Process capability index Cpk for monitoring the thermal performance in the distribution of refrigerated products
Novaes, Antonio Galvão Naclério; Lima Jr, Orlando Fontes; Carvalho, Carolina Corrêa de; Aragão Junior, Dmontier Pinheiro
http://dx.doi.org/10.1590/0103-6513.170514
Production, vol.26, n1, p.54-65, 2015
Abstract
The temperature of refrigerated products along the cold chain must be kept within pre-defined limits to ensure adequate safety levels and high product quality. Because temperature largely influences microbial activities, the continuous monitoring of the time-temperature history over the distribution process usually allows for the adequate control of the product quality along both short- and medium-distance distribution routes. Time-Temperature Indicators (TTI) are composed of temperature measurements taken at various time intervals and are used to feed analytic models that monitor the impacts of temperature on product quality. Process Capability Indices (PCI), however, are calculated using TTI series to evaluate whether the thermal characteristics of the process are within the specified range. In this application, a refrigerated food delivery route is investigated using a simulated annealing algorithm that considers alternative delivery schemes. The objective of this investigation is to minimize the distance traveled while maintaining the vehicle temperature within the prescribed capability level.
Keywords
Refrigerated products. Vehicle routing. Simulated annealing. TTI. PCI.
References
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Bittanti, S., Lovera, M., & Moiraghi, L. (1998). Application of non-normal process capability indices to semiconductor quality control. IEEE Transactions on Semiconductor Manufacturing, 11, 296-303. http://dx.doi.org/10.1109/66.670179
Borch, E., & Arinder, P. (2002). Bacteriological safety issues in red meat and ready-to-eat meat products, as well as control measures. Meat Science, 62, 381-390. http://dx.doi.org/10.1016/S0309-1740(02)00125-0
Breedam, A. V. (1995). Improvement heuristics for the vehicle routing problem based on simulated annealing. European Journal of Operational Research, 86, 480-490. http://dx.doi.org/10.1016/0377-2217(94)00064-J
Bulba, E. A., & Ho, L. L. (2004). Capability index for linear and non-linear functions. Production, 14, 6-11.
Burr, I. W. (1973). Parameters for a general system of distributions to match a grid of a 3 and a 4 . Communications in Statistics – Theory and Methods, 2, 1-21.
Chang, Y. S. (2009). Interval estimation of capability index C pmk for manufacturing processes with asymmetric tolerances. Computers & Industrial Engineering, 56, 312-322. http://dx.doi.org/10.1016/j.cie.2008.06.004
Chang, Y. S., & Bai, D. S. (2001). Control charts for positively-skewed populations with weighted standard deviations. Quality and Reliability Engineering International, 17, 397-406. http://dx.doi.org/10.1002/qre.427
Chang, Y. S., Choi, I. S., & Bai, D. S. (2002). Process capability indices for skewed populations. Quality and Reliability Engineering International, 18, 383-393. http://dx.doi.org/10.1002/qre.489
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Chen, J. P. & Ding, C. G. (2001). A new process capability index for non-normal distributions. The International of Quality and Reliability Management, 18, 762-770. http://dx.doi.org/10.1108/02656710110396076
Elderton, W. P., & Johnson, N. L. (1969). Systems of Frequency Curves. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511569654
Estrada-Flores, S., & Eddy, A. (2006). Thermal performance indicators for refrigerated road vehicles. International Journal of Refrigeration, 29, 889-898. http://dx.doi.org/10.1016/j.ijrefrig.2006.01.012
Flick, D., Hoang, H. M., Alvarez, G., & Laguerre, O. (2012). Combined deterministic and stochastic approaches for modelling the evolution of food products along the cold chain. Part I: Methodology. International Journal of Refrigeration, 35, 907-914. http://dx.doi.org/10.1016/j.ijrefrig.2011.12.010
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Gonçalez, P. U., & Werner, L. (2009). Comparação dos índices de capacidade do processo para distribuições não- normais. Gestão & Produção, 16(1), 121-132. http://dx.doi.org/10.1590/S0104-530X2009000100012
Havelaar, A. H., Brul, S., De Jong, A., De Jonge, R., Zietering, M. H., & Ter Kuile, B. (2010). Future challenges to microbial food safety. International Journal of Food Microbiology, 139, S79-S94. PMid:19913933. http://dx.doi.org/10.1016/j.ijfoodmicro.2009.10.015
Hosseinifard, S. Z., Abassi, B., Ahmad, S., & Abdollahian, M. (2009). A transformation technique to estimate the process capability index for non-normal data. The International Journal of Advanced Manufacturing Technology, 40, 512-517. http://dx.doi.org/10.1007/s00170-008-1376-x
