently, the total utility of a possible measure varies over time, so it is evaluated using FTOPSIS by comparing only possible measures taken during the current time period:
Equation (5) is decomposed into the following constraints,
where
can be derived as
where
The ideal and anti-ideal solutions are defined as
As a result, the following FMBNLP model is formulated:
(FMBNLP model)
s.t.
However, the FMBNLP model is intractable and needs to be converted into a simpler form to be easily solved using existing optimization software.
4.2 Converting the FMBNLP model
A flowchart is provided in Figure 2 to illustrate the steps of converting the FMBNLP model.
A flowchart with ten steps, each step involving defuzzification processes, starting with defuzzifying the fuzzy objective function and ending with defuzzifying the fuzzy normalized performances.Steps of converting the FMBNLP model. Source: Author's composition
A flowchart with ten steps, each step involving defuzzification processes, starting with defuzzifying the fuzzy objective function and ending with defuzzifying the fuzzy normalized performances.Steps of converting the FMBNLP model. Source: Author's composition
First, the objective function can be defuzzified using the center-of-gravity (COG) function [31] as
Constraint (14) can be treated similarly,
Constraint (16) can be converted into the following sub-constraints:
Subsequently, according to the arithmetic for TFNs, Equation (17) is equivalent to
which can be re-organized as
According to Reference [32], Equation (18) is equivalent to
which can be re-organized as
Equation (19) can be converted similarly as
Equations (20) and (21) can be rewritten as
Constraint (22) is decomposed into
Constraint (23) is treated similarly as Constraint (17),
Finally, the FMBNLP model is converted into an equivalent MBNLP problem (see Appendix I) that can be more easily solved using any existing optimization software.
5. Materials and analysis
5.1 Background
A real case is used to illustrate the applicability of the proposed methodology. The real case was based on the initial implementation experience and phased results of building localized wafer fabs by a major wafer foundry. Possible measures that can be taken by the wafer foundry in overcoming supply chain localization challenges include:
Benefiting local residents or leveraging local communities to alleviate cultural differences;
Designing staggered shift systems;
Cross-shift collaboration in problem solving;
Collaboration between wafer fabs in different time zones;
Increasing (or relocating) the proportion of domestic workers;
Further automation [19] and
Accelerating yield learning through early mass production, etc.
These possible measures were to be prioritized. In other words, the purpose of conducting this experiment was not to select a single (i.e. the best) possible measure. The foundry was certainly and willing to take multiple measures simultaneously, for which the following factors were considered critical:
These criteria have been validated by three field experts: a wafer fab manager, a semiconductor industry analyst and a professor specializing in semiconductor supply chain localization. These three experts came together to overcome the challenges of supply chain localization, explore potential measures and determine the optimal sequence of solutions.
Implementation costs and the need for cross-organizational collaboration are smaller-the-better (STB) criteria, while the others are larger-the-better (LTB) criteria. The data of the seven possible measures in these dimensions have been collected or estimated, as shown in Table 2. Based on these data, the performances and/or requirements of these possible measures in optimizing various criteria were evaluated in Table 3.
Data of the seven possible measures in the five dimensions
| q | Implementation costs (million dollars) | Legal compliance | Easiness to implement | Need for cross-organization collaboration | Quick and visible results (years) |
|---|---|---|---|---|---|
| 1 | 0.13 | High | Moderate | Frequent | 0.73 |
| 2 | 4.55 | Very low | Easy | Moderate | 0.95 |
| 3 | 0.39 | High | Difficult | Moderate | 2.54 |
| 4 | 4.81 | Very low | Moderate | Moderate | 2.11 |
| 5 | 4.63 | Moderate | Easy | Very few | 0.24 |
| 6 | 7.79 | Very high | Very difficult | Very few | 3.42 |
| 7 | 8.00 | Very high | Difficult | Very few | 0.81 |
Performances of these possible measures in optimizing the five criteria
| q | Implementation costs | Legal compliance | Easiness to implement | Need for cross-organization collaboration | Quick and visible results |
|---|---|---|---|---|---|
| 1 | (0, 1, 2) | (3, 4, 5) | (1.5, 2.5, 3.5) | (1, 2, 3) | (3, 4, 5) |
| 2 | (1.5, 2.5, 3.5) | (0, 1, 2) | (3, 4, 5) | (1.5, 2.5, 3.5) | (3, 4, 5) |
| 3 | (0, 1, 2) | (3, 4, 5) | (1, 2, 3) | (1.5, 2.5, 3.5) | (1.5, 2.5, 3.5) |
| 4 | (1.5, 2.5, 3.5) | (4, 5, 5) | (1.5, 2.5, 3.5) | (1.5, 2.5, 3.5) | (1.5, 2.5, 3.5) |
| 5 | (1.5, 2.5, 3.5) | (1.5, 2.5, 3.5) | (3, 4, 5) | (4, 5, 5) | (4, 5, 5) |
| 6 | (3, 4, 5) | (4, 5, 5) | (0, 1, 2) | (4, 5, 5) | (1, 2, 3) |
| 7 | (3, 4, 5) | (4, 5, 5) | (1, 2, 3) | (4, 5, 5) | (3, 4, 5) |
5.2 Application of the DFCP approach
This case was organized into a three-level decision hierarchy, as shown in Figure 3. Nevertheless, each factor can be further decomposed into its sub-factors.
