An integrated approach for the selection of operation strategy using fuzzy TOPSIS,sensitivity analysis,and MOLP

Abstract

Operation strategy plays an important role in business improvement and calls for many research attention in recent years. This study aims to propose an integrated approach to determine the most appropriate operational strategies in their companies under multi-conflicting objectives with a limited budget. The novel approach is developed by using the combination of Fuzzy Technique for Order Preference by Similarity to Ideal Situation (Fuzzy TOPSIS), Sensitivity Analysis (SA) and Multi-Objective Linear Programming (MOLP) model. The operation strategies are evaluated through five objectives such as Productivity, Quality, Cost, Time and Importance score. The importance scores of all strategies are firstly obtained from the Fuzzy TOPSIS method. The sets of the weight of criteria are then established by using SA while MOLP approach is used to select appropriate strategies under multi-conflicting objectives with limited resources. A case study with 110 possible scenarios of operational strategies from An Giang Fisheries Import Export Joint Stock Company in Vietnam is considered to illustrate the practicability of the proposed approach. The results found that the proposed approach is suitable to make a decision on operation strategy.

Keywords

Fuzzy TOPSIS operation strategy strategy selection sensitivity analysis multi-objective linear Programming model (MOLP)

1 Introduction

To be successful in a highly competitive global market as today, business owners need to ensure that their business is operating as effectively as possible, by developing and implementing appropriate strategies and actions to manage all capabilities across the entire supply chain. However, how they can build suitable strategies for their companies across the supply chain is a complex issue. Due to its importance, this issue has got significant attention from many researchers in recent years. Different approaches and methods have been suggested to select proper strategies and actions for business and supply chain development. For instance, based on the fuzzy set and Quality Function Deployment (QFD) approach, Bottani and Rizzi [1] successfully enhanced customer services by improving logistics performance. In the study, strategic actions which are translated from logistics service requirements are evaluated and ranked through House of Quality. QFD was also used to develop strategies for improving the performance of the supply chain [2 –4].

The topic of strategy development has studied deeply through combinations of different methods. For example, an effective combination of Strengths, Weaknesses, Opportunities, and Threats analysis (SWOT) and Fuzzy QFD was generated to formulate strategies for Petrokaran film factory [5]. Further, in another research, Fuzzy Analytic Hierarchy Process (AHP) and Fuzzy Technique for Order Preference by Similarity to Ideal Situation (TOPSIS) were suggested to build strategies for green supply chain management through a comparison study [6]. Even though the results show that there is no difference between the ranking orders of strategies by applying these two approaches, each approach has particular advantages. AHP based on pairwise comparisons, which considers relationships between alternatives whilst TOPSIS takes advantage of considering the distance from alternatives to positive ideal solution and negative ideal solution simultaneously. To take the advantages of both mention methods, Kirubakaran and Ilangkumaran [7] developed a methodology based on comprises fuzzy AHP, grey relational analysis (GRA), and TOPSIS technique for the selection of optimum maintenance strategy for pumps used in the paper industry. Solangi et al. [8] proposed an integrated methodology to evaluate energy strategies for sustainable energy planning. Besides that, several researches suggested integrated approach of TOPSIS and balanced score card (BSC) [9, 10], TOPSIS and Bayesian network (BN) [11], SWOT-AHP method [12], SWOT–Fuzzy Analytic Network Process [13]. Despite the success of these studies on strategy development, these researches focus much on the qualitative method through subjective expert opinion. In addition, by using the qualitative method, it is more challenging to measure the performance with accurate quantitative value. Also, these methods are not suitable to solve problems in a hierarchical decision structure and conflicting objectives [14].

To deal with a complex problem, which has some conflicting objectives, the integration between qualitative and quantitative methods is suggested. For example, to develop crucial logistics and supply chain management strategies, an integrated approach of AHP, Fuzzy QFD, and Multi-Objective Linear Programming (MOLP) was applied in the dairy industry [14]. In the study, the weights of objective functions are evaluated using AHP and the outcomes are measured by a quantitative approach. However, in an environment with uncertainty, a specific solution will not be suitable for all circumstances. Developing a model, in which different situations are defined and considered, is necessary for business management. Hence, a combination of linear programming formulation and sensitivity analysis was suggested for optimizing the supply chain of a steel company [15]. In the research, the sensitivity analysis is used to draw a comprehensive picture of conclusions regarding cost minimization with all possible scenarios are considered. Another research, by combining both qualitative and quantitative techniques, Chiadamrong and Tham [16] developed a model using Structural Equation Modeling (SEM), QFD, and MOLP to build and select suitable strategies to improve business performance. The research used House of Quality as a tool to transfer customers’ requirements into strategic actions in the supply chain through the results obtained from SEM. MOLP model was then used to select appropriate strategic actions.

For the selection of operations strategies, there are still some limitations in literatures. Firstly, even though there are several methods that have been proposed to handle strategy selection problem, they solved the problem based mainly on expert opinions that can make some inaccuracy. They have not found optimal solution based on real data of company. In addition, in most previous studies, the weights of objectives or criteria are given in a certain value that is impossible for all cases of companies. In the practice, the company may change their consider criteria’ weights in different situations. Then, while the study of Chiadamrong and Tham [16] takes advantages of sensitivity analysis and MLP, the study uses simple QFD to evaluate importance score of strategies that is not an effective way. To overcome the above deficiencies, this research suggests a new integrated approach of Fuzzy TOPSIS, Sensitivity Analysis and MOLP model. In this integrated approach, Fuzzy TOPSIS is applied to rank the importance score of strategies. SA is then utilized to evaluate objective functions in the model while the MOLP model is applied to determine appropriate strategies under a limited budget.

The study makes significant contributions to the body of knowledge and the economics. Compared to the existing studies, this research provides a systematic approach for evaluating and selecting operation strategies based on both qualitative and quantitative methods. The approach shows a general overview of all possible cases in the selection of operational strategies through sensitivity analysis. The MOLP allows the company to select appropriate strategies based on their preference of the relative importance among multi-conflicting criteria (i.e., time, quality, profit, cost, etc.) to yield the highest objective function value under limited budget. Also, by using the fuzzy theory, the proposed approach allows decision-makers to avoid subjective and conflicting opinions in the selection process. Hence, the proposed approach can provide business organizations with a useful tool to select proper strategies with consideration of their desired goals and business constraints to improve their business performance.

The remaining parts of this paper are arranged as follows. The literature review of related techniques is described in Section 2. An integrated Fuzzy TOPSIS, SA, and MOLP framework is presented in Section 3 while Section 4 validates the proposed approach through a case study in An Giang Fisheries Import Export Joint Stock Company. Section 5 includes the concluding remarks, suggestions, and limitations of the study.

2 Literature review

2.1 Technique for order preference by similarity to ideal situation (TOPSIS)

TOPSIS was firstly presented by Hwang and Yoon [17] and relates to the definition of positive ideal solution and negative ideal solution. The positive ideal solution is defined as the solution, in which the benefit criteria are maximized and the cost criteria are minimized, whilst in the negative ideal solution, the benefit criteria are minimized and the cost criteria are maximized. Hence, the best solution is the solution being nearest from the positive ideal solution and farthest from the negative ideal solution.

Formally, the weights of criteria and the ratings of alternatives are measured by crisp values [18]. However, by using crisp values, decision makers are generally confused with an exact number. Also, in uncertain environments, using crisp values may not provide reliable solutions. Hence, the use of fuzzy logic has been introduced to incorporate uncertainty, vagueness, and imprecision [19]. To develop the fuzzy logic, Lin and Chen [20] proposed a general form of linguistic q-rung orthopair fuzzy sets. Can and Demirok [21] generated a fuzzy multi-criteria decision-making approach with three stages to evaluate universal usability. Li et al. [22] then introduced innovatively interval-value Pythagorean fuzzy weighted averaging (IVPFWA) operator, Tche-bycheff metric distance and interval-value Pythago-rean fuzzy weighted geometric (IVPFWG) operator into the MULTIMOORA sub-methods. The study successfully obtains the risk ranking order for emergencies through the proposed approach.

