# A Novel Hybrid Approach for Evaluation of Resilient 4PL Provider for E-Commerce

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review and Criteria Definition

#### 2.1. Literature Review

#### 2.1.1. The Role of Logistics in E-Commerce

#### 2.1.2. Resilience of the Global Supply Chains

#### 2.1.3. Evaluation and Selection of Logistics Service Providers

#### 2.2. Defining 4PL Evaluation Criteria

## 3. Methodology

#### 3.1. Fuzzy FUCOM

**Step 1—Determine and rank the decision criteria**. In accordance with the literature review, define the criteria that will be used for evaluation. After that, experts should determine the rank of criteria in accordance with the significance of the criteria. The first criterion is the most significant and, therefore, should have the highest weight coefficient. The last criterion should be the least significant. This can be written using Equation (1):

_{j}(1) > C

_{j}(2) > … > C

_{j}(k)

**Step 2—Comparison of the criteria**. The comparison is made with respect to the most significant criterion using fuzzy linguistic expressions from a previously defined scale. After comparison, a fuzzy criterion significance ϖ C

_{j(k}

_{)}is obtained. A fuzzy comparative significance can then be determined using Equation (2).

_{k/(k+1)})

_{k/(k+}

_{1)}represents the significance that the criterion of the C

_{j(k)}rank has compared with the criterion of the C

_{j(k+}

_{1)}rank.

**Step 3—Calculate the optimal fuzzy weights**. In this step, fuzzy weights of observed criteria are determined (w

_{1}, w

_{2}, …, w

_{n})

^{T}. When determining criteria weights, two conditions need to be met, Equations (4) and (5).

**Step 4—Defuzzification in order to obtain crisp values**. The final step includes defuzzification of the obtained values $({w}_{j}^{l},{w}_{j}^{m},{w}_{j}^{u})$, Equation (13), in order to obtain crisp values, which will be later used in order to obtain a weighted decision matrix in the WASPAS method. For defuzzification, the graded mean integration representation (GMIR) method was used [68].

#### 3.2. Evidence Theory and Rule-Based Transformation

#### 3.2.1. Evidence Theory

_{l}(l = 1, …, M) and an L number of criteria e

_{i}(i = 1, …, L), each criterion is assessed using a set of evaluation grades H

_{n}(n = 1, …, N) called a frame of discernment. Each grade H

_{n}is considered to be an individual answer, while each criterion e

_{i}is considered to be a source of information. A set of N grades can be defined by:

_{n+}

_{1}is preferred to H

_{n}, which means that H

_{n}and H

_{1}are the best and the worst grades, respectively. After assessing an alternative a

_{l}with respect to the criterion e

_{i}, a generalized belief structure S(e

_{i}(a

_{l})) is formed, Equation (15):

_{l}is assessed with respect to the criterion e

_{i}, where ${\beta}_{n,i}\left({a}_{l}\right)\ge 0$ and $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)\le 1$. When $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)=1$, then the assessment is considered complete; otherwise, it is incomplete. Additionally, a case of complete ignorance is possible if $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)=0$. On the other hand, ${\beta}_{H,i}\left({a}_{l}\right)$ represents the degree of global ignorance, which means that an alternative a

_{l}can be assessed as any grade in the set H (when assessing with respect to the criterion e

_{i}) due to the lack of supporting evidence. Two conditions that are applied on that occasion are ${\beta}_{H,i}\left({a}_{l}\right)\ge 0$ and $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)+{\beta}_{H,i}\left({a}_{l}\right)\le 1$.

_{l}for the criterion e

_{i}using a set of evaluation grades ${H}^{i}=\left\{{H}_{n}^{i},n=1,\dots ,{N}^{i}\right\}$, which is not in the form of the general grades yet. A degree of belief in which an alternative a

_{l}is assessed as grade ${H}_{n}^{i}$ when considering criterion e

_{i}is denoted as ${\gamma}_{n}^{i}\left({a}_{l}\right)$. On the other hand, when observing quantitative assessment, ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)$ represents a belief structure that is the assessment result of an alternative a

_{l}for the criterion e

_{i}in the form of numerical values or ${h}_{j}^{i}$, and ${\gamma}_{j}^{i}\left({a}_{l}\right)$ is the degree of belief that an alternative a

_{l}is assessed to a value ${h}_{j}^{i}$ for the criterion e

_{i}.

