Research Article

Goal programming associated with the non-archimedean infinitesimal: a case study applied in the agricultural sector

Fabiana Gomes dos Passos; Ademar Nogueira Nascimento; Cristiano Hora de Oliveira Fontes

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Paper aims: This work presents a multi-objective method based on goal programming associated with non-Archimedean infinitesimal (NAI) (Improved Weighted Goal Programming method, input-oriented IWGP-MCDEA-BCC).

Originality: The MCDEA is applied for the first time in a large agricultural company (over 11 hectares). A new method is proposed which consists of an improvement on input-oriented WGP-MCDEA-BCC approaches.

Research method: The performance of the proposed method was compared to the classic Data Envelopment Analysis and the Weighted sum Goal Programming methods. The case study comprises an agricultural company located in the São Francisco Valley (Brazil).

Main findings: The proposed method can help decision makers to improve efficiency in the production of different types of fruits.

Implications for theory and practice: The proposed model is capable of overcoming the deficiencies associated with classical DEA and allows the company to identify effective ways to increase productivity by reducing input costs.


Data envelopment analysis, Multiple criteria data envelopment analysis, Variable return to scale, São Francisco Valley


Adler, N., & Golany, B. (2001). Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an application to Western Europe. European Journal of Operational Research, 132(2), 260-273.

Adler, N., & Yazhemsky, E. (2010). Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction. European Journal of Operational Research, 202(1), 273-284.

Aldamak, A., & Zolfaghari, S. (2017). Review of efficiency ranking methods in data envelopment analysis. Measurement, 106, 161-172.

Almeida, A. T., Ferreira, R. J. P., & Cavalcante, C. A. (2015). A review of the use of multicriteria and multi-objective models in maintenance and reliability. IMA Journal of Management Mathematics, 26(3), 249-271.

Amin, G. R., & Toloo, M. (2007). Finding the most efficient DMUs in DEA: an improved integrated model. Computers & Industrial Engineering, 52(1), 71-77.

Andrade, R. M. D., Lee, S., Lee, P. T. W., Kwon, O. K., & Chung, H. M. (2019). Port efficiency incorporating service measurement variables by the BiO-MCDEA: Brazilian case. Sustainability, 11(16), 4340.

Ângulo-Meza, L., González-Araya, M. G., Iriarte, A., Rebolledo-Leiva, R., & Mello, J. C. S. (2019). A multiobjective DEA model to assess the eco-efficiency of agricultural practices within the CF+DEA method. Computers and Electronics in Agriculture, 161, 151-161.

Aydin, B., & Unakitan, G. (2018). Efficiency analysis in agricultural enterprises in Turkey: case of Thrace Region. Custos e @gronegócio online, 4, 137-160. Retrieved in 28 August 2019, from

Bal, H., & Örkcü, H. H. (2007). A goal programming approach to weight dispersion in data envelopment analysis. Gazi University Journal of Science, 20, 117-125.

Bal, H., Örkcü, H. H., & Celebioglu, S. (2010). Improving the discrimination power and weights dispersion in the data envelopment analysis. Computers & Operations Research, 37(1), 99-107.

Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating tech- nical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092.

Banker, R. D., Charnes, A., Cooper, W. W., Swarts, J., & Thomas, D. A. (1989). An introduction to data envelopment analysis with some of its models and their uses. Research in Governmental and Non-Profit Accounting, 5, 125-163.

Borgheipour, H., Moghaddas, Z., Abbasi, M., & Abbaszadeh Tehrani, N. (2018). Application of DEA technique in SWOT analysis of oily sludge management using fuzzy data. Global Journal of Environmental Science and Management, 4, 183-194.

Caballero, R., Gómez, T., González, M., Muñoz, M. M., Rey, L., & Ruiz, F. (1997). Mathematical programming for economists. Málaga: Servicio de Publicaciones y Divulgación Científica de la Universidad de Málaga.

Cakmakci, M. (2009). Process improvement: performance analysis of the setup time reduction-SMED in the automobile industry. International Journal of Advanced Manufacturing Technology, 41(1-2), 168-179.