Due to its advantages, fuzzy logic was integrated into TOPSIS method to overcome inaccuracy in the uncertainty environment. A hierarchical TOPSIS in the fuzzy environment was suggested for not only measuring uncertainty but also providing useful steps for weighting criteria accurately with additional objectives [23]. Proposing Max and Min operations on fuzzy numbers, TOPSIS was also successfully implemented in a fuzzy environment with a multi-criteria problem [24]. To improve the TOPSIS methods, Lin et al. [25] proposed a novel TOPSIS for linguistic pythagorean fuzzy sets based on correlation coefficient and entropy measure. Case studies in the selection of firewall productions and the security evaluation of computer systems were given to illustrate the proposed method. The most important point of the proposed method is that it uses the correlation coefficient to measure the proximity among alternatives and ideal solution, and achieves the trade-offs among conflicting attributes effectively.

In the strategy development, TOPSIS is considered as a popular and effective technique to evaluate and select proper strategies [9, 26]. TOPSIS approach was used to evaluate and rank supply chain management strategy, including green procurement, green manufacture, customer service, and environment management [6]. The result indicates that manufacturing strategy plays an important role in the green supply chain process, followed by the procurement strategy, customer service, and environment management, respectively. Shojaee and Fallah [9] built and selected appropriate strategies using the integrated approach of TOPSIS and balanced score card (BSC). In the study, TOPSIS is used to rank criteria in four perspectives of customers, processes, learning and finance. The result shows that selecting an appropriate target market for penetration is the priority. The combination of TOPSIS and BSC continuously examined [10]. In the study, a set of the criteria and weights are determined through BSC and Fuzzy AHP while appropriate strategies are selected by Fuzzy TOPSIS method. Esfandiari and Rizvandi [27] proposed using TOPSIS for ranking business development strategies for information technology improvement, including Critical Success Factors Analysis, Business Systems Planning, Porter’s forces model, SWOT analysis, Value chain Analysis and MIN. From the result, MIN method is ranked first, followed by Business Systems Planning, Porter’s forces model, Value chain Analysis, SWOT and Critical Success Factors Analysis. Kirubakaran and Ilangkumaran [7] developed a methodology based on Fuzzy AHP, grey relational analysis (GRA), and TOPSIS technique for the selection of optimum maintenance strategy for pumps used in the paper industry. In which, the Fuzzy AHP is used to weight the criteria while GRA–TOPSIS is used for determining the ranking of alternatives. In the study, four main criteria which were used to find optimal maintenance strategies are safety, cost, added value, and feasibility. Solangi et al. [8] proposes an integrated methodology based on SWOT analysis, Analytic Hierarchy Process (AHP), and Fuzzy TOPSIS to evaluate energy strategies for sustainable energy planning. The SWOT analysis is employed to determine the factors and sub-factors essential for sustainable energy planning. AHP is then used to determine the weights of criteria. Fuzzy TOPSIS method is used to rank the 13 energy strategies under the case study for Pakistan’s to achieve sustainable energy planning. The results indicate that providing low-cost and sustainable electricity to residential, commercial, and industrial sectors (WO5) is highly prioritized energy strategy. Fan et al. [11] introduced hybrid methodology using Bayesian network (BN) and TOPSIS to select the best-fit strategies for maritime accident prevention. The results reveal that the information, clear order, and safety culture are the three most important strategies.

2.2 Sensitivity analysis (SA)

Sensitivity analysis (SA) is a method that investigates possible variations and errors and their effects on model’s solutions [28]. In other words, SA can be seen as the technique used to evaluate differences among alternative outcome solutions obtained by changing independent variables. A decision maker determines a certain scenario. Then, an independent variable in the model is changed to obtain a different solution with the same scenario. It would be ideal if the decision maker can find different solutions instead of a single optimal solution. From these different scenarios and solutions regarding a specific set of variables, the best possible solution will be chosen [29]. In the strategy development issue, SA is applied in combination with a linear programming model. For example, SA was used to build the input parameters with different conditions to maximize the total net profit in the application of an integrated production and distribution strategy [30]. The result indicates that the effectiveness of integrating production and distribution functions can be extremely high in the right condition. In the study of Chiadamrong and Tham [16], SA was used to build a set of scenarios of objectives’ weight in the MOLP model. The set of scenarios obtained through SA reflects all real situations at the company, assisting the manager to select suitable strategies in the decision-making process.

2.3 Multi-objective linear programming model (MOLP)

Multi-Objective Linear Programming Model is a mathematical model, in which several objective functions involved and optimized [31]. In the MOLP model, optimizing all objective functions at the same time is not possible due to the conflicting nature of the objectives. Hence, the trade-offs between these conflicting objectives are considered to obtain optimal solutions [32]. There are different methods used for weighting criteria in the objective function, such as AHP, Analytic Network Process (ANP), TOPSIS, SA, etc. The advantages of MOLP model are the accurate representation of real circumstances with multi-criteria and the reliable solutions [33].

Ayağ et al. [14] proposed an integrated approach of AHP, fuzzy QFD and MOLP to develop crucial logistics and supply chain management strategies. In the study, MOLP is built by four objectives such as cost, benefit, feasibility and technical importance. Using these four objectives again, Chiadamrong and Tham [16] continuously used MOLP for strategy development, applying for the food industry in Vietnam. In the study, structural equation modeling (SEM) is used to build a relationship between supply chain requirements and business performance. Fuzzy QFD is then applied to construct supply chain management strategies whereas MOLP is used to select proper strategies. Even though these studies generated a new point in using a quantitative technique for strategy development, they do not define objective functions clearly. For example, the objective called benefit is a large issue and it is difficult to be measured. Therefore, the result cannot be estimated accurately.

3 Proposed methodology

In this study, an integrated approach combining Fuzzy TOPSIS, SA and MOLP is developed to address the problems to determine the most appropriate strategies for operations in the company under multi-conflicting objectives with a limited budget (see Fig. 1). The proposed method firstly utilizes Fuzzy TOPSIS to obtain the importance scores of each strategy. SA is then used to build various weighting sets among various conflicting objective functions while MOLP model is used to select suitable strategies to be implemented and to maximize the value among the conflicting objective functions with business constraints. The entire proposed methodology is described in detail in this section.

Fig. 1

Proposed Methodology.

3.1 Evaluating the importance score of all strategies based on fuzzy TOPSIS

The importance scores of all possible strategies are evaluated using Fuzzy TOPSIS in the following seven steps [19].

Step 1: Identifying Criteria and Strategies

The list of operation strategies and criteria are identified in this step. The criteria present the overall view of decision makers, who make a decision on which strategies should have a high or low importance score. The criteria weights and the alternative ratings are presented by linguistic variables. Positive triangular fuzzy numbers suggested by Sodhi and Prabhakar [34] are used to express these linguistic variables (as depicted in Table 1). The scale of 1–9 is used in this step, where 1 represents the lowest importance and 9 represents the highest importance.

Table 1
Fuzzy rating for linguistic variables

Fuzzy number Criteria weights Alternative assessment

(1, 1, 3) Very Low Important (VL) Very Poor (VP)

(1, 3, 5) Low Important (L) Poor (P)

(3, 5, 7) Medium Important (M) Medium (M)

(5, 7, 9) High Important (H) Good (G)

(7, 9, 9) Very High Important (VH) Very Good (VG)

Fuzzy number	Criteria weights	Alternative assessment
(1, 1, 3)	Very Low Important (VL)	Very Poor (VP)
(1, 3, 5)	Low Important (L)	Poor (P)
(3, 5, 7)	Medium Important (M)	Medium (M)
(5, 7, 9)	High Important (H)	Good (G)
(7, 9, 9)	Very High Important (VH)	Very Good (VG)

Assume that the survey is conducted by a group of K members (K decision makers), with i alternatives (i = 1, 2, ... , m) and j criteria (j = 1, 2, ... , n). The alternative rating ${\tilde{x}}_{ij}^{k}$ and criterion weight ${\tilde{w}}_{j}^{k}$ (with i_th alternative and j_th criterion) of the k_th decision maker (k = 1, 2, ... , K) are defined as follows: ${\tilde{x}}_{ij}^{k} = (a_{ij}^{k}, b_{ij}^{k}, c_{ij}^{k})$ (1) ${\tilde{w}}_{j}^{k} = (w_{j 1}^{k}, w_{j 2}^{k}, w_{j 3}^{k})$ (2) where i = 1, 2, …, m, and j = 1, 2, …, n. $a_{ij}^{k}, b_{ij}^{k}, c_{ij}^{k}$ are the first, second and third fuzzy values of importance score of strategy i belong to criterion j from decision maker k, respectively. $w_{j 1}^{k}, w_{j 2}^{k}, w_{j 3}^{k}$ are the first, second and third fuzzy values of importance score of criterion j from decision maker k, respectively. The combination of k decision makers’ assessment on criteria weights and alternatives are called aggregated fuzzy weights and aggregated fuzzy rating, respectively.

