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BAR - Brazilian Administration Review

versão On-line ISSN 1807-7692

BAR, Braz. Adm. Rev. vol.9 no.1 Rio de Janeiro jan./mar. 2012 



Determinants of scale efficiency in the Brazilian third-party logistics industry from 2001 to 2009



Peter F. WankeI

IUniversidade Federal do Rio de Janeiro - UFRJ, Rio de Janeiro, RJ, Brazil. Rua Paschoal Lemme, 355. Cidade Universitária, Rio de Janeiro, RJ, 21949-900, Brazil. E-mail address:




This article investigates the Brazilian third-party logistics (3PL) sector which, increasingly competitive, offers clients a wide variety of services/information technologies in the quest to bolster efficiency. The main research objective is to determine which variables significantly impact 3PLs scale efficiency by applying two-stage DEA (Data Envelopment Analysis). Based on an unbalanced panel model, data from the annual study published by Revista Tecnologística (years 2001–2009) were analyzed. Results corroborate evidence in the literature that coordination mechanisms in the supply chain, supported by the availability of real time information and inventory synchronization, favor a more rational allocation of resources (inputs) to client demands (outputs).

Key words: DEA; third-party logistics; scale efficiency; Brazil.




In Brazil, the third-party logistics industry began to gain strength with the Plano Real economic plan and ensuing economic stability (Fleury & Ribeiro, 2003). Currently, two-thirds of logistics-related expenditure in Brazilian firms is earmarked for logistics service providers, a fact which underscores the importance of outsourcing for the country (Centro de Estudos em Logística [CEL], 2009). As such, 3PLs must continually be on the lookout for new ways to stay competitive, with efficiency evaluation techniques serving a fundamental role in this quest.

Specifically, the Data Envelopment Analysis (DEA) technique, developed over 30 years ago (Cook & Seiford, 2009), is considered to be a powerful tool for measuring efficiency. This is primarily due to its capacity to simultaneously process multiple inputs and outputs, thereby aiding managers in decision-making. In conjunction with multivariate data analysis techniques, DEA enables the impact of contextual variables on efficiency levels to be measured (Cooper, Seiford, & Tone, 2007). Despite its major shortcomings, the non-parametric DEA frontier model remains widely used in transportation/logistics efficiency research in general, probably because it has been successfully applied to a wide number of different planning situations (see for example, Hamdan & Rogers, 2007; Lin & Tseng, 2007; Min & Joo, 2009; Panayides, Maxoulis, Wang, & Ng, 2009; Ross & Droge, 2004; Zhou, Min, Xu, & Cao, 2008).

It is worth noting that, while most multivariate data analysis methods - such as ordinary least squares regressions - are oriented towards central tendency estimates, DEA is directed towards optimal estimates for each individual observation represented in a dataset. More precisely, the performance of these observations is evaluated relative to the frontiers formed by the performance that data shows is possible to attain (Cooper et al., 2007). By contrast, DEA is individually, rather than averages, oriented and deals with frontiers rather than central tendencies.

This article focuses on the Brazilian 3PL sector, with the objective of identifying the chief determinants of scale efficiency. To this end, a review of the literature was carried out, both to characterize the sector, and to justify the two-stage model adopted. More precisely, estimation of the DEA efficiency was followed by Tobit regression analysis using unbalanced panel data, thus allowing the estimation of the effect contextual variables have on sector scale efficiency. The results provided support for the positive impact of coordination processes, based on the use of information technologies and inventory synchronization mechanisms – such as just in time and milk run - on logistics performance.

The remainder of the article is comprised of five sections. Next section discusses the role of 3PLs in supply chains, the main services provided and the information technologies available to be adopted. Also presented are the scant previous studies that applied DEA to the 3PL sector in other countries. The section entitled Two-Stage DEA Modeling provides a more detailed presentation of the two-stage DEA model as well as justification for the choice of scale efficiency as a way to evaluate the impact of coordination processes on logistics performance. Then the data are analyzed and the results discussed. Last section presents the paper’s conclusions.