Cao, J., Chen, G., Khoveyni, M., Eslami, R., & Yang, G. (2016). Specification of a performance indicator using the evidential-reasoning approach. Knowledge-Based Systems, 92, 138-150.

Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision-making units. European Journal of Operational Research, 2(6), 429-444.

Clímaco, J. C. N., Mello, J. C. C. B. S., & Ângulo-Meza, L. (2008). Performance measurement: from DEA to MOLP. In F. Adam (Eds.), Encyclopedia of decision making and decision support technologies. Hershey: Information Science Reference.

Daraio, C., & Simar, L. (2007). Advanced robust and nonparametric methods in efficiency analysis: methodology and applications. New York: Springer.

Emrouznejad, A., & Yang, G. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978 e 2016. Socio-Economic Planning Sciences, 61, 1-5.

Entani, T., Maeda, Y., & Tanaka, H. (2002). Dual models of interval DEA and its extensions to interval data. European Journal of Operational Research, 136(1), 32-45.

Fanchon, P. (2003). Variable selection for dynamic measures of efficiency in the computer industry. International Advances in Economic Research, 9(3), 175-188.

Ghasemi, M. R., Ignatius, J., & Emrouznejad, A. (2014). A bi-objective weighted model for improving the discrimination power in MCDEA. European Journal of Operational Research, 233(3), 640-650.

Ghasemi, M. R., Ignatius, J., & Rezaee, B. (2019). Improving discriminating power in data envelopment models based on deviation variables framework. European Journal of Operational Research, 278(2), 442-447.

Gontijo, T. S., Rodrigues, A. C., & Muylder, C. F. (2018). Incorporating managed preferences in the evaluation of public organizations efficiency: a DEA approach. Independent Journal of Management & Production, 9(4), 1108-1126.

Hatami-Marbini, A., & Toloo, M. (2017). An extended multiple criteria data envelopment analysis model. Expert Systems with Applications, 73, 201-219.

Instituto Brasileiro de Geografia e Estatística – IBGE. (2019). Levantamento sistemático da produção 2019. Rio de Janeiro. Retrieved in 28 August 2019, from

Iqbal, N., & Sial, M. (2018). Semi-parametric analysis of agricultural production under dichotomy of inputs. Agricultural Economics, 64, 378-388.

Jenkins, L., & Anderson, M. (2003). A multivariate statistical approach to reducing the number of variables in data envelopment analysis. European Journal of Operational Research, 147(1), 51-61.

Koopmans, L. H., Owen, D. B., & Rosenblatt, J. I. (1964). Confidence intervals for the coefficient of variation for the normal and log normal distributions. Biometrika, 51(1-2), 25-32.

Krcmar, E., & Van Kooter, G. C. (2008). Economic development prospects of forest-dependent communities: Analyzing trade-offs using a compromise-fuzzy programming framework. American Journal of Agricultural Economics, 4(4), 1103-1117.

Li, H., Xiong, J., Xie, J., Zhou, Z., & Zhang, J. (2019). A unified approach to efficiency decomposition for a two-stage network DEA model with application of performance evaluation in banks and sustainable product design. Sustainability, 11(16), 4401.

Li, X. B., & Reeves, G. R. (1999). A multiple criteria approach to data envelopment analysis. European Journal of Operational Research, 115(3), 507-517.

Marttunen, M., Lienert, J., & Belton, V. (2017). Structuring problems for Multi-Criteria Decision Analysis in practice: A literature review of method combinations. European Journal of Operational Research, 263(1), 1-17.

Mello, J. C. C. B. S., Gomes, E. G., Meza, L. A., & Leta, F. R. (2008). DEA advanced models for geometric evaluation of used lathes. WSEAS Transactions on Systems, 7(5), 500-520.

Mota, T. R. A., & Meza, L. A. (2020). The use of DEA as a tool to evaluate public expenditure on education: an analysis of the cities of the state of Rio de Janeiro. Annals of the Brazilian Academy of Sciences, 92(2), e20190187. PMid:32667507.

Nara, E. O. B., Sordi, D. C., Schaefer, J. L., Schreiber, J. N. C., Baierle, I. C., Sellitto, M. A., & Furtado, J. C. (2019). Prioritization of OHS key performance indicators that affecting business competitiveness: a demonstration based on MAUT and Neural Networks. Safety Science, 118, 826-834.