#### 3.2.2. Rule-Based Transformation

#### Rule-Based Transformation Technique for Qualitative Assessment

_{i}is assessed using its own set of grades ${H}^{i}=\left\{{H}_{n}^{i},n=1,\dots ,{N}^{i}\right\}$. After that, the original assessment of an alternative a

_{l}for criterion e

_{i}, or ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)$, can be defined using Equation (16):

^{i}= N), and each grade ${H}_{n}^{i}$ is equal to a grade H

_{n}in H, then ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)$ can be easily transformed into a generalized belief structure $S\left({e}_{i}\left({a}_{l}\right)\right)$ using Equation (17).

^{i}≠ N) and a grade ${H}_{n}^{i}$ does not exactly mean a single grade H

_{n}in H, but a number of grades in H. In that case, only for qualitative assessment, the generalized belief structure from Equation (17) can be transformed into Equation (18).

^{i}be equivalent to grade H

_{k}in H to a degree ${\alpha}_{k,n}$, where 0 ≤ ${\alpha}_{k,n}$≤ 1 and $\sum}_{k=1}^{N}{\alpha}_{k,n}=1$. Then, the equivalence rules can be defined, using the symbol $\leftrightarrow $ to represent the equivalence, using Equation (19).

#### Rule-Based Transformation Technique for Quantitative Assessment

_{n}, n = 1, …, N}, let ${h}_{n}^{i}$ be the numerical value equivalent to the general grade H

_{n}, as shown in Equation (21).

_{l}with respect to the criterion e

_{i}with a belief degree of ${\gamma}_{j}^{i}\left({a}_{l}\right)$, then the original assessment can be defined using Equation (22):

_{l}could be assessed to any grades in the set H, which is a consequence of either unavailable or incomplete information.

_{n})), which is a function between 0 and 1, where u(H

_{n+}

_{1}) > u(H

_{n}). After determining the utility of all grades, the expected utility of an alternative a

_{l}for the criterion e

_{i}can be defined using Equation (28).

_{N}) or the worst (H

_{1}). Based on this, the maximum and minimum utility of each alternative can be determined using Equations (29) and (30).

#### 3.3. WASPAS Method

**Step 1—Defining initial decision matrix X**. In this paper, an initial decision matrix was obtained by implementing previously described methods.

**Step 2—Normalization of the decision matrix**. Depending on the type of criteria, it is necessary to normalize the matrix using Equation (32) for beneficial criteria and Equation (33) for nonbeneficial criteria:

**Step 3—Determining the total relative importance based on WSM**. The total relative importance is determined for every alternative by applying Equation (34).

**Step 4—Determining the total relative importance based on WPM**. The total relative importance is determined for every alternative by applying Equation (35).

**Step 5—Determining the total relative importance (Q**. In order to determine Q

_{i}) of an alternative_{i}, the decision maker must define the value of λ, which can be between 0 and 1. In the end, alternatives are ranked according to the value of Q, where the best alternative has the highest value, Equation (36).

## 4. Results

#### 4.1. Determining Criteria Weights Using Fuzzy FUCOM

#### 4.2. Determining Initial Decision-Making Matrix Using ET and RBT

#### 4.3. Final Ranking of the Alternatives Using WASPAS

## 5. Sensitivity Analysis and Discussion

#### 5.1. Sensitivity Analysis

#### 5.2. Managerial Implications and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Dimension | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Percentage of errors | 0–5% of errors | 6–10% of errors | 11–15% of errors | 16–20% of errors | More than 20% of errors |

Cost of damage | No damages | Minimal damages (1–10% cost of damages) | Medium damages (11–20% cost of damages) | Large damages (21% to 40% cost of damages) | Severe damages (more than 40% cost of damages) |

On-time delivery | 95–100% of on-time delivery | 85–94% of on-time delivery | 75–84% of on-time delivery | 65–74% of on-time delivery | Less than 65% of on-time delivery |

Dimension | 1 | 2 | 3 | 4 |
---|---|---|---|---|

The number of different types of goods a 4PL can ship | 4PL can ship 15 or more types of goods | 4PL can ship 13–15 types of goods | 4PL can ship 10–12 types of goods | 4PL can ship fewer than 10 types of goods |

