Planejamento agregado na indústria de nutrição animal sob incertezas
Production planning in the animal nutrition industry under uncertainty
Augusto, Diego Barreiros; Alem, Douglas; Toso, Eli Angela Vitor
http://dx.doi.org/10.1590/0103-6513.151913
Production, vol.26, n1, p.12-27, 2015
Resumo
Um dos desafios para o planejamento da produção na indústria de nutrição animal consiste em determinar quanto produzir de cada produto em cada período, considerando que existem incertezas associadas às operações de setup, que os produtos são perecíveis e que a capacidade produtiva deve ser ajustada num ambiente de demanda estocástica caracterizada pela sazonalidade dos produtos e das matérias-primas. Este trabalho investiga um problema de planejamento agregado da produção em uma planta que produz suplementos para nutrição animal. Para lidar com esse problema, propôs-se uma extensão do problema clássico de dimensionamento de lotes com restrição de capacidade para incorporar decisões sobre vendas perdidas (lost sales) e as incertezas inerentes ao planejamento da produção: demandas, tempos de preparação e taxa de perecibilidade dos produtos. Para gerar soluções menos sensíveis às variações dos cenários, desenvolveu-se um modelo estocástico com aversão ao risco baseado numa medida de risco do tipo semidesvio absoluto. Analisando-se o valor esperado da informação perfeita e o valor da solução estocástica, confirmou-se o desempenho superior do modelo de programação estocástica no tratamento das incertezas. Além disso, os resultados indicaram que é possível reduzir significativamente a variabilidade dos custos de segundo estágio sem sacrificar demasiadamente o custo total esperado.
Palavras-chave
Problema de dimensionamento de lotes capacitado com lost sales e perecibilidade. Programação estocástica de dois estágios. Gestão de risco. Indústria de nutrição animal.
Abstract
One of the greatest challenges of production planning in the animal nutrition industry is determining the amount of each product that should be produced during each period, given the perishability of the products, the manual execution of the setups and the need to adjust the production capacity in a stochastic demand environment that is characterized by the seasonality of the products and raw materials. This paper investigates an aggregate production planning problem in a plant that produces supplements for horses, cattle, pigs and poultry. To address this problem, we proposed an extension of the classical capacitated lot-sizing problem to incorporate decisions about lost sales and inherent uncertainties in production planning, such as demands, setup times and perishability. To generate solutions that are less sensitive to changes in scenarios, we also developed a risk-averse stochastic model with an absolute semi-deviation-based risk measure. An analysis of the expected value of perfect information and the value of the stochastic solution confirmed that the stochastic approach outperformed the deterministic approximations in handling uncertainty. Furthermore, the results indicated that it is possible to significantly reduce the variability of the second-stage costs without sacrificing the expected total cost.
Keywords
Capacitated Lot-sizing Problem with Lost Sales and Perishability. Two-stage Stochastic Programming. Risk Management. Animal Nutrition Industry.
References
Ahmed, S., & Sahinidis, N. V. (1998). Robust process planning under uncertainty. Industrial & Engineering Chemistry Research, 37(5), 1883-1892. http://dx.doi.org/10.1021/ie970694t
Ahumada, O., & Villalobos, J. R. (2008). Application of planning models in the agri-food supply chain: A review. European Journal of Operational Research, 196(1), 1-20. http://dx.doi.org/10.1016/j.ejor.2008.02.014
Alfares, H. K., Khursheed, S. N., & Noman, S. M. (2005). Integrating quality and maintenance decisions in a production-inventory model for deteriorating items. International Journal of Production Research, 43(5), 899-911. http://dx.doi.org/10.1080/0020754042000298511
Amorim, P., Meyr, H., Almeder, C., & Almada-Lobo, B. (2013). Managing perishability in production-distribution planning: a discussion and review. Flexible Services and Manufacturing Journal, 25(3), 389-413. http://dx.doi.org/10.1007/s10696-011-9122-3
Alem, D., & Morabiro, R. (2013). Risk-averse two- stage stochastic programs in furniture plants. OR Spectrum, 35(4), 773-806 http://dx.doi.org/10.1007/s00291-012-0312-5
Bellman, R. (1957). Dynamic programming. Princeton: Princeton University Press. Bellman, R. E., & Zadeh, L. A. (1970). Decision making in fuzzy environment. Management Science, 17(4), 141-154. http://dx.doi.org/10.1287/mnsc.17.4.B141
Birge, J. R., & Louveax, F. (1997). Introduction to stochastic programming. New York: Springer.
