The analysis approach includes the following three steps:

Step 1, we can analyze the influencing factors of urgent transportation by listing the whole process nodes, then obtain the main factors and their order of importance based on the pairwise comparison by 1 - 9 scale method. At the same time, a judgment matrix can be derived from the importance order. After calculating the eigenvector of the matrix and normalizing the vector, then checking the consistency of the judgment matrix, a weight vector would be obtained.

Step 2, while all factors are being treated as linguistic variables and assigned fuzzy values, the comprehensive time performance evaluation of all factors will be obtained by use of the weight vector combined with fuzzy composite operators, and through matrices operation.

Step 3, by taking the urgent transportation line between China and Thailand as an example, we can compare several different possible routes and derive the relatively optimal solution.

Urgent transportation service normally is provided by air cargo agents with the demand for quick delivery of samples, spare parts, and so on. The following services cover a varied range (IATA, 1994) :

1) SMALL PARCELS SERVICE: for small and medium shipments that have several house waybills(HWBs) and are consolidated under one master air waybill(MAWB) issued by airlines.

2) EXPRESS SERVICE: for shipments that have only one HWB under one MAWB and are not consolidated with other shipments. It is also named NEXT FLIGHT OUT SERVICE, or NFO.

3) COURIER SERVICE: for shipments carried on board passenger aircraft as carry-on or checked luggage and are not consolidated. This kind of service has only one HWB and no MAWB. It is also named ON BOARD COURIER, or OBC.

The above-mentioned services have one common character. The shipments are delivered from door to door. COURIER SERVICE, or ON BOARD COURIER is the most urgent method among them. All these kinds of services consist of logistics operation processing nodes including pick-up at the shipper’s premises, air transportation, customs formalities, and delivery to the consignee’s address at least. The whole process of door-to-door air cargo transportation is shown in Figure 1, while it does not include all nodes of all kinds of transportation modes all the time, i.e., there is a different quantity of nodes for each different mode. Table 1 illustrates the differences among the three modes, with numbers “1” and “0” representing “yes” and “no” respectively.

Lead time performance is the most important quality standard of all for urgent transportation. The shorter the process chain was, or the fewer nodes, the better the time performance would be. Obviously “on board courier” (OBC) mode has the fewest nodes. Taking the OBC mode as an example, consider these nodes as factors influencing time performance. Analyze these factors, establish a mathematical model, and evaluate the comprehensive time performance of each factor.

It is important to analyze these factors, either what they are, or how they influence performance, etc.

First, we group the nodes with similar attributes and refine the influencing factors. There are several main operational component parts for OBC mode transportation, each part includes one or several nodes:

1) Trucking service (pick-up and delivery).

2) Customs brokerage service (export declaration and import clearance).

3) Flight transportation service (airport-to-airport).

Next, the above parts are defined as factors, and each factor is an influencing variable of transportation performance, as Table 2 shows.

Then, when the factors or variables have been defined, it is necessary to determine priorities by making a judgment or pairwise comparison, for it would be very difficult to rank the importance or preference when many factors were compared together at the same time. Pairwise comparison involves comparing criteria or factors and ranking them in relation to each other. This paper uses the ranking method of a 1 - 9 scale, with 1 representing “equal importance” or “equal preference” and 9 representing “absolute importance” or “extreme preference”. The method of the 1 - 9 scale was developed by Saaty (1994) . As shown in Table 3, it helps represent the factors numerically and derive a weight vector of all factors, i.e., the order of their relative importance. However, because the results of such comparison are described by natural language, the sequential representation is not accurate but fuzzy. In other words, even if the factors’ rough ranking can be obtained through a 1 - 9 scale method, it is still hard to get accurately measurable data which can be used to establish a mathematical model to reach a statistical result of factors’ comprehensive influence. This paper combines the above factors’ weight vector with linguistic variables of fuzzy theory so that the language-described factors would have clearer ranges or intervals.

Hence, the approach provides a path to obtain more accurately measurable data which helps set up a mathematical model for performance evaluation. The core of the 1 - 9 scale and fuzzy approach lies in how to derive the weight vector of factors, and “this vector itself is just a fuzzy set” (Hu, 2010) .

On the detailed calculation in the following four steps, pairwise compare all the factors and rank their relative importance:

Step 1, we made a questionnaire survey among 20 logistics experts from three logistics companies, asking them to pairwise compare factors u₁, u₂, and u₃, choosing results out from “equally important”, “slightly more important”, “strongly more important”, “significantly more important”, and “absolutely more important”, by the above 1 - 9 scale method. Scored results are shown in Table 4. Then, confidence intervals of u₁, u₂, and u₃ could be obtained on the scores as follows (shown in Table 5):

• Interval of u₁ equals 1.3 ± 0.29.

