Introduction

The probable origin of the term logistics is from the Greek logistikos, meaning “skilled in calculating” (^{BTRE, 2001}). According to the Council of Logistics Management, logistics can be defined as a part of the supply chain process that plans, implements and controls the efficiency, forward and backward flow, and the storage of goods and services and information between the point of origin and the destination to satisfy the needs of the clients (^{Tilanus, 1997}).

Logistics were initially utilized by the military who, through it, would efficiently plan military strategies in battlefields. Subsequently, logistics became an important part of the integral system of the production process. Its development was originated during the recession of the United States in the 1950s, when the industrial sector placed special importance on the circulation of merchandise. However, the term as such, was not a subject that interested academia until the 1960s.

The concept of logistics as an integrated management arises in the 1980s, where the physical distribution function is added to logistics as a response to the deregulation of transport and the growing globalization (^{Coyle, Langley, Gibson, Novack, & Bardi, 2009}). In the mid1980s, logistics was recognized as a key element of trade, considering within its elements the costs of transport and storage (^{BTRE, 2001}). However, it was in the middle of the 20th century when the rise of studies concerning international trade logistic systems began, as well as the acknowledgment of logistics as a vital element of business activities and to maintain competitiveness (^{Tseng, Yue, & Taylor, 2005}).

A global trade competitive network is the epicenter of international trade (Arvis & et al., 2010). The new competitive reality presents a space where flexibility, speed of entry into the market and productivity will be the key variables that will determine the permanence of companies in the markets. It is here where the foreign trade logistics play a crucial role, parting from the efficient management of the flow of goods and services towards the end consumer (^{Monterroso, 2000}).

Today, due to a stronger interconnection in the markets, foreign trade logistics has become a key factor in foreign trade, mainly due to two factors: costs and time.

Distances have increased the need of an adequate planning for the consumer to access the product they desire at the moment that they so require. To this end, it is essential that the products move through an integrated system at an accessible cost that allows the efficient performance of foreign trade. For these reasons, logistics is extremely important for companies (^{Yardımcıoğlu et al., 2012}).

This research is structured in four sections: the first introduces foreign trade logistics; the second presents a review of the literature on efficiency in foreign trade logistics; the third addresses the methodological elements of the DEA Network model to calculate the global technical, pure technical and scale efficiency, as well as the node benchmarking and slacks variable analyses; and the fourth reviews the results obtained with the DEA Network measurements, thus identifying the economies of the region that comprise the Pacific Rim that efficiently utilized their resources. Lastly, the conclusions are established, highlighting the importance of the efficient use of resources through a logistic network to generate a greater volume and value of foreign trade.

Empirical studies of the efficiency in international trade logistics

According to ^{Tuzun (2015)}, the logistic services, information systems and infrastructure resources are the three components of the system and are intimately linked. As such, the interaction of these main components in the logistic system is interpreted in the following manner: logistics services allow the movement of materials and products, thus logistics services comprise physical activities such as transportation and storage; as well as non-physical activities such as the design of the supply chain, etc.

^{Szymonik (2014)} mentions that international logistics is comprised by two basic elements: the configuration of an international logistics system or network and a dimension of the international supply chain or the international operating channels of international trade. These basic elements include routes for all types of transportation, storage, logistic centers, terminals, containers, transportation equipment and their facilities, means of transmission and tracking, inspection points and skilled human resources throughout the network.

Several authors such as ^{Coskuntunce (2014)}, ^{Loder (2014)} and ^{Gebresenbet and Bosona (2012)}, state that the volume of international trade significantly improves among the countries that possess global networks and efficient logistics infrastructure. Therefore, logistics operations have become more important within the international trade framework. For these reasons, logistics services have become more relevant and are an essential part of the efficiency and effectiveness of foreign trade operations.

There are different perspectives concerning the study of international logistics; while looking to outline the problems that Japanese firms have concerning their operations in China, ^{Yu (2011)} identifies three elements that influence logistics competitiveness: process quality, costs and delivery times. ^{Easton (2003)} indicates in a comparative study of several countries that the international supply chain is highly inefficient and unreliable; additionally, he comments that a poor logistics and operational infrastructure limits the economic development and performance of local and foreign companies.

^{Ta et al. (2000)} analyzed the international logistics performance of Singapore and found that one of the most important limitations for competitiveness in this country are transport problems. ^{Carter et al. (1997)} carried out a study to identify logistic barriers between the United States and China, discovering different problems that affect foreign trade competitiveness between these two countries, problems that include aspects such as transportation, bonded warehouse, import and export services and costs.

