Logistics efficiency in small and medium enterprises: A logistics, data envelopment analysis combined with artificial neural network (DEA-ANN) approach

This article introduces a novel method for measuring logistics efficiency in small and medium enterprises (SME’s) for use with logistics, data envelopment analysis artificial neural network (DEAANN). This method has never been used in logistics before. The research was conducted in Querétaro, Mexico. The sample included 92 SME’s, using a questionnaire of 38 questions, 37 of these questions was related to logistics practices and one was about the monthly logistic costs. The database was used to perform a DEA, taking into account the 37 questions of logistics practices as inputs and the logistics cost as outputs; a model of undesirable outputs was used because it is a cost where increases are always undesirable for any enterprise. With the information from DEA, an ANN was created that features a prediction of the index of logistics efficiency; the results with the neural network were very satisfactory, 0.84 R 2 . While modeling was rather accurate, this highlights the inefficiency detected in a large proportion of SME’s, further representing problems for these types of firms. Logistic inefficiency may be the reason why many SME’s go bankrupt.


INTRODUCTION
Efficiency is the achievement of an objective, utilizing a minimum amount of resources (Koontz and Weihrich, 2004).Keeping the aforementioned definition in mind, it is possible to consider logistic efficiency as a situation where the customer gets the right product, at the right place and at the right time, at the lowest cost (Ballou, 2004).It is important for all companies to become logistic *Corresponding author.E-mail: montse.garcia@uaq.mx.Tel: +52 442 192 1200/ 6023.efficient.In the case of the small and medium enterprises (SME's), this may be the difference between surviving or failing.
SME's constitute a key component of any nation's economy.In Mexico, they represent 99% of the total productive units while contributing to 52% of gross domestic product (GDP) and 72% of total employment (OECD, 2007).This clearly indicates the importance of studying all areas of this firm size.Of course, logistics efficiency is an important issue to consider in this regard.
Efficiency, however, may not be as easy to asses as it might appear.Efficiency in other contexts have been measured using several techniques, one of the most common is the data envelopment analysis (DEA) combined with artificial neural network (ANN).The logistics, data envelopment analysisartificial neural network (DEA-ANN) approach has been used in many research areas, for example, to study bank efficiency in different parts of the world (Mostafa, 2009;Aslania et al., 2009;Belmote Ureña and Plaza Úbeda, 2008;Desheng et al., 2006).In these articles, the authors demonstrate analyses that were conducted between 1977 and 2009.Other applications that used DEA-ANN proved it to be adequate to measure the efficiency in research groups (Özdemir, 2009); in supplier evaluation systems (Pino-Mejías et al., 2010;Azadeh et al., 2011), utilized it to evaluate personnel efficiency; and for performance modeling of business schools (Sreekumar and Mahapatra, 2011).However, there is no evidence that it has been used as a technique to measure logistics efficiency; consequently, this study uses a combination of these techniques to measure the efficiency of logistics in small and medium enterprises in the state of Queretaro, México.
The objective of this paper is to measure the efficiency of SME's in Queretaro, Mexico, and to train a neural network with the information generated from the DEA.This research surveyed 92 small and medium enterprises (SME's) in the state of Querétaro, Mexico, using 37 questions about logistics practices, which were considered independent variables, and one about monthly logistic cost, also known as the dependent variable.The data was used for DEA.When ANN was performed, both the 37 inputs and the output served as independent variables and the final evaluation or benchmarking, that in this case was the logistics efficiency as the dependent variable.
The most evident result of DEA clearly demonstrated that very few enterprises function near the benchmark (100% efficient) and a large proportion of firms are well below the benchmark.This is consistent with the already known fact that it is rather difficult for SME's to become efficient, primarily because most of the variables are not within management's control.
In the case of ANN, an artificial neural network of the generalized regression model form, from which satisfactory results were obtained, was used.This means that the model works perfectly: by answering the questionnaire and getting the logistics costs, it is possible for any firm to determine its logistics efficiency index also referred to as its benchmarking, using this already trained neural network.

Data envelopment analysis
Since it was introduced by Charnes et al. (1978), conventional DEA models have assumed that the outputs should increase as inputs decrease in order to improve performance or to reach the frontier of best practices.If undesirable's outputs are treated as inputs, in a way that undesirable's outputs are reduced, the DEA model results do not reflect the desired process to model.Seiford and Zhu (2002) developed an approach for undesirable envelope models: VRS (variable return to scale).predictions of categories and classifications.Both types of networks were introduced by Specht (1990Specht ( , 1991)).

If
A generalized regression neural network for two independent numeric variables is structured as shown in Figure 1, utilizing only three cases.In order to minimize the error of the trained network, GRN uses optimizing smoothing factors, through the use of a method of conjugate optimization descendent gra-dient.The error measurement used during training to evaluate different sets of smoothing factors is the mean square error.However, when calculating the mean square error of a trained case, that case is temporarily excluded from the pattern layer.This is because the neuron distance calculated would be zero, causing other neurons which would be insignificant for the prediction.