• Interval of u₂ equals 3.6 ± 0.37.

• Interval of u₃ equals 2.7 ± 0.68.

Confidence level is assumed as 0.90 here, it would be 0.95 or 0.99 for more accuracy.

In Table 5, values of the confidence interval show that u₂ ≥ u₃ > u₁. When referring to the 1 - 9 scale of Table 3, it is obvious that u₂ is slightly more important than u₃, and u₂ is strongly more important than u₁.

Step 2, we establish a judgment matrix based on the factors’ importance order and scoring method of a 1 - 9 scale, and then obtain their weight vector. Table 6 illustrates how to get the matrix, to be understood easier, the shown factors’ sequence subjects to u₂ ≥ u₃ > u₁.

^aThe scores do not exceed 5 points, however, it is necessary that we take 1 - 9 scale, for subfactors will possibly need comparing, e.g., u₂ includes subfactors “export declaration” and “import clearance”, according to experience, result will maybe show “import clearance is significantly or absolutely more important than export declaration”, i.e., “7” or “9”.

The following judgment matrix, denoted as A, can be obtained in Table 6:

A = [ 1 3 5 0.33 1 3 0.20 0.33 1 ]

Step 3, we calculate the eigenvector and maximum eigenvalue of the judgment matrix A, where the eigenvector is symbolized by the sign W, and the maximum eigenvalue is λ_max. Normally, if the judgment matrix A is an n-order square matrix,

A = ( a i j ) n × n

where a i j is the importance score of comparison between factor i and factor j, furthermore, let W = (w₁, w₂, …, w_n)^T, where w_i symbolizes the weight of factor i in the whole eigenvector, the superscript T refer to a transposed matrix. Then,

W i = 1 n ∑ j = 1 n a i j ∑ k = 1 n a k j , i = 1 , 2 , ⋯ , n

As the above example judgment matrix A, where n = 3, then obtains the normalized eigenvector W = (0.63, 0.26, 0.11)^T and maximum eigenvalue λ_max = 3.0387.

Step 4, inconsistency is inherent in the judgment process, of experts’ different experiences, knowledge, and available information. Hence, consistency checking of the judgment matrix is a must. There is a method to check whether the matrix is consistent or not, by comparing the deviation between λ_max and n, it means that if the deviation is less than some ratio, e.g. 0.10 (10%), then inconsistency can be considered a tolerable error in measurement. The consistency ratio’s calculating processing is as follows:

C R = ( λ max − n n − 1 ) / R I

where CR is the consistency ratio, λ_max is the maximum eigenvalue, n is the number of square matrix order, and RI is a random index. In this case, if n = 3, then RI = 0.52, thus CR = 0.0372 < 0.10. It means that the judgment matrix A is consistent, and its normalized eigenvector W = (w₁, w₂, …, w_n)^T = (0.63, 0.26, 0.11)^T can be regarded as a weight vector, where w₁ = 0.63 is w_u2, w₂ = 0.26 is w_u3, and w₃ = 0.11 is w_u1 in Table 6. Finally weight vector of factors is W = (w_u1, w_u2, w_u3)^T = (0.11, 0.63, 0.26)^T. Obviously, factor u₂ has the greatest weight, i.e., customs brokerage service is the most important factor.

The outbreak of COVID-19 pandemic has greatly impacted on the operational mode of global and regional supply chains. As the pandemic has been passing slowly, the world economy is going to recover from recession. Many enterprises are increasingly inclined to adopt low-cost strategies. Some Chinese airlines have chosen Don Mueang International Airport (international airport code: DMK) as the destination airport from China to Thailand for the resumed and newly increased flights, rather than Suvarnabhumi International Airport (international airport code: BKK). These air routes depart from some Chinese medium airports, including Wuhan, Ningbo, Nanjing, etc., besides the original bigger ones like Beijing, Shanghai, and Guangzhou. Even from Shanghai, the Chinese biggest economic city, more and more flights seem going to arrive at DMK rather than BKK. This situation would generate two problems. On the one hand, compared with BKK, DMK is inferior to the former in terms of airport support and service capability as shown in Table 8 (CAAT, 2023) . On the other hand, because DMK’s main target market is budget airlines (Hirsh, 2017) , its throughput of passengers has kept increasing year by year. Such increasing passenger service demands would compress its inadequate airport capability, and erode its logistics support, e.g., slowing down terminal cargo break-bulk service, delaying

customs clearance, and so on. This weakening operational ability would negatively impact logistics time performance at last, especially for the urgent transportation solution.

