A tabu list-based algorithm for capacitated multilevel lot-sizing with alternate bills of materials and co-production environments
Un algoritmo basado en listas tabú para el dimensionamiento de lotes de múltiples niveles capacitados con listas de materiales alternativas y entornos de coproducción
Date
2019-04-03
2019-04-03
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Abstract
The definition of lot sizes represents one of the most important decisions in production planning. Lot-sizing turns into an increasingly complex set of decisions that requires efficient solution approaches, in response to the time-consuming exact methods (LP, MIP). This paper aims to propose a Tabu list-based algorithm (TLBA) as an alternative to the Generic Materials and Operations Planning (GMOP) model. The algorithm considers a multi-level, multi-item planning structure. It is initialized using a lot-for-lot (LxL) method and candidate solutions are evaluated through an iterative Material Requirements Planning (MRP) procedure. Three different sizes of test instances are defined and better results are obtained in the large and medium-size problems, with minimum average gaps close to 10.5%
Referencias:
Karimi, B.; Fatemi Ghomi, S.; Wilson, J. The capacitated lot sizing problem: A review of models and algorithms. Omega 2003, 31, 365–378. [CrossRef] Martí, R.; Reinelt, G. Heuristic Methods. In The Linear Ordering Problem; Springer: Berlin, Germany, 2011; pp. 17–40. [CrossRef] Barany, I.; Van Roy, T.J.; Wolsey, L.A. Strong Formulations for Multi-Item Capacitated Lot Sizing. Manag. Sci. 1984, 30, 1255–1261. [CrossRef] Eppen, G.D.; Martin, R.K. Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition. Oper. Res. 1987, 35, 832–848. [CrossRef] Maes, J.; McClain, J.O.; Van Wassenhove, L.N. Multilevel capacitated lotsizing complexity and LP-based heuristics. Eur. J. Oper. Res. 1991, 53, 131–148. [CrossRef] Buschkühl, L.; Sahling, F.; Helber, S.; Tempelmeier, H. Dynamic Capacitated Lot-Sizing Problems: A Classification and Review of Solution Approaches. OR Spectrum. 2010, 32, 231–261. [CrossRef] Drexl, A.; Kimms, A. Lot sizing and scheduling—Survey and extensions. Eur. J. Oper. Res. 1997, 99, 221–235. [CrossRef] Glock, C.H.; Grosse, E.H.; Ries, J.M. The lot sizing problem: A tertiary study. Int. J. Prod. Econ. 2014, 155, 39–51. [CrossRef] Kuik, R.; Salomon, M.; Van Wassenhove, L.N.; Maes, J. Linear Programming, Simulated Annealing and Tabu Search Heuristics for Lotsizing in Bottleneck Assembly Systems. IIE Trans. 1993, 25, 62–72. [CrossRef] AMPL Optimization Inc. Standard Price List—AMPL. Available online: https://ampl.com/products/ standard-price-list/ (accessed on 1 March 2019) Seeanner, F.; Almada-Lobo, B.; Meyr, H. Combining the principles of variable neighborhood decomposition search and the fix&optimize heuristic to solve multi-level lot-sizing and scheduling problems. Comput. Oper. Res. 2013, 40, 303–317. [CrossRef] Hung, Y.F.; Chien, K.L. A Multi-Class Multi-Level Capacitated Lot Sizing Model. J. Oper. Res. Soc. 2000, 51, 1309. [CrossRef] Kang, Y.; Albey, E.; Uzsoy, R. Rounding heuristics for multiple product dynamic lot-sizing in the presence of queueing behavior. Comput. Oper. Res. 2018, 100, 54–65. [CrossRef] Berretta, R.; França, P.M.; Armentano, V.A. Metaheuristic approaches for the multilevel resource-constrained lot-sizing problem with setup and lead times. Asia-Pac. J. Oper. Res. 2005, 22, 261–286. [CrossRef] Kimms, A. Competitive methods for multi-level lot sizing and scheduling: Tabu search and randomized regrets. Int. J. Prod. Res. 1996, 34, 2279–2298. [CrossRef] Oliva San Martín, C.D.; Ramírez Guzmán, G. Algoritmo de tipo búsqueda tabú para un problema de programación de horarios universitarios vespertinos. INGE CUC 2013, 9, 58–65. Maheut, J.; Garcia-Sabater, J.P. La matriz de operaciones y materiales y la matriz de operaciones y recursos, un nuevo enfoque para resolver el problema GMOP basado en el concepto del stroke. Dir. Y Organ. 