Literature Review 

As a consequence of the increasing popularity of logistics outsourcing in business and the concomitant growth in services supplied by service providers, large numbers of papers and research studies have been carried out and published in recent years in an attempt to better understand aspects related to 3PLs. Such aspects include, for example, the definition of 3PLs, the reasons for outsourcing, and the scope of the activities 3PLs provide (Zhou et al., 2008).

In general terms, a 3PL is “an integrated logistics services provider that is prepared to satisfy all or almost all of a client's logistics needs in a customized way” (Fleury, 2000, p. 134). Reasons for the wave of logistics services outsourcing and the hiring of 3PLs include cost reduction, improvement of service levels, increased operational flexibility, and the enhanced ability to focus on core business (Wilding & Juriado, 2004). Based on the variety of reasons for outsourcing parts of logistics operations, the emergence of 3PLs capable of performing a range of tasks with different levels of specialization is a natural consequence (Figueiredo & Mora, 2009).

In a survey of large manufacturing firm users of 3PL services conducted in Brazil, Wanke, Arkader and Hijjar (2007) identified a strong association between the production process structure of these firms on one hand, and on the other, the type of services / technological underpinnings offered by the 3PLs. More specifically, it was evident that firms in the automotive, electric appliances, and aerospace sector tend to hire integrated 3PLs, i.e., that handle transport, storage, and inventory concurrently, and that depend heavily on information technologies. In contrast, foodstuffs, beverages, and fuels firms, for example, tend to hire 3PLs with less of a technology-intense approach – firms more geared towards providing basic transportation services.

The deployment of complex information technologies is ever more commonplace in 3PLs that coordinate a wide range of activities for their clients. In these cases the transmission of the “right information to the right person at the right time so it can be used in real time” is one of challenges of providing logistics services (Youngberg, Olsen, & Hauser, 2009). In particular, Enterprise Resource Planning (ERP) systems standardize and integrate order-related information, rendering it more reliable for the 3PL’s planning of transportation and warehousing resources relative to client inventories, and, thus, making improved operational performance possible (Chou & Chang, 2008). 3PLs have also garnered prominence in the market due to their mastery of sophisticated IT, for example, by making a variety of information, available over the Internet, including tracking of goods (Lieb & Lieb, 2008). In sum, clients consider technological prowess as a basic item expected of 3PLs (Lieb, 2005).

The recognition of the importance of coordination processes on transportation and warehousing, key supply chain functions performed by 3PLs, is by no means new (Ng, Ferrin, & Pearson, 1997). The novelty, however, is the appearance of IT applications that have transformed the operational mode of these activities and leveraged supply chain performance (Mason, Ribera, Farris, & Kirk, 2003; Stefansson & Lumsden, 2009). Transportation and warehousing management systems, for example, are key-technologies used to manage the physical flow of merchandise along the supply chain. Integrated systems (including transportation management systems, warehousing management systems and global inventory visibility via Internet) may potentially drive down costs and improve client services through a better matching of resources with demands, thus reducing shipping/receiving lead times, yielding more accurate shipping and reducing variability in response times (Mason et al., 2003).

Certification processes, such as those developed by the International Organization for Standardization (ISO), are another valued aspect of the 3PL industry. By means of structuring and implementation of standardized procedures, certification tends to be associated with improved service levels. For example, it has been empirically shown that ISO 9000 compliance improves the performance of logistical operations, providing positive results soon after adoption. Better performance translates into shorter lead times for products, and shorter turnover for cash circulating between suppliers, clients and service providers (Lo, Yeung, & Cheng, 2009).

According to Zhou, Min, Xu and Cao (2008), despite the numerous studies on the 3PL sector that had been completed by that time, only two attempted to evaluate the performance of the industry using DEA. This shortcoming clearly suggests a void to be filled. It must be noted, however, that DEA has already been satisfactorily employed in other segments that deal directly with logistics, such as the airline industry, (Schefczyk, 1993), airports (Pacheco & Fernandes, 2003), road passenger transport (Odeck & Alkadi, 2001), container terminals (Cullinane, Song, & Wang, 2005; Min & Park, 2005; Turner, Windle, & Dressner, 2004; Wang, Song, & Cullinane, 2002), ports in general (Panayides et al., 2009) and large petroleum distribution networks (Ross & Droge, 2004).