The aggregated fuzzy weights $({\tilde{w}}_{j})$ of each criterion are given as: ${\tilde{w}}_{j} = (w_{j 1}, w_{j 2}, w_{j 3})$ (3) where $w_{j 1} = min_{k} {w_{jk 1}}$ , $w_{j 2} = \frac{1}{k} \sum_{k = 1}^{K} w_{jk 2}$ , $w_{j 3} = max_{k} {w_{jk 3}}$ and w_j1, w_j2, w_j3 are the first, second and third fuzzy values of aggregated importance score of criterion j from K decision maker, respectively.

Similarly, the aggregated fuzzy rating ${\tilde{x}}_{ij}$ of alternative (i) according to each criterion (j) are obtained by the following equations: ${\tilde{x}}_{ij} = (a_{ij}, b_{ij}, c_{ij})$ (4)

Where $a_{ij} = min_{k} {a_{ij}^{k}}$ , $b_{ij} = \frac{1}{k} \sum_{k = 1}^{K} b_{ij}^{k}$ , $c_{ij} = max_{k} {c_{ij}^{k}}$ , and a_ij, b_ij, c_ij are the first, second and third fuzzy values of aggregated importance score of strategy i belongs to criterion j from K decision maker, respectively.

Step 2: Building Fuzzy Decision Matrix

The fuzzy decision matrix $\tilde{D}$ , which shows the relationships between alternatives and criteria, and the criteria weighting set $\tilde{W}$ are obtained as follows: $\tilde{D} = [\begin{matrix} \begin{matrix} {\tilde{x}}_{11} & {\tilde{x}}_{12} \\ {\tilde{x}}_{21} & {\tilde{x}}_{22} \end{matrix} & \begin{matrix} \dots & {\tilde{x}}_{1 n} \\ \dots & {\tilde{x}}_{2 n} \end{matrix} \\ \begin{matrix} \dots & \dots \\ {\tilde{x}}_{m 1} & {\tilde{x}}_{m 2} \end{matrix} & \begin{matrix} {\tilde{x}}_{ij} & \dots \\ \dots & {\tilde{x}}_{mn} \end{matrix} \end{matrix}]$ (5) $\tilde{W} = ({\tilde{w}}_{1}, {\tilde{w}}_{2}, \dots, {\tilde{w}}_{n})$ (6) where i = 1, 2, …, m (strategies) and j = 1, 2, …, n (criteria) $\begin{matrix} {\tilde{x}}_{ij} = (a_{ij}, b_{ij}, c_{ij}) \\ {\tilde{w}}_{j} = (w_{j 1}, w_{j 2}, w_{j 3}) \end{matrix}$

The fuzzy decision matrix is then used to build normalized decision matrix as in the following step.

Step 3: Building Normalized Decision Matrix

To make the fuzzy decision matrix simple, it should be normalized using a linear scale transformation. The normalized fuzzy decision matrix is obtained by Sodhi and Prabhakar [34]: $\tilde{R} = [{\tilde{r}}_{ij}]_{m \times n}, i = 1, 2, \dots, m and j = 1, 2, \dots, n$ (7) where:

For benefit criteria: ${\tilde{r}}_{ij} = (\frac{a_{ij}}{c_{j}^{*}}, \frac{b_{ij}}{c_{j}^{*}}, \frac{c_{ij}}{c_{j}^{*}})$ (8) $c_{j}^{*} = max_{i} c_{ij}$ (9)

For cost criteria: ${\tilde{r}}_{ij} = (\frac{a_{j}^{-}}{c_{ij}}, \frac{a_{j}^{-}}{b_{ij}}, \frac{a_{j}^{-}}{a_{ij}})$ (10) $a_{j}^{-} = min_{i} a_{ij}$ (11)

The normalized decision matrix is then used to build the weighted normalized decision matrix in the following step.

Step 4: Building the Weighted Normalized Decision Matrix

By combining the weights ${\tilde{w}}_{j}$ and the normalized fuzzy decision matrix ${\tilde{r}}_{ij}$ , the weighted normalized fuzzy decision matrix $\tilde{V}$ is obtained: $\tilde{V} = [{\tilde{v}}_{ij}]_{m \times n}, i = 1, 2, \dots, m, and j = 1, 2, \dots, n$ (12) $Where {\tilde{v}}_{ij} = {\tilde{r}}_{ij} * {\tilde{w}}_{j}$ (13) The result obtained from this step is used to calculate the Fuzzy Positive Ideal Solutions (FPIS) and Fuzzy Negative Ideal Solutions (FNIS).

Step 5: Determining FPIS and FNIS The FPIS (A^*) and FNIS (A^-) of the alternatives are defined as: $A^{*} = ({\tilde{v}}_{1}^{*}, {\tilde{v}}_{2}^{*}, \dots, {\tilde{v}}_{n}^{*})$ (14)

$\begin{matrix} where {\tilde{v}}_{j}^{*} = max_{i} {v_{ij 3}}, i = 1, 2, \dots, m and j = 1, \\ 2, \dots, n \end{matrix}$ (15) $A^{-} = ({\tilde{v}}_{1}^{-}, v_{2}^{-}, \dots, {\tilde{v}}_{n}^{-})$ (16)

$\begin{matrix} where {\tilde{v}}_{j}^{-} = min_{i} {v_{ij 1}}, i = 1, 2, \dots, m and j = 1, \\ 2, \dots, n \end{matrix}$ (17)

The results are then used in the next step to calculate the distances from each alternative to FPIS and FNIS.

Step 6: Calculating the Distance from each Alternative to FPIS and FNIS

The distances from each alternative to the FPIS $(d_{i}^{*})$ and the FNIS $(d_{i}^{-})$ are calculated as: $d_{i}^{*} = \sum_{j = 1}^{n} d_{v} ({\tilde{v}}_{ij}, {\tilde{v}}_{j}^{*}), i = 1, 2, \dots, m$ (18) $d_{i}^{-} = \sum_{j = 1}^{n} d_{v} ({\tilde{v}}_{ij}, {\tilde{v}}_{j}^{-}), i = 1, 2, \dots, m$ (19) where: $d_{v} (\tilde{x}, \tilde{y})$ is the distance between two fuzzy numbers $\tilde{x}$ and $\tilde{y}$ (Chen, 2000), which is obtained by:

$d_{v} (\tilde{x}, \tilde{y}) = \sqrt{\frac{1}{3} [{(x_{1} - y_{1})}^{2} + {(x_{2} - y_{2})}^{2} + {(x_{3} - y_{3})}^{2}]}$ (20)

Where x₁, x₂, x₃ are the first, second and third fuzzy values of $\tilde{x}$ , respectively. y₁, y₂, y₃ are the first, second and third fuzzy values of $\tilde{y}$ , respectively.

The distances from each alternative to FPIS and FNIS are used to obtain the closeness coefficient in the following step.

Step 7: Calculating the Closeness Coefficient and Ranking Alternatives

The closeness coefficient CC_i is defined to compare the distances from each alternative to fuzzy positive ideal solution A^* and fuzzy negative ideal solution A^-. The closeness coefficient of each alternative is computed by: ${CC}_{i} = \frac{d_{i}^{-}}{d_{i}^{-} + d_{i}^{*}}, where i = 1, 2, \dots, m$ (21)

If the closeness coefficient is higher, the closer distance from alternative to fuzzy positive ideal solution would be achieved. The alternative with higher closeness coefficient is closer to the fuzzy positive ideal solution, that is the alternative is better than others.