2011, 45, 46–57. Maheut, J.; Garcia-Sabater, J.P.; Garcia-Sabater, J.J.; Valero Herrero, M. El Stroke y la Matriz de Operaciones y Materiales, nuevo enfoque para resolver el problema GMOP. In Proceedings of the 5th International Conference on Industrial Engineering and Industrial Management, Cartagena, Spain, 7–9 September 2011; pp. 884–893. Garcia-Sabater, J.P.; Maheut, J.; Marin-Garcia, J.A. A new formulation technique to model materials and operations planning: The generic materials and operations planning (GMOP) problem. Eur. J. Ind. Eng. 2013, 7, 119. [CrossRef] Maheut, J.; Garcia Sabater, J.P. Algorithm for complete enumeration based on a stroke graph to solve the supply network configuration and operations scheduling problem. J. Ind. Eng. Manag. 2013, 6, 779–795. [CrossRef] Roca Molina, A. Construcción de Algoritmo Aplicando Relajación Lagrangeana Para la Obtención de un límite Inferior Para el Problema de Lotificación en Sistemas Multinivel en Entornos de Coproducción y Listas de Materiales Alternativas. Ph.D. Thesis, Universidad Tecnológica de Bolívar, Cartagena, Colombia, 2016. Rius Sorolla, G.; Maheut, J.; Coronado-Hernandez, J.; Garcia-Sabater, J.P. Lagrangian relaxation of the GMOP model. In Proceedings of the 11th International Conference on Industrial Engineering and Industrial Management, Valencia, Spain, 5–6 July 2017. Rius-Sorolla, G.; Maheut, J.; Coronado-Hernandez, J.R.; Garcia-Sabater, J.P. Lagrangian relaxation of the generic materials and operations planning model. Cent. Eur. J. Oper. Res. 2018, 1–19. [CrossRef] Maheut, J.; Garcia-Sabater, J.P.; Mula, J. The Generic Materials and Operations Planning (GMOP) problem solved iteratively: A case study in multi-site context. In IFIP Advances in Information and Communication Technology; Springer: Berlin/Heidelberg, Germany, 2012; Volume 384, pp. 66–73. Maheut, J. Modelos y Algoritmos Basados en el Concepto Stroke Para la Planificación y Programación de Operaciones con Alternativas en Redes de Suministro. Ph.D. Thesis, Universitat Politècnica de València, Valencia, Spain, 2013, doi:10.4995/Thesis/10251/29290. Maheut, J.; Garcia-Sabater, J.P. A Parallelizable Heuristic for Solving the Generic Materials and Operations Planning in a Supply Chain Network: A Case Study from the Automotive Industry. In IFIP WG 5.7 International Conference on Advances in Production Management Systems, APMS; Springer: Berlin/Heidelberg, Germany, 2012; pp. 151–157. Coronado-Hernandez, J.R.; Simancas-Mateus, D.; Avila-Martinez, K.; Garcia-Sabater, J.P. Heuristic for Material and Operations Planning in Supply Chains with Alternative Product Structure. J. Eng. Appl. Sci. 2017, 12, 628–635. [CrossRef] Romero-Conrado, A.R. Algoritmo heurístico basado en listas tabú para la planificación de la producción en sistemas multinivel con listas de materiales alternativas y entornos de coproducción. Master’s Thesis, Universidad de la Costa, Barranquilla, Colombia, 2018; pp. 1–141. Glover, F. Tabu Search—Part I. ORSA J. Comput. 1989, 1, 190–206. [CrossRef] Glover, F.; Taillard, E. A user’s guide to tabu search. Ann. Oper. Res. 1993, 41, 1–28. [CrossRef] Batista, M.B.M.; Glover, F. Búsqueda Tabú. Intel. Artif. Rev. Iberoam. De Intel. Artif. 