Response time | 4PL responds rapidly (before company’s expectation) | 4PL responds on time | 4PL responds slightly later (up to 5 h) | 4PL responds very slowly (over 5 h) |

Resource capacity | 4PL has capacity in over 95% of cases | 4PL has capacity in 80–95% of cases | 4PL has capacity in 65–80% of cases | 4PL has capacity in 50–65% of cases |

Criteria | Description | Reference |
---|---|---|

Service price | Price of the product delivery | [50,52,53,54,55,56,57,58] |

Service time | Delivery time (from the moment of ordering up to delivery to the end consumer) | [50,53,54,55,56,57,58] |

Service quality | Service quality was measured through 3 dimensions: percentage of errors, cost of damage, and on-time delivery | [50,52,54,56,57] |

IT capabilities | A number of solutions that enable monitoring, visibility, and information in real time along the entire chain | [50,52,53,55,57] |

Supply chain design | Dispersion and global network coverage by 4PL | [49,59,60] |

Safety stock inventory | 4PL storage capacity that would be used to cover demand in case of unforeseen circumstances | [61,62,63,64] |

Flexibility | Flexibility was observed through 3 dimensions: the number of different types of goods a 4PL can ship, response time, and resource capacity | [50,52,54,55,56,57,58] |

Cooperation | Cooperation quality and the number of years e-commerce company is working with a certain 4PL | [49,60,61,65] |

Redundancy | Number of 3PLs with which the observed 4PL cooperates | [60,65,66] |

Risk management | Number of quality standards that 4PL has | [60,61,65] |

**Table 4.**Original forms of the assessment results [60].

Assessment Results | Mathematical Formulation (i = 1, …, L, l = 1, …, M) |
---|---|

Qualitative assessment | |

Precise and complete | ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n}^{i},1.0\right)\right\}$ |

Uncertain but complete | ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n}^{i},{\gamma}_{n}^{i}\left({a}_{l}\right)\right),n=1,\dots ,{N}^{i}\right\},{\displaystyle {\displaystyle \sum}_{n=1}^{{N}^{i}}}{\gamma}_{n}^{i}\left({a}_{l}\right)=1$ |

Uncertain and incomplete (with a degree of ignorance) | ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n}^{i},{\gamma}_{n}^{i}\left({a}_{l}\right)\right),n=1,\dots ,{N}^{i}\right\},{\displaystyle {\displaystyle \sum}_{n=1}^{{N}^{i}}}{\gamma}_{n}^{i}\left({a}_{l}\right)1$ |

Complete ignorance | n/a (no information to conduct the assessment) |

Quantitative assessment | |

Precise and complete | ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({h}_{j}^{i},1.0\right)\right\}$ |

Uncertain but complete | ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({h}_{j}^{i},{\gamma}_{j}^{i}\left({a}_{l}\right)\right),j=1,\dots ,J\right\},{\displaystyle {\displaystyle \sum}_{j=1}^{J}}{\gamma}_{j}^{i}=1$ |

Uncertain and incomplete (with a degree of ignorance) | ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({h}_{j}^{i},{\gamma}_{j}^{i}\left({a}_{l}\right)\right),j=1,\dots ,J\right\},{\displaystyle {\displaystyle \sum}_{j=1}^{J}}{\gamma}_{j}^{i}1$ |

Complete ignorance | n/a |

**Table 5.**Generalized belief structures after rule-based transformation [60].

Assessment Results | Mathematical Formulation (i = 1, …, L, l = 1, …, M) |
---|---|

Qualitative and quantitative assessment | |

Precise and complete | $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),n=1,\dots ,N\right\},{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{\beta}_{n,i}\left({a}_{l}\right)=1$ |

Uncertain but complete | $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),n=1,\dots ,N\right\},{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{\beta}_{n,i}\left({a}_{l}\right)=1$ |

Uncertain and incomplete (with a degree of ignorance) | $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),n=1,\dots ,N;\left(H,{\beta}_{H,i}\left({a}_{l}\right)\right)\right\},$${\displaystyle \sum}_{n=1}^{N}}{\beta}_{n,i}\left({a}_{l}\right)<1and{\beta}_{H,i}\left({a}_{l}\right)0and{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{\beta}_{n,i}\left({a}_{l}\right)+{\beta}_{H,i}\left({a}_{l}\right)=1$ |