In this methodology, the closeness coefficient is considered as an importance score of strategy. The alternative, which has higher closeness coefficient is more important than others. Further, these importance scores are used as an objective function in the multi-objective linear programming model presented in Section 3.3.

3.2 Building a set of objective weights based on sensitivity analysis

In this methodology, SA is used to determine the weight of objectives. The set of weight is determined as w_y = {w₁, w₂, …, w_l}, respectively. In the assumption that the lowest possible value of each element of w_y is 0.1 (Equation 22). The step of changing criterion weight in each scenario is 0.1, whilst the total weight of all criteria equals to 1 (Equation 23): $0.1 ⩽ w_{y}$ (22) $\sum_{y = 1}^{l} w_{y} = 1$ (23)

In this context, a set of scenarios is obtained and used as input data, called the weights of objective function in the MOLP model.

3.3 Building the mathematical model using MOLP

Assume that there are l objectives with w_y = {w₁, w₂, …, w_l} used to maximize the value of the objective function. The definitions of related notations in the mathematical model are expressed as follows: $\begin{matrix} MaxZ \\ = w_{1} \sum_{j = 1}^{N} {Be}_{j} * X_{j} \\ - w_{2} \sum_{j = 1}^{N} {Tc}_{j} * X_{j} w_{l} \sum_{j = 1}^{N} I_{j} * X_{j} \end{matrix}$ (24)

Subject to: $\sum_{j = 1}^{N} {Tc}_{j} * X_{j} ⩽ B$ (25) $X_{j} \in {0, 1}, \forall j$ (26) where

N: total numbers of operation strategies.

Be_j, Tc_j, I_j: objectives (i.e., benefit, cost or importance level when implementing operation strategy j)

Xj: binary decision variable, Xj = 1 if operation strategy j is selected, and 0 otherwise.

w_y: weight of objective y obtained from the SA method (y = 1, 2, ... l).

B: limited resource

The mathematical model aims to select suitable operation strategies under a limited budget. Equation 24 is the maximum value of objective function while Equation 25 ensures that the available budget is enough for implementing selected strategies. Equation 26 shows binary decision variables.

4 Case study

AnGiang Fisheries Import Export Joint Stock Company in Vietnam is a company in the fishery industry in Mekong Delta, established 20 years ago. In recent years, as competition becomes more and more intense, the company is always seeking the best possible way to improve its business performance by applying suitable strategies and actions. However, how to find suitable strategies to improve business performance effectively is still an open question. Hence, the method developed in this research is applied to assist the company in strategy development as well as to illustrate the practicability of the proposed methodology.

4.1 Applying fuzzy TOPSIS method to evaluate strategies

Based on the literature review, nineteen strategies used in the case study are defined (as seen in Table 2). These are considered as specific strategies to improve operational performance.

Table 2
Criteria set

Item Operational strategies Source

S1 Lean Six Sigma using 5 S (Seiri, Seiton, Seiso, Seiketsu, Shitsuke) [16]

S2 Just-In-Time (JIT) [1 , 14]

S3 Advanced technology using Radio frequency identification system (RFID) [14]

S4 Material Requirements Planning (MRP) [1]

S5 Vendor Manage Inventory (VMI) [16]

S6 Advanced Manufacturing Systems and Automation [2, 16]

S7 Quality control using Statistical Process Control (SPC) [16]

S8 Preventive Maintenance (PM) [16]

S9 Enterprise Resource Planning (ERP) [1]

S10 Electronic Data Interchange (EDI) [1, 14]

S11 Incentive programs (bonuses, profit sharing, and welfare) [16]

S12 Systematic job recruitment (using structured interview, situational judgment tests) [2, 16]

S13 Supply chain management software (SCM software) [1]

S14 Customer survey for new product development and improvement [2]

S15 Job enlargement (employees are trained and assigned more job duties and responsibilities) [16]

S16 International quality standard (ISO 9001, ISO 22000, HACCP) [16]

S17 On the job training [2, 4]

S18 Customer relationship management software (CRM software) [16]

S19 Job enrichment (employees are trained and assigned a higher level of responsibility for their job) [16]

Item	Operational strategies	Source
S1	Lean Six Sigma using 5 S (Seiri, Seiton, Seiso, Seiketsu, Shitsuke)	[16]
S2	Just-In-Time (JIT)	[1 , 14]
S3	Advanced technology using Radio frequency identification system (RFID)	[14]
S4	Material Requirements Planning (MRP)	[1]
S5	Vendor Manage Inventory (VMI)	[16]
S6	Advanced Manufacturing Systems and Automation	[2, 16]
S7	Quality control using Statistical Process Control (SPC)	[16]
S8	Preventive Maintenance (PM)	[16]
S9	Enterprise Resource Planning (ERP)	[1]
S10	Electronic Data Interchange (EDI)	[1, 14]
S11	Incentive programs (bonuses, profit sharing, and welfare)	[16]
S12	Systematic job recruitment (using structured interview, situational judgment tests)	[2, 16]
S13	Supply chain management software (SCM software)	[1]
S14	Customer survey for new product development and improvement	[2]
S15	Job enlargement (employees are trained and assigned more job duties and responsibilities)	[16]
S16	International quality standard (ISO 9001, ISO 22000, HACCP)	[16]
S17	On the job training	[2, 4]
S18	Customer relationship management software (CRM software)	[16]
S19	Job enrichment (employees are trained and assigned a higher level of responsibility for their job)	[16]

Three criteria are used to evaluate the importance score of all strategies are defined:

Benefit: the obtained benefit by implementing operation strategy.

Resource: the resource used to implement operation strategy.

Feasibility: this is to evaluate the feasibility or possibility to implement such strategies in the company.

Assuming that the survey is conducted by a group of K members (in this case study, K = 3, noted DM1, DM2, and DM3), with i alternative strategies (in this case i = 1, 2, ... ,19) and j criteria (in this case j = 1, 2, 3). The survey is firstly conducted by three managers of the company. These managers are strategy decision markers of the company. They used linguistic variables to assess the importance weights of criteria (shown in Table 3) and the ratings of alternatives according to each criterion (as seen in Table 4).

Table 3

The importance weights of criteria

Decision maker (DM)	Criteria
	Benefit	Resource	Feasibility
DM1	H (5,7,9)	M (3,5,7)	VH (7,9,9)
DM2	M (3,5,7)	H (5,7,9)	H (5,7,9)
DM3	M (3,5,7)	H (5,7,9)	H (5,7,9)

Table 4

The ratings of alternatives with respect to each criterion

Strategy	DM	Criteria
		Benefit	Resource	Feasibility
S1	DM1	VG	G	G
	DM2	G	G	G
	DM3	G	VG	VG
S2	DM1	G	G	M
	DM2	M	G	P
	DM3	G	G	P
S3	DM1	G	G	G
	DM2	G	M	VG
	DM3	VG	G	G
S4	DM1	G	VG	G
	DM2	G	M	VG
	DM3	G	M	G
S5	DM1	G	G	M
	DM2	VG	G	P
	DM3	G	M	P
S6	DM1	P	VG	VG
	DM2	M	VG	VG
	DM3	M	G	G
S7	DM1	G	G	VG
	DM2	G	G	G
	DM3	G	G	VG
S8	DM1	G	G	G
	DM2	M	G	G
	DM3	VG	M	M
S9	DM1	M	VG	VG
	DM2	G	G	G
	DM3	M	G	G
S10	DM1	G	G	G
	DM2	M	G	G
	DM3	G	G	VG
S11	DM1	G	VG	G
	DM2	G	G	M
	DM3	M	G	M
S12	DM1	VG	M	G
	DM2	G	M	G
	DM3	G	M	G
S13	DM1	G	VG	M
	DM2	G	VG	G
	DM3	M	G	G
S14	DM1	P	G	G
	DM2	P	VG	M
	DM3	M	M	G
S15	DM1	VP	M	P
	DM2	P	M	P
	DM3	P	M	VP
S16	DM1	M	G	G
	DM2	G	G	G
	DM3	M	M	M
S17	DM1	G	VG	G
	DM2	M	G	G
	DM3	VG	G	VG
S18	DM1	M	G	M
	DM2	M	M	G
	DM3	M	G	M
S19	DM1	G	G	G
	DM2	G	G	G
	DM3	VG	VG	G

Based on Equations 4–13, the aggregate fuzzy decision matrix, the normalized aggregate fuzzy decision matrix and the weighted normalized fuzzy decision matrix are computed and shown in Tables 5 –7, respectively.