^{Yasui (2012)}, in his work “Customs Environmental Scan 2012”, carries out a study of the key factors that concern the international trade of merchandise and transport, measures and regulations of the borders, business practices and reinforcement of customs; where indicators such as the total volume of imports and exports, commercial treaties and agreements, trade facilitation and reinforcement of customs (profit, safety and intellectual property) stand out. ^{Garaviz (2009)}, in his proposal for the development of a logistic cluster for a national and international competitive logistics corridor in Colombia, considers three factors to be key: access to markets, border administration and infrastructure of communication and transport.

The Florida Chamber of commerce, in its logistics study, considers the following as key factors for competitiveness in this sector: international transport systems, commercial flows, penetration of new foreign markets, capacity of the transport system and funds invested by the government sector. The importance of research on logistics operations in the international context has been acknowledged by ^{Sweeney (1994)}, ^{Hayashi et al. (2010)} and ^{Easton and Zhang (2002)}.

The World Bank (2013), in its report “Connecting to Compete 2012 Trade Logistic in the Global Economy”, utilizes the following variables: import and export time, red tape¹ (such as import and export agencies, import and export documents) and delays, reliability and delivery services. The Logistics Performance Index (LPI) of the WB is a comparative tool carried out every two years to help countries identify the challenges and opportunities in their trade logistics performance, and to acknowledge the things that can be improved in said performance. The LPI (2014) allows comparing 160 countries and its results are based on surveys done on almost a thousand logistics professionals who provide qualitative feedback on the logistics reality of different nations.

LPI international: provides qualitative assessments of the countries on six defined areas, carried out by professionals in the world of logistics who work outside the country in question, with their indicators being:

Two-stage DEA Network

The DEA (Data Envelopment Analysis) technique is an application of the linear programming methods, used to measure the relative efficiency of organizational units that have the same goals and objectives. This technique was initially developed by ^{Charnes, Coopers and Rhodes (1978)}, who based it on a preliminary work by ^{Farrell (1957)}.

The DEA technique is an alternative to the ratio and regression models, as it allows working with multiple input and output variables. Moreover, it does not require the variables of the models to collect special statistical characteristics, as this technique measures the efficiency of each country with regard to the other countries in the sample, providing greater flexibility in the selection of variables according to the different types of measures.

To calculate the relative efficiency of a firm, it is preferable to resolve the dual problem, a model that can be written in the following manner (^{Charnes et al., 1978}):

Min 0,λ θ

s a:

-yi + λY ≥ 0

θxi - Xλ ≥ 0

λ ≥ 0

Where:

X = matrix of inputs K x N

Y = matrix of outputs M x N

θ is a scalar. Multiplies the vector of inputs

λ is a vector of constants N x 1. Multiples the matrix of inputs and outputs.

N = number of firms

The model presented assumes that all the cases called DMUs² (countries in the case of this research) are operating at an optimal scale with constant returns to scale (CRS).

Subsequently, Banker et al. (1984) suggest an expansion of the model towards situations of variable returns to scale, modifying the linear program by incorporating a convexity restriction³ (N1’λ= 1). To differentiate it from the former, it is referred to as variable returns to scale (VRS), and the expression of the same is the following:

min 0,λ θ

s a:

- yi + λY ≥ 0

θxi - Xλ ≥ 0

N1 ́λ= 1

λ≥ 0

Where: N1 is a unitary vector N x 1.

Said modification allowed decomposing the technical efficiency into two parts: pure technical efficiency and scale efficiency. For this, the two models-CSR and VRS-must be calculated with the same data: if there is a difference between the two measurements for a specific firm, this means that there is an inefficiency of scale in said firm, and the inefficiency value is the difference between the CSR and VRS measurements.

The pure technical efficiency coincides with the VRS measurement. The inefficiency of scale originates from producing a suboptimal level of scale. The global technical efficiency is the product of the two efficiencies-pure technical and scale.

The two-stage DEA Network model considers that each DMU transforms some external X inputs into the final Y outputs, through the intermediary X measurements in a two-stage process, as shown in Figure 1 below.

Source: Own elaboration, 2016.

Figure 1 Construction of a two-stage model. Source: Own elaboration, 2016. 

An example of this type of studies is the one presented by ^{Charnes (1994)}, where a DEA model is applied in two stages to evaluate the policies and administration in the recruitment of the North American military. For his part, ^{Zhu (2000)} applies a two-stage model to analyze the financial performance of the first 500 companies according to the Fortune journal, through the generation of the best practice frontier through the eight financial performance variables that the journal utilizes for its classification.