Complete ignorance | $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left(H,1.0\right)\right\}$ |

**Table 6.**Fuzzy linguistic scale [67].

Linguistic Terms | Membership Function |
---|---|

Equally important (EI) | (1,1,1) |

Weakly important (WI) | (2/3,1,3/2) |

Fairly important (FI) | (3/2,2,5/2) |

Very important (VI) | (5/2,3,7/2) |

Absolutely important (AI) | (7/2,4,9/2) |

Criteria | Linguistic Variables | TFN |
---|---|---|

Price (C1) | EI | (1,1,1) |

Service time (C2) | EI | (1,1,1) |

Service quality (C3) | EI | (1,1,1) |

IT capabilities (C4) | WI | (2/3,1,3/2) |

Supply chain design (C5) | WI | (2/3,1,3/2) |

Safety stock inventory (C6) | WI | (2/3,1,3/2) |

Flexibility (C7) | FI | (3/2,2,5/2) |

Cooperation (C8) | VI | (5/2,3,7/2) |

Redundancy (C9) | AI | (7/2,4,9/2) |

Risk management (C10) | AI | (7/2,4,9/2) |

Criteria | Subcriteria | Assessment Scale |
---|---|---|

Service price | / | Assessment grades A–C |

(A)—4PL can provide service with a total cost of up to EUR 16.000 | ||

(B)—4PL can provide service with a total cost of up to EUR 20.000 | ||

(C)—4PL can provide service with a total cost of over EUR 20.000 | ||

Service time | / | Assessment grades A–D |

(A)—service time is up to 10 days | ||

(B)—service time is up to 14 days | ||

(C)—service time is up to 30 days | ||

(D)—service time is over 30 days | ||

Service quality | Percentage of errors Cost of damage On-time delivery | Assessment grades A–E |

(A)—0–5% of errors with no damages and 95–100% of on-time delivery | ||

(B)—6–10% of errors with minimal damages and 85–94% of on-time delivery | ||

(C)—11–15% of errors with medium damages and 75–84% of on-time delivery | ||

(D)—16–20% of errors with large damages and 65–74% of on-time delivery | ||

(E)—more than 20% of errors with severe damages and less than 65% of on-time delivery | ||

IT capabilities | / | Assessment grades A–E |

(A)—4PL offers step-by-step tracking updates from ship-out to successful delivery | ||

(B)—4PL offers a tracking ID to monitor shipment if the parcel is already on the way | ||

(C)—4PL offers to track an ID number to monitor in the courier website to track the parcel | ||

(D)—4PL offers a contact number to monitor where the parcel is | ||

(E)—4PL does not offer any tracking monitoring system | ||

Supply chain design | Number of offices in the world Number of countries in which 4PL operates | Assessment grades A–C |

(A)—4PL has over 2000 offices and operates in more than 200 countries | ||

(B)—4PL has 1500–2000 offices and operates in 150–200 countries | ||

(C)—4PL has up to 1500 offices and operates in fewer than 150 countries | ||

Safety stock inventory | / | Assessment grades A–D |

(A)—4PL with his 3PL partners has more than 20 million m2 of warehouse capacity | ||

(B)—4PL with his 3PL partners has 15–20 million m2 of warehouse capacity | ||

(C)—4PL with his 3PL partners has 10–15 million m2 of warehouse capacity | ||

(D)—4PL with his 3PL partners has up to 10 million m2 of warehouse capacity | ||

Flexibility | The number of different types of goods a 4PL can ship Response time Resource capacity | Assessment grades A–D |

(A)—4PL can ship 15 or more types of goods, responds rapidly, and has capacity in over 95% of cases | ||

(B)—4PL can ship 13–15 types of goods, responds on time, and has capacity in 80–95% of cases | ||

(C)—4PL can ship 10–12 types of goods, responds slightly later, and has capacity in 65–80% of cases | ||

(D)—4PL can ship fewer than 10 types of goods, responds very slowly, and has capacity in 50–65% of cases | ||

Cooperation | Cooperation quality Number of years working with 4PL | Assessment grades A–D |