Table 5

The aggregate fuzzy decision matrix

Strategy	Criteria
	Benefit			Resource			Feasibility
	a _ij	b _ij	c _ij	a _ij	b _ij	c _ij	a _ij	b _ij	c _ij
S1	5.00	7.67	9.00	5.00	7.67	9.00	5.00	7.67	9.00
S2	3.00	6.33	9.00	5.00	7.00	9.00	1.00	3.67	7.00
S3	5.00	7.67	9.00	3.00	6.33	9.00	5.00	7.00	9.00
S4	5.00	7.00	9.00	3.00	6.33	9.00	5.00	7.67	9.00
S5	5.00	7.67	9.00	3.00	6.33	9.00	1.00	3.67	7.00
S6	1.00	4.33	7.00	5.00	8.33	9.00	5.00	8.33	9.00
S7	5.00	7.00	9.00	5.00	7.00	9.00	5.00	2.56	9.00
S8	3.00	7.00	9.00	3.00	6.33	9.00	3.00	6.33	9.00
S9	3.00	5.67	9.00	5.00	7.67	9.00	5.00	7.67	9.00
S10	3.00	6.33	9.00	5.00	7.00	9.00	5.00	7.67	9.00
S11	3.00	6.33	9.00	5.00	7.67	9.00	3.00	5.67	9.00
S12	5.00	7.67	9.00	3.00	5.00	7.00	5.00	7.00	9.00
S13	3.00	6.33	9.00	5.00	8.33	9.00	3.00	6.33	9.00
S14	1.00	3.67	7.00	3.00	7.00	9.00	3.00	7.00	9.00
S15	1.00	2.33	5.00	3.00	5.00	7.00	1.00	2.33	5.00
S16	3.00	5.67	9.00	3.00	6.33	9.00	3.00	6.33	9.00
S17	3.00	7.00	9.00	5.00	7.67	9.00	5.00	7.67	9.00
S18	3.00	5.00	7.00	3.00	6.33	9.00	3.00	5.67	9.00
S19	5.00	7.67	9.00	5.00	7.67	9.00	5.00	7.00	9.00

Table 6

The normalized aggregate fuzzy decision matrix

Strategy	Criteria
	Benefit			Resource			Feasibility
	a _ij	b _ij	c _ij	a _ij	b _ij	c _ij	a _ij	b _ij	c _ij
S1	0.56	0.85	1.00	0.33	0.39	0.60	0.56	0.85	1.00
S2	0.33	0.70	1.00	0.33	0.43	0.60	0.11	0.41	0.78
S3	0.56	0.85	1.00	0.33	0.47	1.00	0.56	0.78	1.00
S4	0.56	0.78	1.00	0.33	0.47	1.00	0.56	0.85	1.00
S5	0.56	0.85	1.00	0.33	0.47	1.00	0.11	0.41	0.78
S6	0.11	0.48	0.78	0.33	0.36	0.60	0.56	0.93	1.00
S7	0.56	0.78	1.00	0.33	0.43	0.60	0.56	0.28	1.00
S8	0.33	0.78	1.00	0.33	0.47	1.00	0.33	0.70	1.00
S9	0.33	0.63	1.00	0.33	0.39	0.60	0.56	0.85	1.00
S10	0.33	0.70	1.00	0.33	0.43	0.60	0.56	0.85	1.00
S11	0.33	0.70	1.00	0.33	0.39	0.60	0.33	0.63	1.00
S12	0.56	0.85	1.00	0.43	0.60	1.00	0.56	0.78	1.00
S13	0.33	0.70	1.00	0.33	0.36	0.60	0.33	0.70	1.00
S14	0.11	0.41	0.78	0.33	0.43	1.00	0.33	0.78	1.00
S15	0.11	0.26	0.56	0.43	0.60	1.00	0.11	0.26	0.56
S16	0.33	0.63	1.00	0.33	0.47	1.00	0.33	0.70	1.00
S17	0.33	0.78	1.00	0.33	0.39	0.60	0.56	0.85	1.00
S18	0.33	0.56	0.78	0.33	0.47	1.00	0.33	0.63	1.00
S19	0.56	0.85	1.00	0.33	0.39	0.60	0.56	0.78	1.00

Table 7

The weighted normalized fuzzy decision matrix

Strategy	Criteria
	Benefit			Resource			Feasibility
	a _ij	b _ij	c _ij	a _ij	b _ij	c _ij	a _ij	b _ij	c _ij
S1	1.67	4.83	9.00	1.00	2.48	5.40	2.78	6.53	9.00
S2	1.00	3.99	9.00	1.00	2.71	5.40	0.56	3.12	7.00
S3	1.67	4.83	9.00	1.00	3.00	9.00	2.78	5.96	9.00
S4	1.67	4.41	9.00	1.00	3.00	9.00	2.78	6.53	9.00
S5	1.67	4.83	9.00	1.00	3.00	9.00	0.56	3.12	7.00
S6	0.33	2.73	7.00	1.00	2.28	5.40	2.78	7.10	9.00
S7	1.67	4.41	9.00	1.00	2.71	5.40	2.78	2.18	9.00
S8	1.00	4.41	9.00	1.00	3.00	9.00	1.67	5.40	9.00
S9	1.00	3.57	9.00	1.00	2.48	5.40	2.78	6.53	9.00
S10	1.00	3.99	9.00	1.00	2.71	5.40	2.78	6.53	9.00
S11	1.00	3.99	9.00	1.00	2.48	5.40	1.67	4.83	9.00
S12	1.67	4.83	9.00	1.29	3.80	9.00	2.78	5.96	9.00
S13	1.00	3.99	9.00	1.00	2.28	5.40	1.67	5.40	9.00
S14	0.33	2.31	7.00	1.00	2.71	9.00	1.67	5.96	9.00
S15	0.33	1.47	5.00	1.29	3.80	9.00	0.56	1.99	5.00
S16	1.00	3.57	9.00	1.00	3.00	9.00	1.67	5.40	9.00
S17	1.00	4.41	9.00	1.00	2.48	5.40	2.78	6.53	9.00
S18	1.00	3.15	7.00	1.00	3.00	9.00	1.67	4.83	9.00
S19	1.67	4.83	9.00	1.00	2.48	5.40	2.78	5.96	9.00

The next step, the distances from alternatives to Fuzzy Positive Ideal Solutions and Fuzzy Negative Ideal Solutions are computed. Table 8 shows the distances between each strategy (S1 to S19) to FPIS and FNIS of each criterion. For example, considering the distance between Strategy S1 and a criterion of Benefit, the distance from S1 to FPIS is 4.87 and FNIS is 5.69. It means the distance from S1 to FPIS is nearer than to FNIS in terms of Benefit.

Table 8

The distance from alternatives to FPIS and FNIS

Stra-	Criteria
	tegy	Benefit		Resource		Feasibility
	$d_{m}^{-}$	$d_{m}^{*}$	$d_{m}^{-}$	$d_{m}^{*}$	$d_{m}^{-}$	$d_{m}^{*}$
S1	5.69	4.87	2.68	6.31	6.10	3.86
S2	5.45	5.45	2.73	6.23	4.00	6.05
S3	5.69	4.87	4.76	5.77	5.93	4.00
S4	5.59	5.00	4.76	5.77	6.10	3.86
S5	5.69	4.87	4.76	5.77	4.00	6.05
S6	4.09	6.28	2.65	6.38	6.30	3.76
S7	5.59	5.00	2.73	6.23	5.12	5.33
S8	5.55	5.33	4.76	5.77	5.65	4.72
S9	5.36	5.58	2.68	6.31	6.10	3.86
S10	5.45	5.45	2.73	6.23	6.10	3.86
S11	5.45	5.45	2.68	6.31	5.50	4.87
S12	5.69	4.87	4.90	5.37	5.93	4.00
S13	5.45	5.45	2.65	6.38	5.65	4.72
S14	4.02	6.43	4.72	5.87	5.82	4.58
S15	2.78	7.02	4.90	5.37	2.69	6.74
S16	5.36	5.58	4.76	5.77	5.65	4.72
S17	5.55	5.33	2.68	6.31	6.10	3.86
S18	4.20	5.84	4.76	5.77	5.50	4.87
S19	5.69	4.87	2.68	6.31	5.93	4.00

Then Equation 21 is used to calculate the closeness coefficient of all alternatives. These closeness coefficients are normalized and transferred into a 5-point scale to obtain the importance score, to be used as an objective in the MOLP model. The results are shown in Table 9. From the table, it is clear that S12 has the highest score with 5.00 while S15 has the lowest score with 3.24.