Hsu, C. I., Hung, S. F., & Li, H. C. (2007). Vehicle routing problem with time-windows for perishable food delivery. Journal of Food Engineering, 80, 465-475. http://dx.doi.org/10.1016/j.jfoodeng.2006.05.029
James, S. J., & James, C. (2010). The cold chain and climate change. Food Research International, 43, 1944-1956. http://dx.doi.org/10.1016/j.foodres.2010.02.001
James, S. J., James, C., & Evans, J. A. (2006). Modelling of food transportation systems – a review. International Journal of Refrigeration, 29, 947-957. http://dx.doi.org/10.1016/j.ijrefrig.2006.03.017
Jedermann, R., Ruiz-Garcia, L., & Lang, W. (2009). Spatial temperature profiling by semi-passive RFID loggers for perishable food transportation. Computers and Electronics in Agriculture, 65(2), 145-154. http://dx.doi.org/10.1016/j.compag.2008.08.006
Kaya, I., & Kahraman, C. (2010). A new perspective on fuzzy process capability indices: Robustness. Expert Systems with Applications, 37, 4593-4600. http://dx.doi.org/10.1016/j.eswa.2009.12.049
Kirkpatrick, S., Gellat, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671-680. PMid:17813860. http://dx.doi.org/10.1126/science.220.4598.671
Leung, S. C. H., Zhang, Z., Zhang, D., Hua, X., & Lim, M. K. (2013). A meta-heuristic algorithm for heterogeneous fleet routing problems with two-dimensional loading constraints. European Journal of Operational Research, 225, 199-210. http://dx.doi.org/10.1016/j.ejor.2012.09.023
Lin, P. H., & Chen, F. L. (2006). Process capability analysis of non-normal process data using the Burr XII distribution. The International Journal of Advanced Manufacturing Technology, 27, 975-984. http://dx.doi.org/10.1007/s00170-004-2263-8
Magalhães, M. S., & Moura Neto, F. D. (2011). Economic- statistical design of variable parameters non-central chi-square control chart. Production, 21, 259-270.
Mauri, G. R., & Lorena, L. A. N. (2009). A new approach for the dial-a-ride problem. Production, 19, p. 41-54. McMeekin, T., Bowman, J., McQuestin, O., Mellefont, L., Ross, T., & Tamplin, M. (2008). The future of predictive microbiology: Strategic research, innovative applications and great expectations. International Journal of Food Microbiology, 128, 2-9. PMid:18703250. http://dx.doi.org/10.1016/j.ijfoodmicro.2008.06.026
Mingoti, S. A., & Glória, F. F. F. (2008). Comparing Mingoti and Glória’s and Niverthi and Dey’s multivariate capability indexes. Production, 18, 598-608.
Mingoti, S. A., Oliveira, F. L. P., & Conceição, M. M. C. (2011). Capability indices for independent multivariate processes: extensions of Niverthi and Dey’s and Mingoti and Glória’s indices. Production, 21, 94-105.
Moureh, J., & Derens, E. (2000). Numerical modelling of the temperature increase in frozen food packaged in pallets in the distribution chain. International Journal of Refrigeration, 23, 540-552. http://dx.doi.org/10.1016/S0140-7007(99)00081-X
Osman, I. H. (1993). Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of Operations Research, 41(4), 421-451. http://dx.doi.org/10.1007/BF02023004
Oswald, A., & Stirn, L. Z. (2008). A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food. Journal of Food Engineering, 85, 285-295. http://dx.doi.org/10.1016/j.jfoodeng.2007.07.008
Pearn, W. L., & Lin, P. C. (2004). Testing process performance based on capability index C pk with critical values, Computers & Industrial Engineering, 47, 351-369. http://dx.doi.org/10.1016/j.cie.2003.03.001
Pereira, V. F., Dória, E. C. B, Carvalho Júnior, B. C., Neves Filho, L. C., & Silveira Júnior, V. (2010). Avaliação de temperaturas em câmaras frigoríficas de transporte urbano de alimentos resfriados e congelados. Ciência e Tecnologia de Alimentos, 30, 158-165. http://dx.doi.org/10.1590/S0101-20612010000100024
Sahin, E., Babaï, M. Z., Dallery, Y., & Vaillant, R. (2007). Ensuring supply chain safety through time temperature integrators. International Journal of Logistics Management, 18, 102-124. http://dx.doi.org/10.1108/09574090710748199
Simpson, R., Almonacid, S., Nuñez, H., Pinto, M., Abakarov, A., & Teixeira, A. (2012). Time-temperature indicator to monitor cold chain distribution of fresh salmon (salmo salar). Journal of Food Process Engineering, 35, 742-750. http://dx.doi.org/10.1111/j.1745-4530.2010.00623.x
Smolander, M., Alakomi, H.-L., Ritvanen, T., Vainionpää, J., & Ahvenainen, R. (2004). Monitoring of the quality of modified atmosphere packaged broiler chicken cuts stored in different temperature conditions. A. Time- temperature indicators as quality-indicating tools. Food Control, 15, 217-229. http://dx.doi.org/10.1016/S0956-7135(03)00061-6
Syslo, M. M., Deo, N., & Kowalik, J. S. (2006). Discrete Optimization Algorithms with Pascal Programs. Mineola: Dover Publications.