(A)—company is working jointly with 4PL for over 5 years | ||

(B)—company is in harmony with 4PL and is working for 3–5 years | ||

(C)—company is flexible with 4PL and is working for 1–3 years | ||

(D)—company only shares information with 4PL and is working less than 1 year | ||

Redundancy | / | The number of 3PL companies certain 4PL is working with |

Risk management | / | The number of quality standards 4PL has |

Criteria | Equivalence Rules |
---|---|

Service price (C1) | A ↔ {(Excellent, 1)} |

B ↔ {(Good, 0.5), (Fair, 0.5)} | |

C ↔ {(Poor, 0.7), (Very poor, 0.3)} | |

Service time (C2) | A ↔ {(Excellent, 1)} |

B ↔ {(Good, 0.6), (Fair, 0.4)} | |

C ↔ {(Fair, 0.2), (Poor, 0.6), (Very poor, 0.2)} | |

D ↔ {(Very poor, 1)} | |

Service quality (C3) | A ↔ {(Excellent, 1)} |

B ↔ {(Excellent, 0.3), Good (0.6), (Fair, 0.1)} | |

C ↔ {(Good, 0.2), (Fair, 0.6), (Poor, 0.2)} | |

D ↔ {(Poor, 0.7), (Very poor, 0.3)} | |

IT capabilities (C4) | A ↔ {(Excellent, 1)} |

B ↔ {(Excellent, 0.6), (Good, 0.4)} | |

C ↔ {(Good, 0.7), (Fair, 0.3)} | |

D ↔ {(Fair, 0.6), (Poor, 0.4)} | |

E ↔ {(Poor, 0.8), (Very poor, 0.2)} | |

Supply chain design (C5) | A ↔ {(Excellent, 0.9), (Good, 0.1)} |

B ↔ {(Good, 0.7), (Fair, 0.3)} | |

C ↔ {(Poor, 0.6), (Very poor, 0.4)} | |

Safety stock inventory (C6) | A ↔ {(Excellent, 1)} |

B ↔ {(Excellent, 0.2), Good (0.6), (Fair, 0.2)} | |

C ↔ {(Good, 0.3), (Fair, 0.5), (Poor, 0.2)} | |

D ↔ {(Poor, 0.5), (Very poor, 0.5)} | |

Flexibility (C7) | A ↔ {(Excellent, 1)} |

B ↔ {(Excellent, 0.4), Good (0.4), (Fair, 0.2)} | |

C ↔ {(Good, 0.3), (Fair, 0.5), (Poor, 0.2)} | |

D ↔ {(Poor, 0.8), (Very poor, 0.2)} | |

Cooperation (C8) | A ↔ {(Excellent, 1)} |

B ↔ {(Excellent, 0.3), (Good, 0.7)} | |

C ↔ {(Good, 0.3), (Fair, 0.4), (Poor, 0.3)} | |

D ↔ {(Poor, 0.5), (Very poor, 0.5)} | |

Redundancy (C9) | ≥9 ↔ Excellent |

7 ↔ Good | |

5 ↔ Fair | |

4 ↔ Poor | |

3 ↔ Very poor | |

Risk management (C10) | ≥10 ↔ Excellent |

8 ↔ Good | |

6 ↔ Fair | |

4 ↔ Poor | |

<4 ↔ Very poor |

Criteria/Alternative | Alternative 1 | Alternative 2 | Alternative 3 | Alternative 4 | Alternative 5 |
---|---|---|---|---|---|

Service price (C1) | {(B, 0.7), (C, 0.3)} | {(B, 0.9), (C, 0.1)} | {(A, 0.8), (B, 0.2)} | {(A, 0.4), (B, 0.6)} | {(A, 0.5), (B, 0.5)} |

Service time (C2) | {(A, 0.3), (B, 0.7)} | {(A, 0.5), (B, 0.5)} | {(A, 0.9), (B, 0.1)} | {(A, 0.7), (B, 0.3)} | {(A, 1)} |

Service quality (C3) | {(A, 1)} | {(A, 0.8), (B, 0.2)} | {(A, 1)} | {(A, 0.8), (B, 0.1)} | {(A, 1)} |

IT capabilities (C4) | {(B, 1)} | {(A, 1)} | {(A, 1)} | {(B, 1)} | {(C, 1)} |

Supply chain design (C5) | {(C, 1)} | {(B, 1)} | {(A, 1)} | {(A, 1)} | {(A, 1)} |