Table 9

Closeness coefficient of all alternatives

Strategy	Closeness coefficient	Importance score
S1	0.49	4.54
S2	0.41	3.80
S3	0.53	4.91
S4	0.53	4.91
S5	0.46	4.26
S6	0.44	4.07
S7	0.45	4.17
S8	0.5	4.63
S9	0.47	4.35
S10	0.48	4.44
S11	0.45	4.17
S12	0.54	5.00
S13	0.45	4.17
S14	0.46	4.26
S15	0.35	3.24
S16	0.5	4.63
S17	0.48	4.44
S18	0.47	4.35
S19	0.49	4.54

4.2 Applying the SA method to build sets of objectives’ weight

In this case study, five objectives (Productivity, Quality, Cost, Time and Importance Score) have been selected based on the consultation with the managers in the company to form the objective function in MOLP model. Note that these five objectives are conflicting. Due to that in the practical circumstances to select the best strategies for the maximum benefits to the company, the decision-making process is really difficult. In this research, using SA, all possible strategies are considered with all possible variations of changes in their weights to determine the best possible strategy for the company.

By applying Equations 22–23 with the assumption that the lowest weight is 0.1 and the total weight equals to 1, the step of changing criterion weight in each scenario is 0.1, so the highest weight is 0.6. As a result, the total possible 110 weighted sets for the five objectives are obtained in this study (see Table 12). These weighted sets include all possible scenarios which satisfy all above-mentioned requirements. For example, in the first case, w₁ is assigned the highest value at 0.6; others are equal to 0.1. In the case (2), w₁ is assigned at 0.5, others (_W2; w₃; w₄; w₅) is assigned 0.2; 0.1; 0.1; 0.1, respectively. Similarly, other cases are interpreted.

4.3 Applying the MOLP model to select suitable strategies

Among five objectives used to form the MOLP model, Productivity and Quality can be seen as benefits obtained by implementing strategies (called maximizing objectives), while Cost and Time can be seen as resources used to implement strategies (called minimizing objectives). Importance Score shows the importance of implementing such strategies to the company, obtained from the result of Fuzzy TOPSIS method.

The data of Productivity, Quality, Cost and Time with 19 SCM strategies are shown in Table 10. All data are scaled, ranging from 1 (lowest) to 5 (highest). Five-point scales, which present the recommended range in each level are shown in Table 11. For example, applying strategy number 1 can increase productivity less than 10%, do not affect waste reduction, cost less than $10,000, and take 4 to 6 months for implementing. Importance Scores of strategies are obtained from Table 9. All of them are used as input data in the MOLP model. All data is obtained based on the consultant with managers of An Giang Fisheries Import Export Joint Stock Company.

Table 10
Productivity, quality, cost and time for strategies

Strategy Benefit Resource

Productivity Quality Cost Time

S1 2 1 1 2

S2 3 2 2 2

S3 3 2 2 3

S4 4 2 4 4

S5 4 2 3 2

S6 5 3 5 4

S7 2 5 2 3

S8 4 4 2 3

S9 3 1 3 4

S10 2 1 5 3

S11 4 2 3 2

S12 3 3 2 4

S13 2 2 3 3

S14 1 3 2 5

S15 1 2 2 2

S16 4 5 3 4

S17 2 2 1 1

S18 1 1 3 2

S19 2 3 3 3

Strategy	Benefit	Resource
S1	2	1	1	2
S2	3	2	2	2
S3	3	2	2	3
S4	4	2	4	4
S5	4	2	3	2
S6	5	3	5	4
S7	2	5	2	3
S8	4	4	2	3
S9	3	1	3	4
S10	2	1	5	3
S11	4	2	3	2
S12	3	3	2	4
S13	2	2	3	3
S14	1	3	2	5
S15	1	2	2	2
S16	4	5	3	4
S17	2	2	1	1
S18	1	1	3	2
S19	2	3	3	3

Table 11

Recommended range of productivity, quality, cost and time

Criteria		Scale
	(1)	(2)	(3)	(4)	(5)
Benefit	Productivity (increased productivity)	None	<10%	10–20%	21–30%	>30%
	Quality (waste reduction)	None	<10%	10–20%	21–30%	>30%
Resource	Cost ($US) (implementing cost)	<10,000	10,000 to 25,000	25,000 to 100,000	100,000 to 250,000	>250,000
	Time (months) (implementing time)	<4	4 –6	6 –8	8 –10	>10

To find the maximum value of the objective function with five conflicting objectives, Equations 27–29 can be expressed as follows: $\begin{matrix} MaxZ = w_{1} \sum_{j = 1}^{N} P_{j} * X_{j} + w_{2} \sum_{j = 1}^{N} Q_{j} * X_{j} \\ - w_{3} \sum_{j = 1}^{N} C_{j} * X_{j} \\ - w_{4} \sum_{j = 1}^{N} T_{j} * X_{j} \\ + w_{5} \sum_{j = 1}^{N} I_{j} * X_{j} \end{matrix}$ (27)

Subject to: $\sum_{j = 1}^{N} C_{j} * X_{j} ⩽ B$ (28) $X_{j} is binary, \forall j$ (29) where

N: total number of operation strategies.

P_j: the percentage of increasing productivity by implementing operation strategy j.

Q_j: the percentage of reducing waste product by implementing operation strategy j.

C_j: cost of implementing operation strategy j. This is the estimated implementing expense if the company has to proceed with each strategy.

T_j: time of implementing operation strategy j.

I_j: importance score of implementing operation strategy j (obtained from the Fuzzy TOPSIS method).

X_j: binary decision variable. X_j = 1 if operation strategy j is selected, and 0 otherwise.

w_y: weight of criterion y.

B: the available budget

Based on the managers of the company, strategies are selected under a limited budget, which represents approximately $US 800,000 (or about 18 billion VND). Table 12 shows the results of solving Equations 27–29, in which the objective function value and selected strategy are obtained for all scenarios. For example, in case (1), the weight of five objective functions (Productivity, Quality, Cost, Time and Importance score) are prioritized at 0.6, 0.1, 0.1, 0.1, 0.1 respectively. In this case, the objective function value is 23.96 and strategy numbers such as S1 (5 S), S2 (JIT), S3 (RFID), S5 (VMI), S6 (Advanced Manufacturing Systems and Automation), S7 (SPC), S8 (PM), S11 (Incentive programs), S12 (Systematic job recruitment), S16 (ISO), S17 (On the Job training) are selected.