Hereinafter take company X, a logistics enterprise, as an example, and evaluate the comprehensive time performance of its urgent transportation solution between China and Thailand. There are three main influencing factors including trucking service, customs brokerage service, and flight transportation service. Hence, assign variables u₁, u₂, and u₃ stand for the three factors respectively. First, suppose u₁ be v₂, next, obtain the value of u₂ through an experts’ questionnaire survey, then get the value of u₃ according to the statistical information of flights’ punctuality rate, where the value of u₂ is computed by the following rules in Table 9 and Table 10:

• If a flight arrived at DMK, then u₂ ≈ v₃.

• If a flight arrived at BKK, then u₂ ≈ v₁.

And the value of u₃ is obtained by the following rules in Table 11.

• If the range of flight’s punctuality rate is between 90% and 95%, then u₃ = v₁.

• If the range of flight’s punctuality rate is between 95% and 100%, then u₃ = v₂.

• If the range of flight’s punctuality rate is between 80% and 90%, then u₃ = v₃.

• If the range of flight’s punctuality rate is less than 80%, then ignore this solution.

Finally, we can calculate the value of Z. It is just the evaluation of the comprehensive time performance of this solution. The fuzzy value v₂ means “very”, the best performance of one factor. If the value of Z is closer to 0.81 (value of v₂), better comprehensive performance is achieved. Hence, if there are several solutions based on different alternative routes, the one that has the minimum interval between Z value and 0.81 is the best one of all solutions.

• Route 1: u₁ = v₂, u₂ ≈ v₁, u₃ = v₂, then

A 1 = [ 0 1 0 1 0 0 0 1 0 ]

and V^T = (0.9, 0.81, 0.95)^T, then R₁ = A₁ • V^T = (0.81, 0.9, 0.81)^T. Furthermore, based on the fuzzy operator M(•, +) and combined with weight vector W = (0.11, 0.63, 0.26)^T, we can obtain Z₁ = W • R₁ = 0.8667.

^aSource: data collected by the author on July 18th, 2023.

• Route 2: u₁ = v₂, u₂ ≈ v₁, u₃ = v₃, then

A 2 = [ 0 1 0 1 0 0 0 0 1 ]

and V^T = (0.9,0.81,0.95)^T, then R₂ = A₂ • V^T = (0.81, 0.9, 0.95)^T. Moreover, based on fuzzy operator M(•, +) and combined with weight vector W = (0.11, 0.63, 0.26)^T, we can obtain Z₂ = W • R₂ = 0.9031.

• Route 3: u₁ = v₂, u₂ ≈ v₃, u₃ = v₃, then

A 3 = [ 0 1 0 0 0 1 0 0 1 ]

and V^T = (0.9, 0.81, 0.95)^T, then R₃ = A₃ • V^T = (0.81, 0.95, 0.95)^T. Furthermore, based on the fuzzy operator M(•, +) and combined with weight vector W = (0.11, 0.63, 0.26)^T, we can obtain Z₃ = W • R₃ = 0.9346.

• Route 4: u₁ = v₂, u₂ ≈ v₃, u₃ = v₁, then

A 4 = [ 0 1 0 0 0 1 1 0 0 ]

and V^T = (0.9, 0.81, 0.95)^T, then R₄ = A₄ • V^T = (0.81, 0.95, 0.9)^T. Moreover, based on the fuzzy operator M(•, +) and combined with weight vector W = (0.11, 0.63, 0.26)^T, we can obtain Z₄ = W • R₄ = 0.9216.

• Route 5: u₁ = v₂, u₂ ≈ v₃, u₃ = v₂, then

A 5 = [ 0 1 0 0 0 1 0 1 0 ]

and V^T = (0.9, 0.81, 0.95)^T, then R₅ = A₅ • V^T = (0.81, 0.95, 0.81)^T. Furthermore, based on fuzzy operator M(•, +) and combined with weight vector W = (0.11, 0.63, 0.26)^T, we can obtain Z₅ = W • R₅ = 0.8982.

The above calculation shows Z₁ < Z₅ < Z₂ < Z₄ < Z₃, and Z₁ is the one closest to 0.81(value of v₂). Route 1 has the best evaluation of performance, or it is just the optimal solution. Besides, there are two following points that should be noticed. Comparing routes 2 and 3, supposing u₁ = v₂, u₃ = v₃, route 2 has better performance, for the flight arrived at BKK, superior to DMK. On the other hand, comparing routes 2 and 4, though the flight punctuality rate of route 4 is higher than route 2, the performance of route 4 is inferior to the other, for variable u₂ has a heavier weight than u₃.