2003, 7, 29–48. Chelouah, R.; Siarry, P. Tabu Search applied to global optimization. Eur. J. Oper. Res. 2000, 123, 256–270. [CrossRef] Raza, S.A.; Akgunduz, A.; Chen, M.Y. A tabu search algorithm for solving economic lot scheduling problem. J. Heuristics 2006, 12, 413–426. [CrossRef] Cesaret, B.; Oguz, C.; Sibel Salman, F. A tabu search algorithm for order acceptance and scheduling. ˇ Comput. Oper. Res. 2012, 39, 1197–1205. [CrossRef] Li, X.; Baki, F.; Tian, P.; Chaouch, B.A. A robust block-chain based tabu search algorithm for the dynamic lot sizing problem with product returns and remanufacturing. Omega 2014, 42, 75–87. [CrossRef] Li, J.Q.; Pan, Q.K. Solving the large-scale hybrid flow shop scheduling problem with limited buffers by a hybrid artificial bee colony algorithm. Inf. Sci. 2014, 316, 487–502. [CrossRef] Hindi, K.S. Solving the single-item, capacitated dynamic lot-sizing problem with startup and reservation costs by tabu search. Comput. Ind. Eng. 1995, 28, 701–707. [CrossRef] Hindi, K.S. Solving the CLSP by a Tabu Search Heuristic. J. Oper. Res. Soc. 1996, 47, 151–161. [CrossRef] Gopalakrishnan, M.; Ding, K.; Bourjolly, J.M.; Mohan, S. A Tabu-Search Heuristic for the Capacitated Lot-Sizing Problem with Set-up Carryover. Manag. Sci. 2001, 47, 851–863. [CrossRef] Glover, F. Tabu Search—Part II. ORSA J. Comput. 1990, 2, 4–32. [CrossRef] Orlicky, J. Material Requirements Planning; McGraw-Hill: New York, NY, USA, 1975. Minitab 18. Overview for Create General Full Factorial Design, 2019. Available online: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/doe/howto/factorial/create-factorial-design/create-general-full-factorial/before-you-start/overview/ (accessed on 1 March 2019) Perttunen, J. On the Significance of the Initial Solution in Travelling Salesman Heuristics. J. Oper. Res. Soc. 1994, 45, 1131. [CrossRef] Escobar Z, A.H.; Gallego R, R.A.; Romero L, R.A. Using traditional heuristic algorithms on an initial genetic algorithm population applied to the transmission expansion planning problem. Ing. E Investig. 2011, 31, 127–143. Elaziz, M.A.; Mirjalili, S. A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowl.-Based Syst. 2019, 172, 42–63. [CrossRef] Chen, C.F.; Wu, M.C.; Lin, K.H. Effect of solution representations on Tabu search in scheduling applications. Comput. Oper. Res. 2013, 40, 2817–2825. [CrossRef] Romero-Conrado, A.R. Tabu List Based Algorithm Datasets, 2019. Available online: https://github.com/ alfonsoromeroc/tlba-gmop (accessed on 1 March 2019)
Karimi, B.; Fatemi Ghomi, S.; Wilson, J. The capacitated lot sizing problem: A review of models and algorithms. Omega 2003, 31, 365–378. [CrossRef] Martí, R.; Reinelt, G. Heuristic Methods. In The Linear Ordering Problem; Springer: Berlin, Germany, 2011; pp. 17–40. [CrossRef] Barany, I.; Van Roy, T.J.; Wolsey, L.A. Strong Formulations for Multi-Item Capacitated Lot Sizing. Manag. Sci. 1984, 30, 1255–1261. [CrossRef] Eppen, G.D.; Martin, R.K. Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition. Oper. Res. 1987, 35, 832–848. [CrossRef] Maes, J.; McClain, J.O.; Van Wassenhove, L.N. Multilevel capacitated lotsizing complexity and LP-based heuristics. Eur. J. Oper. Res. 1991, 53, 131–148. [CrossRef] Buschkühl, L.; Sahling, F.; Helber, S.; Tempelmeier, H. Dynamic Capacitated Lot-Sizing Problems: A Classification and Review of Solution Approaches. OR Spectrum. 2010, 32, 231–261. [CrossRef] Drexl, A.; Kimms, A. Lot sizing and scheduling—Survey and extensions. Eur. J. Oper. Res. 1997, 99, 221–235. [CrossRef] Glock, C.H.; Grosse, E.H.; Ries, J.M. The lot sizing problem: A tertiary study. Int. J. Prod. Econ. 2014, 155, 39–51. [CrossRef] Kuik, R.; Salomon, M.; Van Wassenhove, L.N.; Maes, J. Linear Programming, Simulated Annealing and Tabu Search Heuristics for Lotsizing in Bottleneck Assembly Systems. IIE Trans. 1993, 25, 62–72. [CrossRef] AMPL Optimization Inc. Standard Price List—AMPL. Available online: https://ampl.com/products/ standard-price-list/ (accessed on 1 March 2019) Seeanner, F.; Almada-Lobo, B.; Meyr, H. Combining the principles of variable neighborhood decomposition search and the fix&optimize heuristic to solve multi-level lot-sizing and scheduling problems. Comput. Oper. Res. 2013, 40, 303–317. [CrossRef] Hung, Y.F.; Chien, K.L. A Multi-Class Multi-Level Capacitated Lot Sizing Model. J. Oper. Res. Soc. 2000, 51, 1309. [CrossRef] Kang, Y.; Albey, E.; Uzsoy, R. Rounding heuristics for multiple product dynamic