The diagram illustrates a decision hierarchy with a central box labeled 'Possible Measure for Overcoming Challenges' connected to five branches: 'Implementation costs', 'Legal compliance', 'Easiness to implement', 'Need for cross-organizational collaboration', and 'Quick and visible results'. Each of these branches further connects to specific measures: 'Leveraging local communities', 'Designing staggered shift systems', 'Cross-shift collaboration in problem solving', 'Collaboration between wafer fabs', 'Increasing domestic workers', 'Further automation', and 'Early mass production'. The diagram shows the relationships and flow between these elements.Decision hierarchy. Source: Author's composition
The diagram illustrates a decision hierarchy with a central box labeled 'Possible Measure for Overcoming Challenges' connected to five branches: 'Implementation costs', 'Legal compliance', 'Easiness to implement', 'Need for cross-organizational collaboration', and 'Quick and visible results'. Each of these branches further connects to specific measures: 'Leveraging local communities', 'Designing staggered shift systems', 'Cross-shift collaboration in problem solving', 'Collaboration between wafer fabs', 'Increasing domestic workers', 'Further automation', and 'Early mass production'. The diagram shows the relationships and flow between these elements.Decision hierarchy. Source: Author's composition
The relative weights of the critical factors were compared in pairs. The results are summarized using a heat map in Figure 4.
A matrix comparing the importance of various factors in a decision-making process. The matrix has five rows and five columns, with each cell indicating the relative importance of one factor compared to another. The factors compared are Implementation cost, Legal compliance, Easiness to implement, Need for cross-organization collaboration, and Quick and visible results. The color gradient ranges from white to dark red, indicating the level of importance, with darker colors signifying higher importance. The diagonal cells are white, indicating that each factor is as important as itself. Notable trends include the high importance placed on Implementation cost and Legal compliance compared to other factors, as indicated by the darker colors in those cells.Heat map for summarizing the pairwise comparison results. Source: Author's composition
A matrix comparing the importance of various factors in a decision-making process. The matrix has five rows and five columns, with each cell indicating the relative importance of one factor compared to another. The factors compared are Implementation cost, Legal compliance, Easiness to implement, Need for cross-organization collaboration, and Quick and visible results. The color gradient ranges from white to dark red, indicating the level of importance, with darker colors signifying higher importance. The diagonal cells are white, indicating that each factor is as important as itself. Notable trends include the high importance placed on Implementation cost and Legal compliance compared to other factors, as indicated by the darker colors in those cells.Heat map for summarizing the pairwise comparison results. Source: Author's composition
The fuzzy consistency ratio of the pairwise comparison results was about 0.097 < 0.1, supporting the consistency among the pairwise comparison results. The fuzzy weights of factors were derived using the calibrated FGM (cFGM) [32], which calibrated the results of FGM to ensure the correctness in deriving the cores of fuzzy weights. The derivation results are shown using grouped gradient bar charts [41] in Figure 5.