As mentioned, studies that discuss the application of DEA, specifically in the 3PL sector, are scarce and relatively recent. Min and Joo (2006), for example, applied the technique to a group of six leading US-based 3PLs. The authors developed a benchmark as a way to identify the 3PLs developing best practices and to allow other 3PLs to emulate them. According to the authors, the DEA technique helps guide financial investments as well as assesses the impacts of investments on firm performance. The results indicated that US 3PLs, which rank among the 25 largest in 2000, could not be considered efficient during any part of the period investigated (1999-2002). It was also noted that the fall in the growth rate of US manufacturing in 2001 correlated with a decline in the operational performance of the 3PLs studied.

Hamdan and Rogers (2007) applied the DEA technique to 3PL warehousing operations. Nineteen warehouses belonging to a US 3PL were studied. The study reflects the importance of warehousing processes for the sector. For purposes of modeling, inputs were chosen that represented work, space, technology and equipment, and outputs that represented quantity produced, order fulfillment and use of space. The analyses were validated by the 3PL: four of the six warehouses classified as efficient ranked among the firm’s highest performers.

Zhou et al. (2008) subsequently applied the DEA technique to the 3PL sector in China. Their intention, beyond establishing a benchmark for the sector, was to identify factors that could affect the performance of the 3PLs. To do so, after having measured the operational performance of the group under study, DEA scores were regressed against four potential impacting factors. Among the main conclusions was the fact that company size does not necessarily impact 3PL efficiency in a positive way, as would be expected. It was also discovered that accumulated sales revenues enabled a better use of 3PL resources, and that investments in staff team training, as well as being good for personnel retention, positively influenced 3PL performance.

In general, the greatest challenge to studies that apply DEA to logistics firms is the identification of environmental factors or contextual variables that significantly affect efficiency (Zhou et al., 2008). In this study, our interest in scale efficiency is not merely to determine whether a particular 3PL is operating at – or close to – its optimum level, given the set of inputs used and the level of outputs generated: it is also to determine the objective conditions under which this can take place, analogous to the study by Ross and Droge (2004). In other words, scale efficiency can be used to determine how close each 3PL of the sample is to its corresponding most productive scale size and to what extent such distance is a consequence of coordination processes in the supply chain: management of information flows, inventory synchronization mechanisms, and scaling of resources (Wanke, 2003).

In large-scale distribution systems (the typical situation of a 3PL), different coordination processes frequently lead to different patterns of resource allocation among activities, potentially making adjustments of the scale to the operation more flexible (Ross & Droge, 2004). In this case, the results of scale efficiency may indicate opportunities for downsizing (decreasing returns to scale) or consolidation of operations (increasing returns to scale). For example, depending on alternative uses for information technologies (ITs) and mechanisms to synchronize and move the inventories by 3PLs, there may be situations in which the warehouse experiences decreasing (increasing) returns to scale due to its very large (small) size compared to inventory levels, movement of cargoes, and orders that have been allocated (Ross & Droge, 2004).

The basic idea is, therefore, to verify the role of these coordination processes when computing the scale efficiency of the 3PL, assessing whether, in fact, the 3PL engenders a more rational allocation of resources (inputs) to the demand (outputs) and, consequently, an operation close to the most productive scale size, with real time information availability as a cornerstone.

So, in this research, the Brazilian 3PL sector was analyzed for the period 2001–2009 using a two-stage DEA model. The model involved first calculating efficiency scores, followed by an analysis of unbalanced panel data using a Tobit regression model. The modeling is presented next.