Brahimi, N., Dauzere-Peres, S., Najid, N. M., & Nordli, A. (2006). Single item lot sizing problems. European Journal of Operational Research, 168(1), 1-16. http://dx.doi.org/10.1016/j.ejor.2004.01.054
Charnes, A., & Cooper, W. (1959). Chance constrained programming. Management Science, 6(1), 73-79. http://dx.doi.org/10.1287/mnsc.6.1.73
Clark, A. R., Morabito, R., & Toso, E. A. V. (2010). Production setup-sequencing and lot-sizing at an animal nutrition plant through ATSP subtour elimination and patching. Journal of Scheduling, 13(2), 111-121. http://dx.doi.org/10.1007/s10951-009-0135-7
Costa, A. M., Santos, L. M. R., Alem, D. J., & Santos, R. H. S. (2014). Sustainable vegetable crop supply problem with perishable stocks. Annals of Operations Research, 219(1), 265-283.
Dantzig, G. (1955). Linear programming under uncertainty. Management Science, 1(3-4), 197-206. http://dx.doi.org/10.1287/mnsc.1.3-4.197
Di Domenica, N., Lucas, C., Mitra, G., & Valente, P. (2009). Scenario generation for stochastic programming and simulation: a modelling perspective. IMA Journal of Management Mathematics, 20(1), 1-38. http://dx.doi.org/10.1093/imaman/dpm027
Drexl, A., & Kimms, A. (1997). Lot sizing and scheduling: survey and extensions. European Journal of Operational Research, 99(2), 221-235. http://dx.doi.org/10.1016/S0377-2217(97)00030-1
Escudero, L. F., Garin, A., Merino, M., & Perez, G. (2007). The value of the stochastic solution in multistage problems. TOP, 15(1), 48-64. http://dx.doi.org/10.1007/s11750-007-0005-4
Jans, R., & Degraeve, Z. (2008). Modeling industrial lot sizing problems: a review. International Journal of Production Research, 46(6), 1619-1643. http://dx.doi.org/10.1080/00207540600902262
Kall, P., & Wallace, S. (1994). Stochastic programming. New York: Wiley.
Karimi, B., Ghomi, S. F., & Wilson, J. (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega, 31(14), 365-378. http://dx.doi.org/10.1016/S0305-0483(03)00059-8
Miranda, J. L. (2007). Optimização em sistemas de processos químicos: generalização de modelos com planeamento e sequenciamento (Tese de doutorado). Lisboa: Universidade Técnica de Lisboa.
Mula, J., Poler, R., Garcia-Sabater, J. P., & Lario, F. C. (2006). Models for production planning under uncertainty: A review. International Journal of Production Economics, 103(1), 271-285. http://dx.doi.org/10.1016/j.ijpe.2005.09.001
Mulvey, J., Vanderbei, R., & Zenios, S. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264-281. http://dx.doi.org/10.1287/opre.43.2.264
Pahl, J., Voβ, S., & Woodruff, D. (2011). Discrete lot-sizing and scheduling with sequence-dependent setup times and costs including deterioration and perishability constraints. In 44th Hawaii International Conference on
System Sciences, Kauai, Hawaii. Pochet, Y., & Wolsey, L. (2006). Production planning by mixed integer programing. New York: Springer.