The bar graph displays the derived fuzzy weights of five factors. The x-axis is labeled with the factors w 1, w 2, w 3, w 4, and w 5. The y-axis ranges from 0.000 to 0.700. The bars are vertical and show the following approximate values: w 1 is around 0.150, w 2 is around 0.650, w 3 is around 0.350, w 4 is around 0.450, and w 5 is around 0.350. The color scheme is a gradient of brown shades. All values are approximated.Derived fuzzy weights of the factors. Source: Author's composition
The bar graph displays the derived fuzzy weights of five factors. The x-axis is labeled with the factors w 1, w 2, w 3, w 4, and w 5. The y-axis ranges from 0.000 to 0.700. The bars are vertical and show the following approximate values: w 1 is around 0.150, w 2 is around 0.650, w 3 is around 0.350, w 4 is around 0.450, and w 5 is around 0.350. The color scheme is a gradient of brown shades. All values are approximated.Derived fuzzy weights of the factors. Source: Author's composition
Based on the derived fuzzy weights, a long-term plan for the implementation of seven possible measures was developed by using the DFCP approach taking into account the limited budget and available resources. T = 6 (years); B = 25 (million dollars); Q = 7. The budget was not sufficient to cover all possible measures within the planning horizon, so a compromise between these measures also needed to be made. The formulated MBNLP problem for this case is shown in Appendix II, which has one objective function, 497 variables and 2,309 constraints. A branch-and-bound algorithm was implemented using MATLAB to solve the MBNLP problem. The optimal solution is presented in Table 4. The fuzzy optimal objective function giving .
6. Results and discussion
According to the experimental results, the following discussion was made:
To ensure that the fuzzy weights of the criteria estimated using cFGM were precise enough to generate a trustworthy decision, time-consuming alpha cut operations (ACO) was also applied to derive the exact values of the fuzzy weights for comparison, against the results estimated by FGM, fuzzy extent analysis (FEA) and fuzzy inverse of column sum (FICSM) [42]. The comparison results are shown in Figure 6. The sum of deviations using FGM, FEA, FICSM and cFGM were 0.018, 0.206, 0.018 and 0.017, respectively. Obviously, cFGM used TFNs to most precisely approximate the exact values of fuzzy weights to facilitate subsequent operations.
The most important criterion for comparing possible measures to overcome semiconductor supply chain localization challenges was “legal compliance”, which was not surprising since it was already in the execution/control phase and the wafer foundry should strive to minimize risks and run new wafer fabs well under way [43].
Table 5 summarizes the cumulative completion rates for these possible measures after each time period. Obviously, every possible measure was accomplished over several consecutive time periods, which fulfilled the second requirement.
The plan to implement these possible measures is illustrated using a stacked Gantt chart in Figure 7(a), in which the height of a bar is directly proportional to the completion rate of the measure during a time period, which helps visualize the total workload of the wafer foundry within the time period. According to this figure, multiple possible measures were implemented during each time period, which fulfilled the first requirement.
To further elaborate the effectiveness of the proposed methodology, several existing methods have also been applied to this case. The first existing method was the static FTOPSIS [1, 15, 17], in which all possible measures were compared in the beginning of the project and then executed in sequence according to their overall performances. The planning results are shown in Figure 7(b). Obviously, only few (less than three) possible measures were implemented, which was risky by over-concentrating resources. Furthermore, usually only one possible measure was implemented per period, failing to satisfy the first requirement. The second existing method to be compared was the dynamic fuzzy linear programming method [44], which was a NP-complete fuzzy knapsack problem (see Appendix III). The planning results are shown in Figure 7(c). Apparently, to optimize the sum of utilities, the plan was full of disconnected segments, violating the second requirement.
More budget and resources were allocated to possible measures with higher priorities to fulfill the first requirement. For example, in the first time period, the fuzzy closenesses of possible measure #2 and #7 were (0, 0, 0.932) and (0.043, 1, 1), respectively. As a result, 0.63 and 1.37 were allocated to the two measures accordingly.
In this case, four possible measures were completed, including alleviating cultural differences, designing staggered shift systems, cross-shift collaboration in problem solving and accelerating yield learning through early mass production. In contrast, collaboration between wafer fabs, increasing the proportion of domestic workers and further automation were not finished during the planning horizon.
If the existing FTOPSIS method is applied to this case, “further automation” will receive higher priority than “accelerating yield learning through early mass production”, so the former will be completed before the latter. In contrast, in the DFCP approach, only possible measures implemented within the same time period were compared in FTOPSIS. “Further automation” and “accelerating yield learning through early mass production” were not implemented during the same period, and therefore, it was compared with other possible measures. Therefore, “further automation” was not prioritized.