Tarantilis, C. D., & Kiranoudis, C. T. (2002). Distribution of fresh meat. Journal of Food Engineering, 51, 85-91. http://dx.doi.org/10.1016/S0260-8774(01)00040-1
Tso, C. P., Yu, S. C. M., Poh, H. J., & Jolly, P. G. (2002). Experimental study on the heat and mass transfer characteristics in a refrigerated truck. International Journal of Refrigeration, 25, p. 340-350. http://dx.doi.org/10.1016/S0140-7007(01)00015-9
Wu, C. W., Pearn, W. L., & Kotz, S. (2009). An overview of theory and practice on process capability indices for quality assurance. International Journal of Production Economics, 117, 338-359. http://dx.doi.org/10.1016/j.ijpe.2008.11.008
Anis, M. Z. (2008). Basic process capability indices: An expository review. International Statistical Review, 76, 347-367. http://dx.doi.org/10.1111/j.1751-5823.2008.00060.x
Azi, N., Gendreau, M., & Potvin, J. Y. (2007). An exact algorithm for a simple-vehicle routing problem with time windows and multiple routes. European Journal of Operational Research, 178, 755-766. http://dx.doi.org/10.1016/j.ejor.2006.02.019
Barriga, G. D. C., Ho, L. L., & Borges, W. S. (2003). Process capability index for one-sided specification limit. Production, 13, 40-49.
Bittanti, S., Lovera, M., & Moiraghi, L. (1998). Application of non-normal process capability indices to semiconductor quality control. IEEE Transactions on Semiconductor Manufacturing, 11, 296-303. http://dx.doi.org/10.1109/66.670179
Borch, E., & Arinder, P. (2002). Bacteriological safety issues in red meat and ready-to-eat meat products, as well as control measures. Meat Science, 62, 381-390. http://dx.doi.org/10.1016/S0309-1740(02)00125-0
Breedam, A. V. (1995). Improvement heuristics for the vehicle routing problem based on simulated annealing. European Journal of Operational Research, 86, 480-490. http://dx.doi.org/10.1016/0377-2217(94)00064-J
Bulba, E. A., & Ho, L. L. (2004). Capability index for linear and non-linear functions. Production, 14, 6-11.
Burr, I. W. (1973). Parameters for a general system of distributions to match a grid of a 3 and a 4 . Communications in Statistics – Theory and Methods, 2, 1-21.