Sahinidis, N. V. (2004). Optimization under uncertainty: state-of-the-art and opportunities. Computers and Chemical Engineering, 28(6-7), 971-983. http://dx.doi.org/10.1016/j.compchemeng.2003.09.017
Sen, S., & Higle, J. L. (1999). An introductory tutorial on stochastic linear programming models. Interfaces, 29(2), 33-61. http://dx.doi.org/10.1287/inte.29.2.33
Shapiro, A., Dentcheva, D., & Ruszczynski, A. (2009). Lectures on stochastic programming: modeling and theory. Philadelphia: SIAM. http://dx.doi.org/10.1137/1.9780898718751
Sindicato Nacional da Indústria de Alimentação Animal. (2013). Boletim Informativo do Setor. São Paulo: Sindirações. Recuperado em 22 de junho de 2013, de http://sindiracoes.org.br
Toso, E. A. V., Morabito, R., & Clark, A. R. (2008). Combinação de abordagens GLSP e ATSP para o problema de dimensionamento e sequenciamento de lotes de produção de suplementos para nutrição animal. Pesquisa Operacional, 28(3), 423-450. http://dx.doi.org/10.1590/S0101-74382008000300003
Toso, E. A. V., Morabito, R., & Clark, A. R. (2009). Lot-Sizing and sequencing optimisation at an animal-feed plant. Computers & Industrial Engineering, 57(3), 813-821. http://dx.doi.org/10.1016/j.cie.2009.02.011
Verderame P. M., Elia, J. A., Li, J., & Floudas, C. (2010). Planning and scheduling under uncertainty: a review across multiple sectors. Industrial & Engineering Chemistry Research, 49(9), 3993-4017. http://dx.doi.org/10.1021/ie902009k
Vladimirou, H., & Zenios, S. (1997). Stochastic linear programs with restricted recourse. European Journal of Operational Research, 101(1), 177-192. http://dx.doi.org/10.1016/0377-2217(95)00370-3
Ahumada, O., & Villalobos, J. R. (2008). Application of planning models in the agri-food supply chain: A review. European Journal of Operational Research, 196(1), 1-20. http://dx.doi.org/10.1016/j.ejor.2008.02.014
Alfares, H. K., Khursheed, S. N., & Noman, S. M. (2005). Integrating quality and maintenance decisions in a production-inventory model for deteriorating items. International Journal of Production Research, 43(5), 899-911. http://dx.doi.org/10.1080/0020754042000298511
Amorim, P., Meyr, H., Almeder, C., & Almada-Lobo, B. (2013). Managing perishability in production-distribution planning: a discussion and review. Flexible Services and Manufacturing Journal, 25(3), 389-413. http://dx.doi.org/10.1007/s10696-011-9122-3
Alem, D., & Morabiro, R. (2013). Risk-averse two- stage stochastic programs in furniture plants. OR Spectrum, 35(4), 773-806 http://dx.doi.org/10.1007/s00291-012-0312-5
Bellman, R. (1957). Dynamic programming. Princeton: Princeton University Press. Bellman, R. E., & Zadeh, L. A. (1970). Decision making in fuzzy environment. Management Science, 17(4), 141-154. http://dx.doi.org/10.1287/mnsc.17.4.B141
Birge, J. R., & Louveax, F. (1997). Introduction to stochastic programming. New York: Springer.
Brahimi, N., Dauzere-Peres, S., Najid, N. M., & Nordli, A. (2006). Single item lot sizing problems. European Journal of Operational Research, 168(1), 1-16. http://dx.doi.org/10.1016/j.ejor.2004.01.054
Charnes, A., & Cooper, W. (1959). Chance constrained programming. Management Science, 6(1), 73-79. http://dx.doi.org/10.1287/mnsc.6.1.73
Clark, A. R., Morabito, R., & Toso, E. A. V. (2010). Production setup-sequencing and lot-sizing at an animal nutrition plant through ATSP subtour elimination and patching. Journal of Scheduling, 13(2), 111-121. http://dx.doi.org/10.1007/s10951-009-0135-7
Costa, A. M., Santos, L. M. R., Alem, D. J., & Santos, R. H. S. (2014). Sustainable vegetable crop supply problem with perishable stocks. Annals of Operations Research, 219(1), 265-283.