A sensitivity analysis has been conducted to observe how changes in the available budget (B) affected the optimal planning performance. The results are summarized in Figure 8. As expected, the optimal planning performance improved with the increase of B. However, when B exceeded 25, the available budget exceeded the requirements, and the optimal planning performance was not further improved.
Another sensitivity analysis was conducted to investigate the impact of the planning horizon (T) on the optimal planning performance, as shown in Figure 9. The sensitivity analysis results showed that if time was insufficient, the plan could not be fully completed, leading to a decline in the optimal planning performance. Conversely, when more than seven periods were available, the completion rate of the plan remained at 100%, and the optimal planning performance remained unchanged.
As various possible measures were implemented, their priorities changed. Only by reallocating available resources to the best possible measures at present could these resources be used most effectively, which also explained the failure of static FTOPSIS.
A line graph compares fuzzy weights derived using different methods. The horizontal axis represents the variable w 1 ranging from 0 to 0.2. The vertical axis represents the variable mu of w 1 ranging from 0 to 1. The graph includes five lines representing different methods: ACO in solid black, FGM in blue dashed, FEA in solid orange, FICSM in green dotted, and cFGM in red dashed-dotted. Each line shows a peak and then a decline, with the peaks occurring at different points along the w 1 axis.Comparing the fuzzy weights derived using FGM, cFGM and ACO. Source: Author's composition
A line graph compares fuzzy weights derived using different methods. The horizontal axis represents the variable w 1 ranging from 0 to 0.2. The vertical axis represents the variable mu of w 1 ranging from 0 to 1. The graph includes five lines representing different methods: ACO in solid black, FGM in blue dashed, FEA in solid orange, FICSM in green dotted, and cFGM in red dashed-dotted. Each line shows a peak and then a decline, with the peaks occurring at different points along the w 1 axis.Comparing the fuzzy weights derived using FGM, cFGM and ACO. Source: Author's composition
Cumulative completion rates for these possible measures after each time period
| t | |||||||
|---|---|---|---|---|---|---|---|
| 1 | 0% | 31% | 0% | 0% | 0% | 0% | 39% |
| 2 | 69% | 46% | 0% | 20% | 19% | 0% | 56% |
| 3 | 100% | 61% | 0% | 39% | 39% | 0% | 72% |
| 4 | 100% | 75% | 0% | 58% | 57% | 12% | 88% |
| 5 | 100% | 87% | 58% | 74% | 73% | 23% | 100% |
| 6 | 100% | 100% | 100% | 95% | 94% | 36% | 100% |
The image contains three graphs comparing completion ratios over time using different methodologies. The first graph, labeled 'Proposed methodology,' shows a combination of box plots and line graphs. The x-axis represents time periods labeled 1 through 6, and the y-axis represents the completion ratio. Different colored segments within each box plot represent possible measures, with arrows indicating changes over time. The second graph, labeled 'Static FTOPSIS,' displays a series of box plots with the same x and y axes. Each box plot is color-coded to represent different possible measures, with arrows showing transitions between measures. The third graph, labeled 'DFLP,' combines box plots and line graphs, similar to the first graph. The x-axis and y-axis are consistent with the other graphs. The arrows and color-coded segments indicate changes and interactions among the possible measures over time. All values are approximated.Planning results using various methods. Source: Author's composition
The image contains three graphs comparing completion ratios over time using different methodologies. The first graph, labeled 'Proposed methodology,' shows a combination of box plots and line graphs. The x-axis represents time periods labeled 1 through 6, and the y-axis represents the completion ratio. Different colored segments within each box plot represent possible measures, with arrows indicating changes over time. The second graph, labeled 'Static FTOPSIS,' displays a series of box plots with the same x and y axes. Each box plot is color-coded to represent different possible measures, with arrows showing transitions between measures. The third graph, labeled 'DFLP,' combines box plots and line graphs, similar to the first graph. The x-axis and y-axis are consistent with the other graphs. The arrows and color-coded segments indicate changes and interactions among the possible measures over time. All values are approximated.Planning results using various methods. Source: Author's composition
A scatter plot representing the relationship between two variables, B and COG(Z*). The horizontal axis represents B, ranging from 0 to 60. The vertical axis represents COG(Z*), ranging from 19 to 23. The data points show a distinct upward trend, forming a steep curve that levels off as B increases. There are approximately 20 data points, with a noticeable cluster at the higher end of the B axis and COG(Z*) axis.Sensitivity analysis results for the impact of B. Source: Author's composition