Chang, Y. S. (2009). Interval estimation of capability index C pmk for manufacturing processes with asymmetric tolerances. Computers & Industrial Engineering, 56, 312-322. http://dx.doi.org/10.1016/j.cie.2008.06.004
Chang, Y. S., & Bai, D. S. (2001). Control charts for positively-skewed populations with weighted standard deviations. Quality and Reliability Engineering International, 17, 397-406. http://dx.doi.org/10.1002/qre.427
Chang, Y. S., Choi, I. S., & Bai, D. S. (2002). Process capability indices for skewed populations. Quality and Reliability Engineering International, 18, 383-393. http://dx.doi.org/10.1002/qre.489
Chen, H. K., Hsueh, C. F. & Chang, M. S. (2009). Production scheduling and vehicle routing with time windows for perishable food products. Computers & Operations Research, 36, 2311-2319. http://dx.doi.org/10.1016/j.cor.2008.09.010
Chen, J. P. & Ding, C. G. (2001). A new process capability index for non-normal distributions. The International of Quality and Reliability Management, 18, 762-770. http://dx.doi.org/10.1108/02656710110396076
Elderton, W. P., & Johnson, N. L. (1969). Systems of Frequency Curves. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511569654
Estrada-Flores, S., & Eddy, A. (2006). Thermal performance indicators for refrigerated road vehicles. International Journal of Refrigeration, 29, 889-898. http://dx.doi.org/10.1016/j.ijrefrig.2006.01.012
Flick, D., Hoang, H. M., Alvarez, G., & Laguerre, O. (2012). Combined deterministic and stochastic approaches for modelling the evolution of food products along the cold chain. Part I: Methodology. International Journal of Refrigeration, 35, 907-914. http://dx.doi.org/10.1016/j.ijrefrig.2011.12.010
Food Refrigeration & Process Engineering Research Centre – FRPERC (2000). Coolvan Manual (Version 3.0). University of Bristol, UK.
Giannakourou, M. C., & Taoukis, P. S. (2003). TTI- based distribution management system for quality optimization of frozen vegetables at the consumer end. Journal of Food Science, 68, 201-209. http://dx.doi.org/10.1111/j.1365-2621.2003.tb14140.x
Giannakourou, M. C., Koutsoumanis, K., Nychas, G. J., & Taoukis, P. S. (2005). Field evaluation of the application of time temperature integrators for monitoring fish quality in the chill chain. International Journal of Food Microbiology, 102, 323-336. PMid:16014299. http://dx.doi.org/10.1016/j.ijfoodmicro.2004.11.037
Gigiel, A. J., James S. J., & Evans, J. A. (1998). Controlling temperature during distribution and retail. In Proceedings 3 rd Karlsruhe Nutrition Symposium , Karlsruhe, Germany.
Gonçalez, P. U., & Werner, L. (2009). Comparação dos índices de capacidade do processo para distribuições não- normais. Gestão & Produção, 16(1), 121-132. http://dx.doi.org/10.1590/S0104-530X2009000100012
Havelaar, A. H., Brul, S., De Jong, A., De Jonge, R., Zietering, M. H., & Ter Kuile, B. (2010). Future challenges to microbial food safety. International Journal of Food Microbiology, 139, S79-S94. PMid:19913933. http://dx.doi.org/10.1016/j.ijfoodmicro.2009.10.015
Hosseinifard, S. Z., Abassi, B., Ahmad, S., & Abdollahian, M. (2009). A transformation technique to estimate the process capability index for non-normal data. The International Journal of Advanced Manufacturing Technology, 40, 512-517. http://dx.doi.org/10.1007/s00170-008-1376-x
Hsu, C. I., Hung, S. F., & Li, H. C. (2007). Vehicle routing problem with time-windows for perishable food delivery. Journal of Food Engineering, 80, 465-475. http://dx.doi.org/10.1016/j.jfoodeng.2006.05.029
James, S. J., & James, C. (2010). The cold chain and climate change. Food Research International, 43, 1944-1956. http://dx.doi.org/10.1016/j.foodres.2010.02.001
James, S. J., James, C., & Evans, J. A. (2006). Modelling of food transportation systems – a review. International Journal of Refrigeration, 29, 947-957. http://dx.doi.org/10.1016/j.ijrefrig.2006.03.017
Jedermann, R., Ruiz-Garcia, L., & Lang, W. (2009). Spatial temperature profiling by semi-passive RFID loggers for perishable food transportation. Computers and Electronics in Agriculture, 65(2), 145-154. http://dx.doi.org/10.1016/j.compag.2008.08.006
Kaya, I., & Kahraman, C. (2010). A new perspective on fuzzy process capability indices: Robustness. Expert Systems with Applications, 37, 4593-4600. http://dx.doi.org/10.1016/j.eswa.2009.12.049
Kirkpatrick, S., Gellat, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671-680. PMid:17813860. http://dx.doi.org/10.1126/science.220.4598.671
Leung, S. C. H., Zhang, Z., Zhang, D., Hua, X., & Lim, M. K. (2013). A meta-heuristic algorithm for heterogeneous fleet routing problems with two-dimensional loading constraints. European Journal of Operational Research, 225, 199-210. http://dx.doi.org/10.1016/j.ejor.2012.09.023
Lin, P. H., & Chen, F. L. (2006). Process capability analysis of non-normal process data using the Burr XII distribution. The International Journal of Advanced Manufacturing Technology, 27, 975-984. http://dx.doi.org/10.1007/s00170-004-2263-8
Magalhães, M. S., & Moura Neto, F. D. (2011). Economic- statistical design of variable parameters non-central chi-square control chart. Production, 21, 259-270.