Safety stock inventory (C6) | {(D, 1)} | {(D, 1)} | {(C, 1)} | {(A, 1)} | {(D, 1)} |

Flexibility (C7) | {(D, 1)} | {(A, 1)} | {(C, 1)} | {(C, 1)} | {(B, 1)} |

Cooperation (C8) | {(A, 1)} | {(A, 1)} | {(B, 1)} | {(D, 1)} | {(C, 1)} |

Redundancy (C9) | 9 | 7 | 4 | 3 | 5 |

Risk management (C10) | 10 | 5 | 8 | 4 | 6 |

Criteria/Alternative | Alternative 1 | Alternative 2 | Alternative 3 | Alternative 4 | Alternative 5 |
---|---|---|---|---|---|

Service price (C1) | {(Good, 0.35), (Fair, 0.35), (Poor, 0.21), (Very poor, 0.09)} | {(Good, 0.45), (Fair, 0.45), (Poor, 0.07), (Very poor, 0.03)} | {(Excellent, 0.8), (Good, 0.1), (Fair, 0.1)} | {(Excellent, 0.4), (Good, 0.3), (Fair, 0.3)} | {(Excellent, 0.5), (Good, 0.25), (Fair, 0.25)} |

Service time (C2) | {(Excellent, 0.3), (Good, 0.42), (Fair, 0.28)} | {(Excellent, 0.5), (Good, 0.3), (Fair, 0.2)} | {(Excellent, 0.9), (Good, 0.06), (Fair, 0.04)} | {(Excellent, 0.7), (Good, 0.18), (Fair, 0.12)} | {(Excellent, 1)} |

Service quality (C3) | {(Excellent, 1)} | {(Excellent, 0.86), (Good, 0.12), (Fair, 0.02)} | {(Excellent, 1)} | {(Excellent, 0.83), (Good, 0.06), (Fair, 0.01), (H, 0.1)} | {(Excellent, 1)} |

IT capabilities (C4) | {(Excellent, 0.6), (Good, 0.4)} | {(Excellent, 1)} | {(Excellent, 1)} | {(Excellent, 0.6), (Good, 0.4)} | {(Good, 0.7), (Fair, 0.3)} |

Supply chain design (C5) | {(Poor, 0.6), (Very poor, 0.4)} | {(Good, 0.7), (Fair, 0.3)} | {(Excellent, 0.9), (Good, 0.1)} | {(Excellent, 0.9), (Good, 0.1)} | {(Excellent, 0.9), (Good, 0.1)} |

Safety stock inventory (C6) | {(Poor, 0.5), (Very poor, 0.5)} | {(Poor, 0.5), (Very poor, 0.5)} | {(Good, 0.3), (Fair, 0.5), (Poor, 0.2)} | {(Excellent, 1)} | {(Poor, 0.5), (Very poor, 0.5)} |

Flexibility (C7) | {(Poor, 0.8), (Very poor, 0.2)} | {(Excellent, 1)} | {(Good, 0.3), (Fair, 0.5), (Poor, 0.2)} | {(Good, 0.3), (Fair, 0.5), (Poor, 0.2)} | {(Excellent, 0.4), Good (0.4), (Fair, 0.2)} |

Cooperation (C8) | {(Excellent, 1)} | {(Excellent, 1)} | {(Excellent, 0.3), (Good, 0.7)} | {(Poor, 0.5), (Very poor, 0.5)} | {(Good, 0.3), (Fair, 0.4), (Poor, 0.3)} |

Redundancy (C9) | {(Excellent, 1)} | {(Good, 1)} | {(Poor, 1)} | {(Very poor, 1)} | {(Fair, 1)} |

Risk management (C10) | {(Excellent, 1)} | {(Fair, 0.5), (Poor, 0.5)} | {(Good, 1)} | {(Poor, 1)} | {(Fair, 1)} |

Criteria/Alternative | A1 | A2 | A3 | A4 | A5 | |||||
---|---|---|---|---|---|---|---|---|---|---|

u_{max} | u_{min} | u_{max} | u_{min} | u_{max} | u_{min} | u_{max} | u_{min} | u_{max} | u_{min} | |