Assume n DMUs (j = 1, ..., n), each one using m external entries xij, i = 1, ..., m in the first stage to produce q outputs zpj, p = 1, ..., q of this stage. The results obtained from the first stage are then utilized as inputs in the second stage to produce final products yrj, r = 1,..., s. In this basic context, only the external outputs to the first stage enter the system, and only the outputs of the second stage enter the system. Following the notation below:

j ϵ J = {1, ..., n}: Overall indices of the n DMUs.

j ϵ 2 J: Denotes the evaluated DMU.

Xj = (xij, i = 1, ..., m): The vector of the external inputs utilized by DMUj, j ϵ J

Zj = (zpj, p = 1, ..., q): The vector of the intermediate variables by DMUj, j ϵ J

Yj = (yrj, r = 1, ..., s): The vector utilized by the final products by DMUj, j ϵ J

n = (n1, ..., nm): The weight vector in the fractional model

v = (v1, ..., vm): The weight vector for the external inputs in the linear model.

u = (u1, ..., uq): The weight vector for the intermediate measures in the fractional model.

w = (w1, ..., wq): The weight vector for the intermediate measures in the linear model.

x = (x1, ..., xs): The weight vector for the final outputs in the fractional model.

m = (m1, ..., ms): The weight vector for the final outputs in the linear model.

e.g. o: The global efficiency of DMUj, j ϵ J

e.g. 1: The first stage efficiency by DMUj, j ϵ J

e.g. 2: The second stage efficiency by DMUj, j ϵ J

The model employed for this research has an output orientation, given that the objective of the logistics system is to increase the value and volume of international trade using the different elements that comprise the logistics network.

The DEA Network model proposed for this study has two stages comprised by nodes and intermediate variables. To this end, three tests (one for node 1, another for node 2 and a third one to verify the relation between the initial inputs and final outputs) were carried out through the factorial analysis, using the main components analysis technique to determine the validity of the inputs and outputs to be used in the study, as well as KMO⁴ tests for each analysis (see annex). Finally, it was determined that the models to be carried out in the research will be as follows:

The first node or station is that of logistics and infrastructure, and is comprised by the Customs variable and the Infrastructure variable as inputs. The second node or station is that of international trade, and its outputs are the Value and Volume of the exports. The intermediate variables (that will act as outputs in the first station and as inputs in the second station) are International shipments, Logistics services, Traceability and Tracking, and Execution Time. The structure of the model can be better appreciated in Figure 2.

Source: Own elaboration, 2016.

Figure 2 DEA model network proposed in the logistics of international trade. 

The data of the variables presented in Figure 2 were obtained from the database of the World Trade Organization, the World Customs Organization, and the World Bank for the year 2014, and are defined in the following manner:

a) Inputs

Customs personnel. Is comprised by the total number of people directly employed in customs.

Investment in infrastructure. This variable encompasses the infrastructure that is normally utilized to carry out logistics services such as storage, road, railroad, port and airport networks, employed and skilled personnel, construction, maintenance and investment in logistics infrastructure.

International freight services. This encompass all the transport services (maritime, air, land, internal rivers, spatial and duct) provided by the residents from one economy to the other, which involves the movement of goods (freight), the lease of carriers with crew, as well as the corresponding support and auxiliary services.

b) Intermediate outputs/inputs variables

Logistics Services. Includes the insurance and financial services, and other services related to the logistics of exported goods such as: freight insurance on exported goods and other direct insurance policies, such as life insurance; financial intermediation services, such as commissions, exchange transactions and brokerage services; and auxiliary services, such as operation and market regulation services.

Cost of exports. The cost calculates the rates applied to a 20 feet container in US dollars. All the charges linked to the realization of the procedures to export the products are included. These include documentation costs, administrative fees for customs clearance and technical control, fees of the customs clearance agents, handling expenses at the terminal and land transport. The calculation of the cost does not include fees or commercial taxes. Only the official costs are registered.

Execution Time. Refers to the delivery of products within the established time frames. The time is registered in calendar days. The calculation of time for a procedure starts at the moment in which it is initiated and executed until it has been concluded. If a procedure can be accelerated at an additional cost, the faster legal procedure is chosen. The waiting time between procedures-for example, during the unloading of the product-is included in the measurement.

c) Outputs

Value of the exports. Represent the overall value the goods and other market services provided to the rest of the world, including the value of the goods, freights, insurance, transport and other services.

Volume of the exports. Represent the overall volume of the goods and other market services provided to the rest of the world, including the value of the goods, freights, insurance, transport and other services.