Two-Stage DEA Modeling 

DEA is a non-parametric method, first introduced by Charnes, Cooper and Rhodes (1978). Although published over 30 years ago, the technique continues to receive widespread attention in academia (Cook & Seiford, 2009). Based on linear programming, DEA is used to compute the relative efficiency of a group of decision-making units (DMU), based on several measures for inputs and outputs. For a given set of DMUs, inputs and outputs, the DEA computes for each DMU an efficiency score obtained from the ratio of weighted outputs to weighted inputs. There are several technical variations, differing, for example, with respect to economies of scale and the way in which the distance between inefficient DMUs and the frontier is calculated (Zhu, 2003).

Assuming there are  production units, with  inputs and  outputs. Vector-columns  and  form the s-th column of matrices X and Y. In addition, let us assume  is a non-negative vector and  is a vector of unit values. Models DEA-CCR (Charnes, Cooper, & Rhodes, 1978) and DEA-BCC (Banker, Charnes, & Cooper, 1984) are shown in equations (1) and (2) and illustrated in Figure 1:





One advantage of DEA models is that the relative weights of variables need not be known a priori. Their efficient frontier envelops the limit of a convex polytope created from the space of inputs/outputs, where each vertex is an efficient DMU (Dulá & Helgason, 1996). Besides estimating efficiency scores, DEA also provides other information relevant to the inefficient DMUs. DEA identifies the efficient facet being used for comparison, the combination of the inputs that are being inefficiently used, and the deviation of specific outputs from the efficient level. It should be noted that efficient DMUs tend not to present any slack, such information being available only to inefficient DMUs (Green, Doyle, & Cook, 1996; Lin & Tseng, 2007).

The scale inefficiency is due to the increase or decrease of returns to scale, which can be computed by inspecting the sum of the weights under the CCR model specification. If the sum is equal to one, the law of constant returns to scale prevails; however, if the sum is less than one or more than one, increasing returns to scale and decreasing returns to scale prevail, respectively, assuming an input-oriented model. Also according to Cooper, Seiford and Tone (2007), in order to identify the degree to which the inefficiency of a DMU is due to inefficient operations or to its scale efficiency, scale efficiency is computed using the ratio , where  and  denote, respectively, the CCR and BCC efficiency scores for a given DMU . It is important to point out that the maximum value of SE is 1, indicating that the DMU is operating at the most productive scale size.

The approaches to the statistical treatment of the variations in the scores produced using DEA have evolved over the course of the years; see, for example Banker (1993) and Simar and Wilson (2007). As a depiction of this evolution, Cooper et al. (2007) point to the growing number of studies that combine the results of DEA, in a first stage, with those of multivariate data analysis, such as regression analysis and stochastic frontier analysis (SFA), in a second stage. According to Fried, Lovell, Schmidt and Yaisawarng (2002), such two-stage DEA approaches are the fruit of recognition on the part of researchers that environmental factors or contextual variables can significantly influence efficiency scores. For example, according to those authors, managerial competence (or incompetence) is insufficient to explain individual variations in efficiency, given that environmental factors, contextual variables, or even statistical noise could exercise some influence over measured performance. The adequate control for these impacts might suggest possible paths for a DMU to become more efficient (see, for example, Souza, Gomes, Magalhães, & Ávila, 2007).

In this article, the multivariate analysis in the second stage makes use of Tobit regression applied to an unbalanced panel of data relative to the Brazilian 3PL industry, for the period 2001–2009. According to Turner, Windle and Dressner (2004), because the dependent variable (scale efficiency) is continuous, but truncated at 1, the ordinary least squares approach is inappropriate, since it could produce inconsistent estimators. Along general lines, the base case model for Tobit regression is similar to that for ordinary least squares; however, the former assumes a truncated normal distribution in lieu of a normal distribution and employs maximum likelihood estimation (Greene, 2007). Banker (1993), nevertheless, also opens up the possibility of using other adequate distributions to the Tobit regression, such as the exponential distribution and the half-normal distribution.