Dantzig, G. (1955). Linear programming under uncertainty. Management Science, 1(3-4), 197-206. http://dx.doi.org/10.1287/mnsc.1.3-4.197
Di Domenica, N., Lucas, C., Mitra, G., & Valente, P. (2009). Scenario generation for stochastic programming and simulation: a modelling perspective. IMA Journal of Management Mathematics, 20(1), 1-38. http://dx.doi.org/10.1093/imaman/dpm027
Drexl, A., & Kimms, A. (1997). Lot sizing and scheduling: survey and extensions. European Journal of Operational Research, 99(2), 221-235. http://dx.doi.org/10.1016/S0377-2217(97)00030-1
Escudero, L. F., Garin, A., Merino, M., & Perez, G. (2007). The value of the stochastic solution in multistage problems. TOP, 15(1), 48-64. http://dx.doi.org/10.1007/s11750-007-0005-4
Jans, R., & Degraeve, Z. (2008). Modeling industrial lot sizing problems: a review. International Journal of Production Research, 46(6), 1619-1643. http://dx.doi.org/10.1080/00207540600902262
Kall, P., & Wallace, S. (1994). Stochastic programming. New York: Wiley.
Karimi, B., Ghomi, S. F., & Wilson, J. (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega, 31(14), 365-378. http://dx.doi.org/10.1016/S0305-0483(03)00059-8
Miranda, J. L. (2007). Optimização em sistemas de processos químicos: generalização de modelos com planeamento e sequenciamento (Tese de doutorado). Lisboa: Universidade Técnica de Lisboa.
Mula, J., Poler, R., Garcia-Sabater, J. P., & Lario, F. C. (2006). Models for production planning under uncertainty: A review. International Journal of Production Economics, 103(1), 271-285. http://dx.doi.org/10.1016/j.ijpe.2005.09.001
Mulvey, J., Vanderbei, R., & Zenios, S. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264-281. http://dx.doi.org/10.1287/opre.43.2.264
Pahl, J., Voβ, S., & Woodruff, D. (2011). Discrete lot-sizing and scheduling with sequence-dependent setup times and costs including deterioration and perishability constraints. In 44th Hawaii International Conference on
System Sciences, Kauai, Hawaii. Pochet, Y., & Wolsey, L. (2006). Production planning by mixed integer programing. New York: Springer.
Sahinidis, N. V. (2004). Optimization under uncertainty: state-of-the-art and opportunities. Computers and Chemical Engineering, 28(6-7), 971-983. http://dx.doi.org/10.1016/j.compchemeng.2003.09.017
Sen, S., & Higle, J. L. (1999). An introductory tutorial on stochastic linear programming models. Interfaces, 29(2), 33-61. http://dx.doi.org/10.1287/inte.29.2.33
Shapiro, A., Dentcheva, D., & Ruszczynski, A. (2009). Lectures on stochastic programming: modeling and theory. Philadelphia: SIAM. http://dx.doi.org/10.1137/1.9780898718751
Sindicato Nacional da Indústria de Alimentação Animal. (2013). Boletim Informativo do Setor. São Paulo: Sindirações. Recuperado em 22 de junho de 2013, de http://sindiracoes.org.br
Toso, E. A. V., Morabito, R., & Clark, A. R. (2008). Combinação de abordagens GLSP e ATSP para o problema de dimensionamento e sequenciamento de lotes de produção de suplementos para nutrição animal. Pesquisa Operacional, 28(3), 423-450. http://dx.doi.org/10.1590/S0101-74382008000300003
Toso, E. A. V., Morabito, R., & Clark, A. R. (2009). Lot-Sizing and sequencing optimisation at an animal-feed plant. Computers & Industrial Engineering, 57(3), 813-821. http://dx.doi.org/10.1016/j.cie.2009.02.011
Verderame P. M., Elia, J. A., Li, J., & Floudas, C. (2010). Planning and scheduling under uncertainty: a review across multiple sectors. Industrial & Engineering Chemistry Research, 49(9), 3993-4017. http://dx.doi.org/10.1021/ie902009k
Vladimirou, H., & Zenios, S. (1997). Stochastic linear programs with restricted recourse. European Journal of Operational Research, 101(1), 177-192. http://dx.doi.org/10.1016/0377-2217(95)00370-3
Facebook
Google+
Twitter
LinkedIn
Mendeley
StumbleUpon
CiteULike
Reddit
Email