Table 12

Solutions of sensitivity analysis for all cases

Case	Weighted sets of five objectives	Objective function value	Selected strategy
	w ₁	w ₂	w ₃	w ₄	w ₅
1	0.6	0.1	0.1	0.1	0.1	23.96	1,2,3,5,6,7,8,11,12,16,17
2	0.5	0.2	0.1	0.1	0.1	23.46	1,2,3,5,6,7,8,11,12,16,17
3	0.5	0.1	0.2	0.1	0.1	17.76	1,2,3,5,6,7,8,11,12,16,17
4	0.5	0.1	0.1	0.2	0.1	17.36	1,2,3,5,6,7,8,11,12,16,17
5	0.5	0.1	0.1	0.1	0.2	25.22	1,2,3,5,6,7,8,11,12,16,17
6	0.4	0.3	0.1	0.1	0.1	23.13	1,2,3,5,7,8,11,12,14,16,17,19
7	0.4	0.1	0.3	0.1	0.1	11.56	1,2,3,5,6,7,8,11,12,16,17
8	0.4	0.1	0.1	0.3	0.1	10.76	1,2,3,5,6,7,8,11,12,16,17
9	0.4	0.1	0.1	0.1	0.3	27.04	1,2,3,5,7,8,9,11,12,14,16,17
10	0.4	0.2	0.2	0.1	0.1	17.26	1,2,3,5,6,7,8,11,12,16,17
11	0.4	0.2	0.1	0.2	0.1	16.86	1,2,3,5,6,7,8,11,12,16,17
12	0.4	0.2	0.1	0.1	0.2	25.07	1,2,3,5,7,8,11,12,14,16,17,19
13	0.4	0.1	0.2	0.2	0.1	11.16	1,2,3,5,6,7,8,11,12,16,17
14	0.4	0.1	0.2	0.1	0.2	19.02	1,2,3,5,6,7,8,11,12,16,17
15	0.3	0.4	0.1	0.1	0.1	23.13	1,2,3,5,7,8,11,12,14,16,17,19
16	0.3	0.1	0.4	0.1	0.1	5.55	1,2,3,5,7,8,11,12,16,17
17	0.3	0.1	0.1	0.4	0.1	4.26	1,2,3,5,6,7,8,11,16,17
18	0.3	0.1	0.1	0.1	0.4	28.93	1,2,3,5,7,8,11,12,14,16,17,19
19	0.3	0.3	0.2	0.1	0.1	17.13	1,2,3,5,7,8,11,12,14,16,17,19
20	0.3	0.3	0.1	0.2	0.1	16.53	1,2,3,5,7,8,11,12,15,16,17,19
21	0.3	0.3	0.1	0.4	0.2	15.56	1,2,3,5,7,8,11,12,15,16,17,19
22	0.3	0.1	0.3	0.2	0.1	5.05	1,2,3,5,7,8,11,12,16,17
23	0.3	0.1	0.3	0.1	0.2	13.07	1,2,3,5,7,8,11,12,14,16,17,19
24	0.3	0.2	0.3	0.1	0.1	11.13	1,2,3,5,7,8,11,12,14,16,17,19
25	0.3	0.2	0.1	0.3	0.1	10.26	1,2,3,5,6,7,8,11,12,16,17
26	0.3	0.2	0.1	0.1	0.3	27.00	1,2,3,5,7,8,11,12,14,16,17,19
27	0.3	0.1	0.2	0.3	0.1	4.56	1,2,3,5,6,7,8,11,12,16,17
28	0.3	0.1	0.2	0.1	0.3	21.00	1,2,3,5,7,8,11,12,14,16,17,19
29	0.3	0.1	0.1	0.2	0.3	20.39	1,2,3,5,7,8,11,12,15,16,17,19
30	0.3	0.2	0.2	0.2	0.1	10.66	1,2,3,5,6,7,8,11,12,16,17
31	0.3	0.2	0.2	0.1	0.2	19.07	1,2,3,5,7,8,11,12,14,16,17,19
32	0.3	0.2	0.1	0.2	0.2	18.46	1,2,3,5,7,8,11,12,15,16,17,19
33	0.3	0.1	0.2	0.2	0.2	12.56	1,2,3,5,7,8,11,12,15,16,17,19
34	0.2	0.5	0.1	0.1	0.1	23.13	1,2,3,5,7,8,11,12,14,16,17,19
35	0.2	0.1	0.5	0.1	0.1	1.08	1,7,8,17
36	0.2	0.1	0.1	0.5	0.1	0.69	5,11,17
37	0.2	0.1	0.1	0.1	0.5	30.87	1,2,3,5,7,8,11,12,14,16,17,19
38	0.2	0.4	0.2	0.1	0.1	17.13	1,2,3,5,7,8,11,12,14,16,17,19
39	0.2	0.4	0.1	0.2	0.1	16.43	1,2,3,5,7,8,11,12,15,16,17,19
40	0.2	0.4	0.1	0.1	0.2	25.07	1,2,3,5,7,8,11,12,14,16,17,19
41	0.2	0.1	0.4	0.2	0.1	0.86	1,8,17
42	0.2	0.1	0.4	0.1	0.2	7.07	1,2,3,5,7,8,11,12,14,16,17,19
43	0.2	0.2	0.4	0.1	0.1	5.25	1,2,3,5,7,8,11,12,16,17
44	0.2	0.1	0.1	0.4	0.2	5.56	1,2,3,5,7,8,11,12,15,16,17,19
45	0.2	0.2	0.1	0.4	0.1	3.85	1,2,3,5,7,8,11,16,17
46	0.2	0.1	0.2	0.4	0.1	0.55	5,8,11,17
47	0.2	0.2	0.1	0.1	0.4	28.93	1,2,3,5,7,8,11,12,14,16,17,19
48	0.2	0.1	0.2	0.1	0.4	22.93	1,2,3,5,7,8,11,12,14,16,17,19
49	0.2	0.1	0.1	0.2	0.4	22.23	1,2,3,5,7,8,11,12,15,16,17,19
50	0.2	0.3	0.3	0.1	0.1	11.13	1,2,3,5,7,8,11,12,14,16,17,19
51	0.2	0.3	0.1	0.3	0.1	10.03	1,2,3,5,7,8,11,12,15,16,17,19
52	0.2	0.3	0.1	0.1	0.3	27.00	1,2,3,5,7,8,11,12,14,16,17,19
53	0.2	0.1	0.3	0.3	0.1	0.66	1,8,17
54	0.2	0.1	0.3	0.1	0.3	15.00	1,2,3,5,7,8,11,12,14,15,16,17
55	0.2	0.1	0.1	0.3	0.3	13.83	1,2,3,5,7,8,11,12,15,16,17,19
56	0.2	0.3	0.2	0.2	0.1	10.53	1,2,3,5,7,8,11,12,15,16,17,19
57	0.2	0.3	0.2	0.1	0.2	19.07	1,2,3,5,7,8,11,12,14,16,17,19
58	0.2	0.3	0.1	0.2	0.2	18.36	1,2,3,5,7,8,11,12,15,16,17,19
59	0.2	0.1	0.3	0.2	0.2	6.56	1,2,3,5,7,8,11,12,15,16,17,19
60	0.2	0.2	0.3	0.2	0.1	4.75	1,2,3,5,7,8,11,12,16,17
61	0.2	0.2	0.3	0.1	0.2	13.07	1,2,3,5,7,8,11,12,14,16,17,19
62	0.2	0.2	0.1	0.3	0.2	11.96	1,2,3,5,7,8,11,12,15,16,17,19
63	0.2	0.1	0.2	0.3	0.2	6.06	1,2,3,5,7,8,11,12,15,16,17,19
64	0.2	0.2	0.2	0.3	0.1	4.25	1,2,3,5,7,8,11,12,16,17
65	0.2	0.2	0.2	0.1	0.3	21.00	1,2,3,5,7,8,11,12,14,16,17,19
66	0.2	0.2	0.1	0.2	0.3	20.29	1,2,3,5,7,8,11,12,15,16,17,19
67	0.2	0.1	0.2	0.2	0.3	14.39	1,2,3,5,7,8,11,12,15,16,17,19
68	0.1	0.6	0.1	0.1	0.1	23.13	1,2,3,5,7,8,11,12,14,16,17,19
69	0.1	0.1	0.6	0.1	0.1	0.14	17
70	0.1	0.1	0.1	0.6	0.1	014	17
71	0.1	0.1	0.1	0.1	0.6	33.80	1,2,3,5,7,8,11,12,14,16,17,19
72	0.1	0.5	0.2	0.1	0.1	17.13	1,2,3,5,7,8,11,12,14,16,17,19
73	0.1	0.5	0.1	0.2	0.1	16.33	1,2,3,5,7,8,11,12,14,16,17,19
74	0.1	0.5	0.1	0.1	0.2	25.07	1,2,3,5,7,8,11,12,14,16,17,19
75	0.1	0.1	0.5	0.2	0.1	0.14	17
76	0.1	0.1	0.5	0.1	0.2	2.30	1,2,3,7,8,12,17
77	0.1	0.2	0.5	0.1	0.1	1.28	1,7,8,17
78	0.1	0.1	0.1	0.5	0.2	1.17	1,2,5,8,11,17
79	0.1	0.2	0.1	0.5	0.1	0.44	17
80	0.1	0.1	0.2	0.5	0.1	0.14	17
81	0.1	0.2	0.1	0.1	0.5	30.87	1,2,3,5,7,8,11,12,14,16,17,19
82	0.1	0.1	0.2	0.1	0.5	24.87	1,2,3,5,7,8,11,12,14,16,17,19
83	0.1	0.1	0.1	0.2	0.5	24.07	1,2,3,5,7,8,11,12,14,16,17,19
84	0.1	0.4	0.3	0.1	0.1	11.13	1,2,3,5,7,8,11,12,14,16,17,19
85	0.1	0.4	0.1	0.3	0.1	9.93	1,2,3,5,7,8,11,12,15,16,17,19
86	0.1	0.4	0.1	0.1	0.3	27.00	1,2,3,5,7,8,11,12,14,16,17,19
87	0.1	0.1	0.4	0.3	0.1	0.14	17
88	0.1	0.1	0.4	0.1	0.3	9.00	1,2,3,5,7,8,11,12,14,16,17,19
89	0.1	0.3	0.4	0.1	0.1	5.14	1,2,3,5,7,8,12,14,15,16,17,19
90	0.1	0.1	0.1	0.4	0.3	7.44	1,2,3,5,7,8,11,12,15,16,17,18
91	0.1	0.3	0.1	0.4	0.1	3.64	1,2,5,7,8,11,15,16,17,19
92	0.1	0.1	0.3	0.4	0.1	0.14	17
93	0.1	0.3	0.1	0.1	0.4	28.93	1,2,3,5,7,8,11,12,14,16,17,19
94	0.1	0.1	0.3	0.1	0.4	16.93	1,2,3,5,7,8,11,12,14,16,17,19
95	0.1	0.1	0.1	0.3	0.4	15.73	1,2,3,5,7,8,11,12,15,16,17,19
96	0.1	0.4	0.2	0.2	0.1	10.03	1,2,3,5,7,8,11,12,15,16,17,19
97	0.1	0.4	0.2	0.1	0.2	19.07	1,2,3,5,7,8,11,12,14,16,17,19
98	0.1	0.4	0.1	0.2	0.2	18.27	1,2,3,5,7,8,11,12,14,16,17,19
99	0.1	0.1	0.4	0.2	0.2	1.70	1,2,3,7,8,17
100	0.1	0.2	0.4	0.1	0.2	7.07	1,2,3,5,7,8,11,12,14,16,17,19
101	0.1	0.2	0.4	0.2	0.1	0.98	1,7,8,17
102	0.1	0.2	0.1	0.4	0.2	5.46	1,2,3,5,7,8,11,12,15,16,17,19
103	0.1	0.2	0.2	0.4	0.1	0.52	7,8,17
104	0.1	0.1	0.2	0.4	0.2	1.17	1,2,5,8,11,17
105	0.1	0.2	0.2	0.1	0.4	22.93	1,2,3,5,7,8,11,12,14,16,17,19
106	0.1	0.1	0.2	0.2	0.4	16.23	1,2,3,5,7,8,11,12,15,16,17,19
107	0.1	0.2	0.1	0.2	0.4	22.13	1,2,3,5,7,8,11,12,14,16,17,19
108	0.1	0.3	0.2	0.2	0.2	12.36	1,2,3,5,7,8,11,12,15,16,17,19
109	0.1	0.2	0.3	0.2	0.2	6.46	1,2,3,5,7,8,11,12,15,16,17,19
110	0.1	0.2	0.2	0.2	0.3	14.29	1,2,3,5,7,8,11,12,15,16,17,19