Results

The results are presented in three sections; the first corresponds to the efficiency values obtained with respect to different types of efficiency, these being Global Technical Efficiency, Pure Technical Efficiency and Scale Efficiency. The second section shows the benchmarking behavior by node, thus making it possible to see the countries considered a point of reference according to the use of their resources and the results obtained (inputs-outputs). Finally, in the third part of the results the slacks variables are presented, as well as the projections. This is done in order to not only determine the efficiency or inefficiency of the countries with respect to the variables, but also to present proposals to correct the use of logistics resources for international trade in the inefficient countries.

Benchmarking results

When analyzing benchmarking by nodes, it can be observed that for the first node (logistics and infrastructure) more countries are used as points of reference than in the second node (international trade). This stipulates that despite the fact that the Customs, Infrastructure and Transport variables are highly significant in the efficiency of international trade, it is not necessarily the same countries that are being referenced in both nodes.

In the case of node 1, the Philippines is the country most used as a reference point with nine mentions for constant returns (CRS) and seven for variable returns (VRS), followed by New Zealand with six mentions, for both constant and variable returns, and Mexico with six mentions for constant returns and five for variable returns. It is worth noting cases such as that of Peru and Singapore. For constant returns, Peru is taken as a point of reference seven times, while for constant returns it is referenced only twice. Meanwhile Singapore shows the opposite effect, for variable returns it is referenced six times, and for constant returns only once (see Figure 3).

Source: Own elaboration based in the results of the DEA Network.

Figure 3 Benchmarking of node 1: logistics and infrastructure. 

For the case of node 2 (see Figure 4): international trade, it is clear that China is the most referenced country as a role model, obtaining 15 mentions for constant returns and nine for variable returns; following China, it is Hong Kong, Korea and Singapore (the three with constant returns) that are referenced; six times the first, and four times the second and third.

Source: Own elaboration based on the results of the DEA Network.

Figure 4 Benchmarking of node 2: international trade. 

Conclusions

The theoretical foundations of the research are based on the concept of logistics and efficiency. Logistics taken as an example of a systems approach to solve problems within foreign trade, and efficiency as a part of competitiveness that references the achievement of goals with the least amount of resources, or operating so that resources are more adequately utilized.

Counteracting the theory with the results, it can be observed that there are more countries, with regards to global technical efficiency, that show efficiency. With these being China, Indonesia, Mexico, New Zealand, Peru, Singapore and Thailand; said results indicate that the countries that showed efficiency in this column are adequately utilizing their available physical resources. There are several researches that utilize the same technique (DEA) in matters of logistics, particularly transport, where the authors conclude that investment in infrastructure and transport is very important, as it increases their quality and network, and allows reducing costs and times in the transport of people and goods, creating a greater coverage and connectivity.

The aim of this research is to identify the degree of efficiency or inefficiency of the logistics network of foreign trade, particularly of the exports of 17 countries that comprise the Pacific Rim region, as well as to analyze the variables that can be improved and to what extent so that the inefficient countries are able to optimize their resources. According to the objective of the research in this work, the measurement of the technical scale and pure efficiency of a constant return model with output orientation is presented through the DEA methodology. The variables of 17 countries in the Pacific Rim region are analyzed for the year 2014.

Based on the input and output data utilized to carry out the calculation of the efficiency levels for each country concerning foreign trade, it is possible to observe and conclude that Singapore is the country that shows the three types of analyzed efficiency (Global Technical Efficiency, Pure Technical Efficiency, and Scale Efficiency). While the countries of China, Indonesia, Mexico, New Zealand, Peru, Singapore and Thailand showed Pure Technical Efficiency, thus it can be concluded that they are adequately utilizing their available physical resources.

Regarding the benchmarking analysis, it can be concluded that the country with the best practices is the Philippines, while in the second node, it is China.

For the case of Mexico, it can be observed that despite a proper utilization of the available resources, it is not achieving an optimal level given the existing technology. Mexico will have to increase its Scale Efficiency and Global Technical Efficiency by 82.17 percent. The projections to achieve efficiency for Mexico are: an ideal execution time of 3 days, with an approximate cost of 1,499.30 dollars, with customs personnel of 7,347 people, mainly.

It should be noted that the technique utilized only analyzes the use of the existing resources and the results obtained with the utilization of the same, as well as comparatively with respect to the set of analyzed countries; therefore, the level of lag in the logistics infrastructure of some of the countries is not considered in this research.

Finally, the results show the need to implement an industrial policy that improves the technological lag and is more focused on the improvement of innovation and technology, strengthening labor training, specifically in micro, small and medium-sized companies, which are the ones that integrate most of the export sector.