In fact, DEA-based procedures using Tobit regression in the second stage perform as well as the best of the parametric methods in the estimation of the impact contextual variables have on productivity (Banker & Natarajan, 2008). Finally, it should be noted that the use of non-parametric tests, such as those presented in Banker and Natarajan (2004) and Gomes, Soares-de-Melo, Angulo-Meza and Mangabeira (2009), constitute an alternative used just as commonly as Tobit regressions in similar situations.

Differently from other non-parametric methods, Tobit regression can be easily applied to (un)balanced panel data (Greene, 2007). Generally speaking, panel data models allow the examination of fixed or random effects of a specific firm or of time periods on efficiency scores (Park, 2005). Fixed effects are tested by the (incremental) F test, while random effects are examined by the Lagrange Multiplier (LM) test (Breusch & Pagan, 1980). If data are severely unbalanced, a random effects model is preferable due to the lack of discerning of fixed effects on how group and time affect the intercept (Park, 2005).

For random effects models — according to Greene (2007), the model most frequently used —, the basic assumptions are: the random effect  is the same for all periods and should not be correlated with other regressors; the angular coefficients are the same for all groups and periods; and , the stochastic component of the model, does not correlate across periods.


Analysis of Data and Discussion of Results

Taking the preceding discussion as a starting point, this study intends to determine the main factors that affect scale efficiency in the Brazilian 3PL industry. The data used was collected from the special edition dedicated to the 3PL sector in Revista Tecnologística (2001–2009), published each year in June or July. In addition, it should be noted that the original datasets were cleaned up, rejecting the independent variables that were not collected for all of the individuals listed in the panel, in order to render the information sufficiently homogeneous for the analysis.

Conducting a secondary analysis of existing data saved the time and resources needed to collect primary data. However, the benefits of saving time and effort must be weighted against the limitations due to the level of data and the lack of specificity of the data for the secondary project (Shepard et al., 1999). All the data collected from Revista Tecnologística are objective measures based on explicit criteria, represented by metric (inputs and outputs) and nominal scales (most of the contextual variables, with the exception of age). As single-item indicators of objective measures, data can be valid and reliable indicators of the variables under consideration (Youngblut & Casper, 1993).

Although the data set provided by Revista Tecnologística might not have been collected in the context of a theoretical model, a theoretical model can still be identified and applied to the research process and data that are theoretically consistent can be identified (Moriarty et al., 1999; Zill & Daly, 1993). The importance of this step in secondary analysis cannot be underestimated (Shepard et al., 1999). As with any quantitative method of research, selection of the variables to be studied must first involve combing through the model to identify critical concepts. The theoretical concepts are then matched with appropriate variables form the data set.

In order to build the DEA models, four inputs and two outputs common to all 3PLs in the study were initially selected. Following the example of previous studies (Zhou et al., 2008), measurement units were chosen that would represent resources that are critical not only financially, but also for the execution of logistical services. With respect to inputs, the 3PL’s total number of staff involved in either strategic activities or operational activities is the measure used to represent labor force utilization.

Beyond that measure, selection of measures that translate how the 3PLs handle warehousing is also necessary, warehousing being the activity that grew the most over the time period (until 2008) in Brazil (Marino, 2008). According to the author, the availability of warehousing services is greater than transportation services in the 3PL sector. This being the case, the total area of owned warehouses was selected as an input for the model. It is also important to take into account those situations where the 3PL operates the warehouse, although the asset itself belongs to the client (Marino, 2008). In the latter case, that warehouse, which functions as one of the 3PL’s operational resources but not as one of its assets, is computed based on the total number of the client's warehouses, constituting the model’s last input.

On the outputs side, measures that would represent financial and operational aspects were initially selected. As such, since the 3PL’s gross revenues portray the product of service-provided sales, gross revenues were selected as an output. The firm’s total number of clients, in a similar way, reflects its operational complexity — a large client roster looks good, not only in the market, but also in terms of suggesting greater ability in the management of different logistics services needs.