Based on the results obtained (showed in Table 12 and Fig. 2), the recommended solutions are summarized and discussed below:

Fig. 2

Objective function values of 110 cases.

+The case (71), in which weights of five objectives including Productivity, Quality, Cost, Time and Importance score are 0.1, 0.1, 0.1, 0.1, 0.6 respectively, gives the highest objective function value, at 33.80 (shown in Table 12). In this case, strategy numbers such as S1 (5 S), S2 (JIT), S3 (RFID), S5 (VMI), S7 (SPC), S8 (PM), S11 (Incentive programs), S12 (Systematic job recruitment), S14 (Customer survey), S16 (ISO), S17 (On the Job training), S19 (Job enrichment) are selected. In this case, the Importance score is prioritized at 0.6, meaning that the company considers decision makers’ assessment more important than other criteria. These assessments comprise the consideration of total benefit provided, the total resource required and the feasibility of such strategies when these strategies are implemented at the company. Above mentioned strategies have high assessment values (importance score) from decision makers due to their high benefit, the low resource required or appropriated application. Also, the total benefit provided value (increased productivity and quality) by implementing these strategies may higher than their implementing cost and time. Hence, they are selected to obtain the highest objective function value.

+In contrast, six cases (e.g., 69, 70, 75, 80, 87, 92) in which weights of five objectives (Productivity, Quality, Cost, Time and Importance score) are (0.1, 0.1, 0.6, 0.1, 01), (0.1, 0.1, 0.1, 0.6, 01), (0.1, 0.1, 0.5, 0.2, 01), (0.1, 0.1, 0.2, 0.5, 01), (0.1, 0.1, 0.4, 0.3, 01), and (0.1, 0.1, 0.3, 0.4, 01), respectively gives the lowest objective function value at 0.14. In these cases, cost and time criteria are prioritized at a high value (0.7 in total) so to maximize objective function value, only strategy which has lower cost and time consumption is selected. On the job training (S17) is the strategy, in which new employees are trained in specific actions by older employees or managers at job environment. This process does not consume much time and money compared to others. Hence, this strategy is selected in these cases.

+Strategies like S1 (5 S), S2 (JIT), S3 (RFID), S5 (VMI), S7 (SPC), S8 (PM), S11 (Incentive programs), S12 (Systematic job recruitment), S16 (ISO), S17 (On the Job training), S19 (Job enrichment) are selected in most cases. This can be likely explained by these strategies have high values in benefits provided (increased productivity and quality) and importance score, but have low implementing cost or time. Hence, these strategies are selected to maximize the objective function.

+Strategies such as S4 (MRP), S9 (ERP), S10 (EDI), S13 (SCM software), and 18 (CRM software) are not selected in all cases due to their high implementing cost, long implementing time, or low benefit value.

The results draw a general overview of the operational strategy, in which all possible scenarios for real cases are presented. Hence, under a limited investment budget, the company can select suitable strategies based on their preference of the relative importance among five conflicting criteria in order to achieve the highest objective function value. By applying proper strategies, the company can obtain higher benefits that may lead to increase revenue, profit and customer satisfaction. Further, the proposed methodology allows avoiding subjective and conflicting opinions among managers in the selection process. The model is not only used for operation strategy selection but also used for other selection problems such as in human resource strategy selection, marketing strategy selection or supply chain management strategy selection, etc.

5 Conclusions

This study proposes a useful methodology for evaluating and selecting operation strategies, based on the integration of Fuzzy TOPSIS, Sensitivity Analysis and MOLP model under multi-conflicting objectives with budget constraint. Fuzzy TOPSIS method is employed to obtain the importance score of all strategies under consideration of three significant criteria: benefit, resource and feasibility. Sensitivity analysis allows building a wide range of criteria weights, in which all possible scenarios are covered. MOLP model is then utilized to select suitable strategies according to the preferred scenarios. This proposed approach provides a critical overview for companies to consider what strategy should be implemented under multi-conflicting objectives to improve their business performance.

There are still some further researches to be explored since this study is conducted with a limited number of criteria and operation strategies. Further extensions of those would be desirable to consider more practical applications. The second limitation can be recognized as a limited range of linguistic variables. Also, further studies should be integrated with other effective strategies as well as criteria through surveying and analyzing the current situation at the company. More linguistic variables should be applied with different ranges to obtain more practical answers for decision makers. Finally, the proposed methodology has not applied fuzzy theory in the mathematical model (F-MOLP), hence this is an important point for improving the model in further research.

Footnotes

Acknowledgments

Authors would like to express their gratitude to An Giang Fisheries Import Export Joint Stock Company in Vietnam.

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