METHODOLOGY
The main objective of this paper is to measure the logistic efficiency regarding SME's in Queretaro, Mexico using DEA, and then to train a neural network utilizing the information generated by the DEA.
First, a survey to collect data on logistics practices of SME's (Campos-Garcia et al., 2011) was designed and applied.The survey selected for this study had 38 questions, 4 related to purchasing activities, 7 to sales, 7 to production, 9 to storage, 10 to transport, and 1 to logistic costs.The first 37 questions were measured by using a scale of 1 to 5, where 1 was the simplest way to perform the logistic practice in question and 5 the most sophisti-cated.The question of cost was answered with a percentage of monthly cost designated to logistics.
From a population of 571 SME's in Queretaro, a sample of 99 was taken, with a 90% confidence level and a 2% margin of error.92 of which were designated here as Decision Making Units (DMU).They were used in this study because they met the requirements for the DEA.With the data obtained from the survey, a DEA of undesirable outputs was performed.The first 37 questions of the survey, were used here as inputs, asking questions regarding logistics practices and the output used was logistic cost, an undesirable output.Frontier Analyst 4 software was used to run the DEA.
Finally, a generalized regression neural network was trained, using survey data and the results from DEA.Later the ANN was trained.Any firm can enter its 38 values to obtain the actual efficiency index as compared to the benchmark.The PC-based software NeuralTools v5.5 of Palisade Corporation was used for this purpose.
The process that was conducted in this research can be applied in other areas; consequently, it is shown here that it can be used to perform a study using DEA-ANN for any area and is illustrated in Figure 2.This figure also shows, as an example, the information used for this research.

RESULTS
As was expected from the type of analysis conducted, only one firm ranked at the top; the DEA gives it the value of 100% efficient as it showed the best actual combination among higher values for logistic practices and lower logistic costs (Table 1).Only one other firm received a high score which was near 90%.Another seven firms scored above 40%, but below 70%.The final 83 units scored around 20%.The score distribution from DEA in Figure 3 shows empirically, the fact that small and medium sized enterprises are frail in their logistic decisions and only a few are aware of the importance of these activities known to be essential in order to survive in today's globally competitive market.
Next, an artificial neural network of a generalized regression model was used, and very satisfactory results were obtained, R 2 of 0.84.In this part of the research, the 37 inputs as well as the output or logistic cost served as independent variables and the final evaluation or benchmarking as the dependent variable.Because it was possible for the ANN to build a model such that it can predict the observed values from a database of 92 cases with 39 values, which also included the new logistic efficiency index as the output, it means that the results from DEA are not only solid but, by the high-quality results from ANN, confirmed that the DEA results are robust.
Consequently, because the model works nearly perfectly, any new firm or one currently existing, but not considered herein, can now determine the level of logistical efficiency also known as benchmarking by using the trained neural network and entering its logistic practice values and the logistic costs (Table 2 and Figure  4).

DISCUSSION AND CONCLUSION
This study features a tool that permits an evaluation of logistics efficiency for SME's.Enterprises can answer the survey, obtaining their index of efficiency.This in turn permits owners or management to make decisions based on concrete results.It is recommendable that, if an enterprise obtains a low index of logistic efficiency, it seeks to use logistics practices possessing lower qualifications and try to improve these practices with the objective of improving the final logistics efficiency index.
The most important contribution of this investigation was the use of a combination of methods (DEA-ANN) to measure the logistics efficiency of SME's.There is currently no evidence that these methods have previously been used together in logistics.It is also noteworthy that they functioned very well when ascertaining an index of the logistics of SME's.The authors think that this   38 (input1, input2, input3, input4, input5, input6, input7, input8, input9, input10, input11, input12, input13, input14, input15, input16, input17, input18, input19, input20, input21, input22, input23, input24, input25, input26, input27, input28, input29, input30, input31, input32, input33, input34, input35, input36,  15.12 2.666 methodology can be used in almost all areas, provided a survey or information containing inputs or independent variables and at least one output or dependent variable exists.As in any other study, this one does have certain limitations that require further investigation.For example, it is not always possible for SME's to become efficient.This is because sometimes certain inputs cannot be within the control of the company.In such cases the logistics practices and these inputs may decrease the final logistics index.It is also noteworthy to mention that this investigation could be expanded by taking different samples and stratifying these by sector, capital origin, or other aspects, with the objective of comparing the enterprises with other similar ones.The universe of the study might also be expanded, taking into account the SME's of all the states within a given country.This would permit global conclusions regarding the logistic efficiency of SME's of a particular country.Universidad Autonoma de Queretaro for providing the resources for this research.They also would like to thank Silvia C. Stroet of the Engineering Faculty at Universidad Autonoma de Queretaro for checking the English content of this document.

Figure 4 .
Figure 4. Prediction and real information of ANN training.

Table 2 .
Resume of neural network training.