Several methods have been proposed in the literature that suggest limiting the number of variables in relation to the number of DMUs (Wagner & Shimshak, 2007). Some studies have suggested that judgment should be performed by specialists in order to indicate which variables are the most relevant for the DEA model (Golany & Roll, 1989). Other studies have suggested regression analysis, in order to indicate highly correlated variables as redundant (Lewin, Morey, & Cook, 1982); or even application of DEA to smaller models, in order to rank the effect of variables on efficiency scores (Wagner & Shimshak, 2007).

So, in order to check on the possibility of reducing the number of inputs and outputs to be considered for the analysis, correlation analyses were performed. Table 1 shows the correlation coefficients between the pairs of inputs and the pair of outputs. Because the serial correlations are relatively low, we decided to keep all inputs and outputs in the analysis.

In the first stage, the DEA-CCR and BBC models were executed nine times using Frontier Analyst 4.0.10, i.e., once for each year for the period 2001–2009. More specifically, the unbalanced panel data pertaining to the Brazilian 3PL industry comprises 122 individuals; totaling 213 observations distributed over the course of these nine years (see Appendix).

Table 2 shows descriptive statistics of the scores computed for the CCR and BCC models and for scale efficiency for the 2001–2009 years. As expected, the CCR models returned efficiency scores that were lower than those computed for the BCC models. In other words, the CCR models identified fewer efficient 3PLs than the BCC models for each year. This result is unsurprising, given that the CCR model assumes a production technology with constant (linear) returns of scale (cf. Figure 1). The BCC model, on the other hand, assumes variable returns to scale, which more closely parallels reality since they reflect the technical efficiency of different DMUs. In addition, it can be seen that very few 3PLs operate at the most productive scale size (when SE is equal to 1).

In the second stage, in order to identify the determinants of scale efficiency of 3PLs operating nationally, traditional characteristics and services commonly offered by 3PLs in Brazil were researched. Once again, datasets from Revista Tecnologística were used. Such characteristics/services serve as study control variables, since they comprise neither process inputs nor products, but, rather, their attributes, in a total of twenty-five contextual variables. Table 3 shows the list of binary control variables (i.e., that use a dummy scale) considered in the study. These variables are terminal, i.e., they assume the value of a unit if the observation has the mentioned characteristic and zero otherwise. It is understood that k-1 dummy variables are required to represent a variable with k categories (Levine, Stephan, Krehbiel, & Berenson, 2007). The base-category is the absence itself of this characteristic. Besides these variables, the only exception should be mentioned: age of the 3PL, measured in months (metric scale).

Given the large number of potential contextual variables to be considered, data reduction techniques assume particular relevance here. Several authors have used some of these techniques together with DEA. Adler and Golany (2001) and Adler and Berechman (2001), for instance, employed principal component analysis. The use of factor analysis was proposed by Vargas and Bricker (2000) and implemented in Jenkins and Anderson (2003) and Nadimi and Jolai (2008). Specifically, factor analysis is an appropriate procedure for data reduction based on observed variables and on existing theoretical constructs (Hair, Anderson, Tatham, & Black, 2005).

In order to make the concept of coordination processes and information technologies operational, a factor analysis with Varimax standardized rotation was conducted – with the use of SPSS 15.0 package - in order to reduce these 25 categorical variables into a smaller number of dimensions. Specifically, factor analysis is an appropriate procedure for data reduction based on observed variables and on existing theoretical constructs (Hair et al., 2005). Table 4 presents the six factors related to coordination processes and information technologies – the theoretical constructs of this research - , obtained from the variables presented in Table 3.

LIMDEP 9.0 econometric software was used to carry out the Tobit regression on the unbalanced panel data, using the random effects model. The results were adjusted as a function of the heteroscedasticity generated due to the fact the groups are of differing sizes (Greene, 2007). With respect to the acceptable level of significance, the range 0.05–0.10 was established, as has been customary in exploratory research studies on logistics (Mentzer & Flint, 1997; Wanke & Hijjar, 2009). Table 5 shows the Tobit regression results for each one of these six factors.