Mauri, G. R., & Lorena, L. A. N. (2009). A new approach for the dial-a-ride problem. Production, 19, p. 41-54. McMeekin, T., Bowman, J., McQuestin, O., Mellefont, L., Ross, T., & Tamplin, M. (2008). The future of predictive microbiology: Strategic research, innovative applications and great expectations. International Journal of Food Microbiology, 128, 2-9. PMid:18703250. http://dx.doi.org/10.1016/j.ijfoodmicro.2008.06.026
Mingoti, S. A., & Glória, F. F. F. (2008). Comparing Mingoti and Glória’s and Niverthi and Dey’s multivariate capability indexes. Production, 18, 598-608.
Mingoti, S. A., Oliveira, F. L. P., & Conceição, M. M. C. (2011). Capability indices for independent multivariate processes: extensions of Niverthi and Dey’s and Mingoti and Glória’s indices. Production, 21, 94-105.
Moureh, J., & Derens, E. (2000). Numerical modelling of the temperature increase in frozen food packaged in pallets in the distribution chain. International Journal of Refrigeration, 23, 540-552. http://dx.doi.org/10.1016/S0140-7007(99)00081-X
Osman, I. H. (1993). Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of Operations Research, 41(4), 421-451. http://dx.doi.org/10.1007/BF02023004
Oswald, A., & Stirn, L. Z. (2008). A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food. Journal of Food Engineering, 85, 285-295. http://dx.doi.org/10.1016/j.jfoodeng.2007.07.008
Pearn, W. L., & Lin, P. C. (2004). Testing process performance based on capability index C pk with critical values, Computers & Industrial Engineering, 47, 351-369. http://dx.doi.org/10.1016/j.cie.2003.03.001
Pereira, V. F., Dória, E. C. B, Carvalho Júnior, B. C., Neves Filho, L. C., & Silveira Júnior, V. (2010). Avaliação de temperaturas em câmaras frigoríficas de transporte urbano de alimentos resfriados e congelados. Ciência e Tecnologia de Alimentos, 30, 158-165. http://dx.doi.org/10.1590/S0101-20612010000100024
Sahin, E., Babaï, M. Z., Dallery, Y., & Vaillant, R. (2007). Ensuring supply chain safety through time temperature integrators. International Journal of Logistics Management, 18, 102-124. http://dx.doi.org/10.1108/09574090710748199
Simpson, R., Almonacid, S., Nuñez, H., Pinto, M., Abakarov, A., & Teixeira, A. (2012). Time-temperature indicator to monitor cold chain distribution of fresh salmon (salmo salar). Journal of Food Process Engineering, 35, 742-750. http://dx.doi.org/10.1111/j.1745-4530.2010.00623.x
Smolander, M., Alakomi, H.-L., Ritvanen, T., Vainionpää, J., & Ahvenainen, R. (2004). Monitoring of the quality of modified atmosphere packaged broiler chicken cuts stored in different temperature conditions. A. Time- temperature indicators as quality-indicating tools. Food Control, 15, 217-229. http://dx.doi.org/10.1016/S0956-7135(03)00061-6
Syslo, M. M., Deo, N., & Kowalik, J. S. (2006). Discrete Optimization Algorithms with Pascal Programs. Mineola: Dover Publications.
Tarantilis, C. D., & Kiranoudis, C. T. (2002). Distribution of fresh meat. Journal of Food Engineering, 51, 85-91. http://dx.doi.org/10.1016/S0260-8774(01)00040-1
Tso, C. P., Yu, S. C. M., Poh, H. J., & Jolly, P. G. (2002). Experimental study on the heat and mass transfer characteristics in a refrigerated truck. International Journal of Refrigeration, 25, p. 340-350. http://dx.doi.org/10.1016/S0140-7007(01)00015-9
Wu, C. W., Pearn, W. L., & Kotz, S. (2009). An overview of theory and practice on process capability indices for quality assurance. International Journal of Production Economics, 117, 338-359. http://dx.doi.org/10.1016/j.ijpe.2008.11.008