Service price (C1) | 0.49 | 0.49 | 0.83 | 0.83 | 0.925 | 0.925 | 0.775 | 0.775 | 0.8125 | 0.8125 |

Service time (C2) | 0.755 | 0.755 | 0.825 | 0.825 | 0.965 | 0.965 | 0.895 | 0.895 | 1 | 1 |

Service quality (C3) | 1 | 1 | 0.96 | 0.96 | 1 | 1 | 0.98 | 0.88 | 1 | 1 |

IT capabilities (C4) | 0.9 | 0.9 | 1 | 1 | 1 | 1 | 0.9 | 0.9 | 0.675 | 0.675 |

Supply chain design (C5) | 0.15 | 0.15 | 0.675 | 0.675 | 0.975 | 0.975 | 0.975 | 0.975 | 0.975 | 0.975 |

Safety stock inventory (C6) | 0.125 | 0.125 | 0.125 | 0.125 | 0.525 | 0.525 | 1 | 1 | 0.125 | 0.125 |

Flexibility (C7) | 0.2 | 0.2 | 1 | 1 | 0.525 | 0.525 | 0.525 | 0.525 | 0.8 | 0.8 |

Cooperation (C8) | 1 | 1 | 1 | 1 | 0.825 | 0.825 | 0.125 | 0.125 | 0.5 | 0.5 |

Redundancy (C9) | 1 | 1 | 0.75 | 0.75 | 0.25 | 0.25 | 0 | 0 | 0.5 | 0.5 |

Risk management (C10) | 1 | 1 | 0.375 | 0.375 | 0.75 | 0.75 | 0.25 | 0.25 | 0.5 | 0.5 |

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | |
---|---|---|---|---|---|---|---|---|---|---|

Type | min | min | max | max | max | max | max | max | max | max |

Weight | 0.124 | 0.124 | 0.131 | 0.147 | 0.121 | 0.107 | 0.072 | 0.050 | 0.056 | 0.069 |

A1 | 0.49 | 0.755 | 1 | 0.9 | 0.15 | 0.125 | 0.2 | 1 | 1 | 1 |

A2 | 0.83 | 0.825 | 0.96 | 1 | 0.675 | 0.125 | 1 | 1 | 0.75 | 0.375 |

A3 | 0.925 | 0.965 | 1 | 1 | 0.975 | 0.525 | 0.525 | 0.825 | 0.25 | 0.75 |

A4 | 0.775 | 0.895 | 0.93 | 0.9 | 0.975 | 1 | 0.525 | 0.125 | 0 | 0.25 |

A5 | 0.8125 | 1 | 1 | 0.675 | 0.975 | 0.125 | 0.8 | 0.5 | 0.5 | 0.5 |

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | |
---|---|---|---|---|---|---|---|---|---|---|

Weight | 0.124 | 0.124 | 0.131 | 0.147 | 0.121 | 0.107 | 0.072 | 0.050 | 0.056 | 0.069 |

A1 | 1 | 1 | 1 | 0.9 | 0.15 | 0.13 | 0.2 | 1 | 1 | 1 |

A2 | 0.59 | 0.92 | 0.96 | 1 | 0.69 | 0.13 | 1 | 1 | 0.75 | 0.38 |

A3 | 0.53 | 0.78 | 1 | 1 | 1 | 0.53 | 0.53 | 0.83 | 0.25 | 0.75 |

A4 | 0.63 | 0.84 | 0.93 | 0.9 | 1 | 1 | 0.53 | 0.13 | 0 | 0.25 |

A5 | 0.60 | 0.76 | 1 | 0.68 | 1 | 0.13 | 0.8 | 0.5 | 0.5 | 0.5 |

Total Relative Importance Based on WSM | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | Q^{(1)} | |

A1 | 0.12 | 0.12 | 0.13 | 0.13 | 0.02 | 0.01 | 0.01 | 0.05 | 0.06 | 0.07 | 0.73 |

A2 | 0.07 | 0.11 | 0.13 | 0.15 | 0.08 | 0.01 | 0.07 | 0.05 | 0.04 | 0.03 | 0.75 |

A3 | 0.07 | 0.10 | 0.13 | 0.15 | 0.12 | 0.06 | 0.04 | 0.04 | 0.01 | 0.05 | 0.76 |

A4 | 0.08 | 0.10 | 0.12 | 0.13 | 0.12 | 0.11 | 0.04 | 0.01 | 0.00 | 0.02 | 0.73 |

A5 | 0.07 | 0.09 | 0.13 | 0.10 | 0.12 | 0.01 | 0.06 | 0.02 | 0.03 | 0.03 | 0.68 |

Total Relative Importance Based on WPM | |||||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | Q^{(2)} | |