The results presented in Table 5 confirm the impact of coordination processes on the supply chain and, in particular, the impact of ITs on increased scale efficiency for Brazilian 3PLs. The adoption of express logistics related ITs and services (FACTOR 4) merit attention: radio and satellite tracking (outsourced), ERP, just in time, milk run, and intermodal management.

Embedded within these results, it should be noted that inventory-related coordination processes, such as just in time and milk run, presented significant positive impacts on efficiency. A possible justification for this effect is the fact that inventory-related coordination processes allow for a greater integration of client product flow with the 3PL transportation and warehousing resources needed for their movement.

It should also be noted that the age (FACTOR 6) of the 3PL also has a positive effect on scale efficiency. In addition to the experience accumulated from operating for a longer time in the market, we should also take into account the fact that the relationship between the contracting company and the 3PL tends to become more focused, thereby allowing for a better tailoring of resources to client exigencies (Bhatnagar, Sohal, & Millen, 1999).

3PL managers may use these results as guidance for future steps towards higher levels of scale efficiency. What ITs should be developed (acquired) first? and what kinds of logistics services should be offered to shippers? constitute example of questions that may direct 3PLs through a shorter path to the most productive scale size, helping them in establishing a business plan or a course of action over time.

The findings of this study may also serve as a valuable tool for shippers to benchmark their logistics services providers against each other. Even though no link among scale efficiency, costs, and service levels is claimed in the evidence presented and discussed in this paper, it serves as indication of the directions shippers should take when hiring 3PL services. The basic underlying idea is that 3PLs with higher levels of scale efficiency may simultaneously achieve lower costs and higher service levels, thus benefiting shippers in terms of competitive advantages.



This research differs from previous studies by analyzing the Brazilian 3PL sector between 2001 and 2009 using a two-stage DEA model. In the first stage, DEA is used to calculate efficiency scores for each 3PL firm and, in the second stage, these scores are used as the dependent variable in the corresponding Tobit regression model for unbalanced panel data. Contextual variables such as ITs adopted and services provided by the 3PLs constituted the regressors or the independent variables.

Previous attempts to apply DEA to 3PL industry indicate that the identification of contextual variables (environmental factors) that significantly affect efficiency is, in general, the most relevant methodological issue to studies that apply DEA to logistics firms. Particularly, only Zhou et al. (2008) managed to regress DEA scores against contextual variables. However, other DEA methodological issues - related to the sample size adequacy required in order to avoid concentration of scores in one, the proper use of Tobit regression in order to handle with truncated scores in zero and one, and the use of panel data models so as to adequately regress different efficiency scores against contextual variables - were not observed in the scant previous studies.

The results presented here provide support for the evidence in the literature that coordination mechanisms in the supply chain, including exploitation of IT and inventory synchronization mechanisms, favor a more rational allocation of 3PL resources (inputs) to client demands (outputs) and, as a corollary, favor an operation that, supported by the availability of real time information, is close to the most productive scale size.

The results also lend a contribution of a practical nature to the 3PL sector in Brazil. More precisely, the study enables managers and investors to use the results presented in Table 6 as a resource for decision-making. A range of drivers were statistically validated, revealing areas where there is space not only for more investment, but also for the development of future studies to enable a better understanding of the relationship between these drivers and sector scale efficiency.

Brazilian 3PLs are more and more geared towards an increased availability of services, with steadily falling costs, in an effort to buttress an ever-more competitive marketplace. As such, it is hoped that 3PLs often turn to ways to evaluate their performance as they expand, both quantitatively as well as qualitatively. The structure used in this article can be applied as a tool in both senses. DEA models the situation of the 3PL at the moment of application, aiding to direct resources to critical areas that significantly affect performance. The model constructed above can easily be modified to develop in parallel with a firm's structural parameters and to present up to date results.

Finally, the fact of working with secondary data instead of primary data brings certain limitations to this work, mainly with respect to the set of inputs, outputs, and contextual variables used in the analysis, which may not cover all aspects relevant to build and assess an efficiency frontier.



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Received 8 April 2010; received in revised form 17 December 2010.

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