Passos, F. G., Fontes, C. H. O., & Do Nascimento, A. N. (2020). Efficiency evaluation of a mango exporter in the São Francisco Valley, Brazil: a model on data envelopment analysis. Custos e @gronegócio online, 16, 105-141. Retrieved in 28 August 2019, from

Pastor, J. T., Ruiz, J. L., & Sirvent, I. (2002). A statistical test for nested radial DEA models. Operations Research, 50(4), 728-735.

Pereira, E. R., & & Mello, J. C. C. B. S. (2015). Smoothed frontier to determine a single set of weights in CCR models. Production, 25(3), 585-597.

Podinovski, V. V., & Bouzdine-Chameeva, T. (2013). Weight restrictions and free production in data envelopment analysis. Operations Research, 61(2), 426-437.

Raheli, H., Rezaei, R. M., Jadidi, M. R., & Mobtaker, H. G. (2017). A two-stage DEA model to evaluate sustainability and energy efficiency of tomato production. Information Processing in Agriculture, 4(4), 342-350.

Rubem, A. P. S. (2016). Resolution of the Li and Reeves model using goal programming (PhD thesis). Graduate Program in Production Engineering, Universidade Federal Fluminense, Rio de Janeiro.

Rubem, A. P. S., Mello, J. C. C. B. S., & Ângulo-Meza, L. (2017). A goal programming approach to solve the multiple criteria DEA model. European Journal of Operational Research, 260(1), 134-139.

Ruggiero, J. (2005). Impact assessment of input omission on DEA. International Journal of Information Technology & Decision Making, 4(3), 359-368.

Shen, W., Zhang, D., Liu, W., & Yang, G. (2016). Increasing discrimination of DEA evaluation by utilizing distances to anti-efficient frontiers. Computers & Operations Research, 75, 163-173.

Silva, A. F., Marins, F. A. S., & Dias, E. X. (2019). Improving the discrimination power with a new multi-criteria data envelopment model. Annals of Operations Research, 37, 1-33.

Silva, A. F., Marins, F. A. S., Tamura, P. M., & Dias, E. X. (2017a). Bi-Objective multiple criteria data envelopment analysis combined with the overall equipment effectiveness: an application in an automotive company. Journal of Cleaner Production, 157, 278-288.

Silva, J. S., Ferreira, M. O., & Lima, J. R. F. (2017b). Eficiência técnica dos produtores de manga do Vale do São Francisco. Revista de Economia e Agronegócio, 15(1), 28-49.

Silva, J. L. M., & Sampaio, Y. S. B. (2002). A eficiência técnica dos colonos nos perímetros irrigados em Petrolina, Juazeiro: uma análise de modelos de fronteiras de produção. Revista Economica do Nordeste, 33(2), 159-179.

Simar, L., & Wilson, P. W. (2001). Testing restrictions in nonparametric efficiency models. Communications in Statistics. Simulation and Computation, 30(1), 159-184.

Tan, X., Na, S., Guo, L., Chen, J., & Ruan, Z. (2019). External financing efficiency of rural revitalization listed companies in China: based on two-stage DEA and grey relational analysis. Sustainability, 11(16), 4413.

Ueda, T., & Hoshiai, Y. (1997). Application of principal component analysis for parsimonious summarization of DEA inputs and/or outputs. Journal of the Operations Research Society of Japan, 40(4), 466-478.

Wagner, J. M., & Shimshak, D. G. (2007). Stepwise selection of variables in data envelopment analysis: procedures and managerial perspectives. European Journal of Operational Research, 180(1), 57-67.

Yamada, Y., Matui, T., & Sugiyam, M. (1994). New analysis of efficiency based on DEA. Journal of the Operations Research Society of Japan, 37(2), 158-167.

Zare, K., Mehri-Tekmeh, J., & Karimi, S. (2015). A SWOT framework for analyzing the electricity supply chain using na integrated AHP methodology combined with fuzzy-Topsis. International Strategic Management Review, 3(1-2), 66-80.

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