A1 | 1.00 | 1.00 | 1.00 | 0.98 | 0.80 | 0.80 | 0.89 | 1.00 | 1.00 | 1.00 | 0.56 |

A2 | 0.94 | 0.99 | 0.99 | 1.00 | 0.96 | 0.80 | 1.00 | 1.00 | 0.98 | 0.93 | 0.65 |

A3 | 0.92 | 0.97 | 1.00 | 1.00 | 1.00 | 0.93 | 0.95 | 0.99 | 0.93 | 0.98 | 0.72 |

A4 | 0.94 | 0.98 | 0.99 | 0.98 | 1.00 | 1.00 | 0.95 | 0.90 | 0.00 | 0.91 | 0.00 |

A5 | 0.94 | 0.97 | 1.00 | 0.94 | 1.00 | 0.80 | 0.98 | 0.97 | 0.96 | 0.95 | 0.60 |

Alternative | Q^{(1)} | Q^{(2)} | Q | Final Rank |
---|---|---|---|---|

A1 | 0.73 | 0.56 | 0.646 | 3 |

A2 | 0.75 | 0.65 | 0.697 | 2 |

A3 | 0.76 | 0.72 | 0.740 | 1 |

A4 | 0.73 | 0.00 | 0.363 | 5 |

A5 | 0.68 | 0.60 | 0.637 | 4 |

λ = 0 | λ = 0.1 | λ = 0.2 | λ = 0.3 | λ = 0.4 | λ = 0.5 | λ = 0.6 | λ = 0.7 | λ = 0.8 | λ = 0.9 | λ = 1 | |
---|---|---|---|---|---|---|---|---|---|---|---|

A1 | 0.560 | 0.577 | 0.594 | 0.612 | 0.629 | 0.646 | 0.663 | 0.680 | 0.698 | 0.715 | 0.732 |

A2 | 0.649 | 0.658 | 0.668 | 0.678 | 0.687 | 0.697 | 0.707 | 0.716 | 0.726 | 0.736 | 0.745 |

A3 | 0.718 | 0.723 | 0.727 | 0.731 | 0.736 | 0.740 | 0.745 | 0.749 | 0.753 | 0.758 | 0.762 |

A4 | 0.000 | 0.073 | 0.145 | 0.218 | 0.291 | 0.363 | 0.436 | 0.509 | 0.581 | 0.654 | 0.726 |

A5 | 0.597 | 0.605 | 0.613 | 0.621 | 0.629 | 0.637 | 0.645 | 0.653 | 0.661 | 0.669 | 0.677 |

Final ranking | |||||||||||

λ = 0 | λ = 0.1 | λ = 0.2 | λ = 0.3 | λ = 0.4 | λ = 0.5 | λ = 0.6 | λ = 0.7 | λ = 0.8 | λ = 0.9 | λ = 1 | |

A1 | 4 | 4 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |

A2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

A3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

A4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 4 |

A5 | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 |

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## Share and Cite

**MDPI and ACS Style**

Pajić, V.; Kilibarda, M.; Andrejić, M.
A Novel Hybrid Approach for Evaluation of Resilient 4PL Provider for E-Commerce. *Mathematics* **2023**, *11*, 511.
https://doi.org/10.3390/math11030511

**AMA Style**

Pajić V, Kilibarda M, Andrejić M.
A Novel Hybrid Approach for Evaluation of Resilient 4PL Provider for E-Commerce. *Mathematics*. 2023; 11(3):511.
https://doi.org/10.3390/math11030511

**Chicago/Turabian Style**

Pajić, Vukašin, Milorad Kilibarda, and Milan Andrejić.
2023. "A Novel Hybrid Approach for Evaluation of Resilient 4PL Provider for E-Commerce" *Mathematics* 11, no. 3: 511.
https://doi.org/10.3390/math11030511