A scatter plot representing the relationship between two variables, B and COG(Z*). The horizontal axis represents B, ranging from 0 to 60. The vertical axis represents COG(Z*), ranging from 19 to 23. The data points show a distinct upward trend, forming a steep curve that levels off as B increases. There are approximately 20 data points, with a noticeable cluster at the higher end of the B axis and COG(Z*) axis.Sensitivity analysis results for the impact of B. Source: Author's composition
A scatter plot representing the relationship between T and COG(Z*). The horizontal axis represents T with a range from 0 to 12. The vertical axis represents COG(Z*) with a range from 0 to 25. The plot contains several data points that show an increasing trend as T increases. Initially, the data points rise steeply, but they start to level off and cluster around a COG(Z*) value of 22 as T approaches 10.Sensitivity analysis results for the impact of T. Source: Author's composition
A scatter plot representing the relationship between T and COG(Z*). The horizontal axis represents T with a range from 0 to 12. The vertical axis represents COG(Z*) with a range from 0 to 25. The plot contains several data points that show an increasing trend as T increases. Initially, the data points rise steeply, but they start to level off and cluster around a COG(Z*) value of 22 as T approaches 10.Sensitivity analysis results for the impact of T. Source: Author's composition
7. Conclusions, implications, limitations and future scope
In recent years, to be closer to chip designers, major wafer foundries have built wafer fabs in the United States of America, Japan and Europe, forming a trend of semiconductor supply chain localization. Although semiconductor supply chain localization is undoubtedly one of the most advanced manufacturing models in the semiconductor industry, related discussions have been relatively limited to date. Furthermore, wafer foundries face numerous challenges in the process of semiconductor supply chain localization, requiring various measures to overcome them. Given the limited budgets and resources for these measures, and the inherent high uncertainty of semiconductor supply chain localization, it is necessary to prioritize these measures. To this end, this study proposes a DFCP approach, which dynamically allocates limited budgets and resources based on the priority of various measures within different time periods. The DFCP approach embeds the FTOPSIS mechanism into the FMBNLP model, thus differing from most existing fuzzy compromise programming methods.
Compared with the NCI method of Chiu and Chen [9], the proposed methodology was more tractable without considering indeterminacy and therefore was more comprehensible [45]. In addition, compared with the FAM–decomposition AHP–TOPSIS method of Chen et al. [11], more possible measures could be taken in the proposed methodology by rolling planning in the long term.
The DFCP approach has been applied to a real case. Based on the experimental results, the following conclusions were drawn:
The most important criterion for comparing possible measures to overcome semiconductor supply chain localization challenges was “legal compliance”. In contrast, “implementation costs” was least emphasized.
The planning results using the DFCP approach fulfilled the three requirements of the wafer foundry. In comparison, existing approaches either over-focused resources on a small number of possible measures or generated discontinuous planning fragments.
Four of the seven possible measures could be completed in a timely manner, including alleviating cultural differences, designing staggered shift systems, cross-shift collaboration in problem solving and accelerating yield learning through early mass production. In contrast, collaboration between wafer fabs, increasing the proportion of domestic workers, and further automation were not finished during the planning horizon.
An implication for wafer fab managers is that possible measures for overcoming supply chain localization challenges should be initiated and completed promptly to gain practical experience in evaluating their costs and benefits. In addition, the experimental results also indicated that further automation and collaboration between wafer fabs have not yet been completed during the planning phase, as their effects took considerable time to materialize. Nevertheless, for these lower-priority but potentially crucial possible measures, a viable long-term strategy for wafer foundries is to allocate resources to these measures prior to planning.
One limitation of the proposed methodology is that it does not always guarantee finding the global optimal solution, even for the defuzzified model. Furthermore, other methods exist for converting the FMBNLP model into a crisp one. The method used in this study may not be the most suitable. The further development of semiconductor supply chain localization obviously depends on whether wafer foundries have good and successful experiences in building localized wafer fabs and how these localized wafer fabs perform in the future, which will become an additional input to the DFCP approach but take time to evaluate. This is the first topic to be investigated in future research. In addition, other fuzzy MCDM mechanisms can also be embedded into the FMBNLP model, which may change the planning results. Furthermore, bio-inspired algorithms, such as genetic algorithms, can be employed to enhance the global optimality of the solution [46]. These constitute some directions for future research.
The supplementary material for this article can be found online.