lot-sizing in the presence of queueing behavior. Comput. Oper. Res. 2018, 100, 54–65. [CrossRef] Berretta, R.; França, P.M.; Armentano, V.A. Metaheuristic approaches for the multilevel resource-constrained lot-sizing problem with setup and lead times. Asia-Pac. J. Oper. Res. 2005, 22, 261–286. [CrossRef] Kimms, A. Competitive methods for multi-level lot sizing and scheduling: Tabu search and randomized regrets. Int. J. Prod. Res. 1996, 34, 2279–2298. [CrossRef] Oliva San Martín, C.D.; Ramírez Guzmán, G. Algoritmo de tipo búsqueda tabú para un problema de programación de horarios universitarios vespertinos. INGE CUC 2013, 9, 58–65. Maheut, J.; Garcia-Sabater, J.P. La matriz de operaciones y materiales y la matriz de operaciones y recursos, un nuevo enfoque para resolver el problema GMOP basado en el concepto del stroke. Dir. Y Organ. 2011, 45, 46–57. Maheut, J.; Garcia-Sabater, J.P.; Garcia-Sabater, J.J.; Valero Herrero, M. El Stroke y la Matriz de Operaciones y Materiales, nuevo enfoque para resolver el problema GMOP. In Proceedings of the 5th International Conference on Industrial Engineering and Industrial Management, Cartagena, Spain, 7–9 September 2011; pp. 884–893. Garcia-Sabater, J.P.; Maheut, J.; Marin-Garcia, J.A. A new formulation technique to model materials and operations planning: The generic materials and operations planning (GMOP) problem. Eur. J. Ind. Eng. 2013, 7, 119. [CrossRef] Maheut, J.; Garcia Sabater, J.P. Algorithm for complete enumeration based on a stroke graph to solve the supply network configuration and operations scheduling problem. J. Ind. Eng. Manag. 2013, 6, 779–795. [CrossRef] Roca Molina, A. Construcción de Algoritmo Aplicando Relajación Lagrangeana Para la Obtención de un límite Inferior Para el Problema de Lotificación en Sistemas Multinivel en Entornos de Coproducción y Listas de Materiales Alternativas. Ph.D. Thesis, Universidad Tecnológica de Bolívar, Cartagena, Colombia, 2016. Rius Sorolla, G.; Maheut, J.; Coronado-Hernandez, J.; Garcia-Sabater, J.P. Lagrangian relaxation of the GMOP model. In Proceedings of the 11th International Conference on Industrial Engineering and Industrial Management, Valencia, Spain, 5–6 July 2017. Rius-Sorolla, G.; Maheut, J.; Coronado-Hernandez, J.R.; Garcia-Sabater, J.P. Lagrangian relaxation of the generic materials and operations planning model. Cent. Eur. J. Oper. Res. 2018, 1–19. [CrossRef] Maheut, J.; Garcia-Sabater, J.P.; Mula, J. The Generic Materials and Operations Planning (GMOP) problem solved iteratively: A case study in multi-site context. In IFIP Advances in Information and Communication Technology; Springer: Berlin/Heidelberg, Germany, 2012; Volume 384, pp. 66–73. Maheut, J. Modelos y Algoritmos Basados en el Concepto Stroke Para la Planificación y Programación de Operaciones con Alternativas en Redes de Suministro. Ph.D. Thesis, Universitat Politècnica de València, Valencia, Spain, 2013, doi:10.4995/Thesis/10251/29290. Maheut, J.; Garcia-Sabater, J.P. A Parallelizable Heuristic for Solving the Generic Materials and Operations Planning in a Supply Chain Network: A Case Study from the Automotive Industry. In IFIP WG 5.7 International Conference on Advances in Production Management Systems, APMS; Springer: Berlin/Heidelberg, Germany, 2012; pp. 151–157. Coronado-Hernandez, J.R.; Simancas-Mateus, D.; Avila-Martinez, K.; Garcia-Sabater, J.P. Heuristic for Material and Operations Planning in Supply Chains with Alternative Product Structure. J. Eng. Appl. Sci. 2017, 12, 628–635. [CrossRef] Romero-Conrado, A.R. Algoritmo heurístico basado en listas tabú para la planificación de la producción en sistemas multinivel con listas de materiales alternativas y entornos de coproducción. Master’s Thesis, Universidad de la Costa, Barranquilla, Colombia, 2018; pp. 1–141. Glover, F. Tabu Search—Part I. ORSA J. Comput. 1989, 1, 190–206. [CrossRef] Glover, F.; Taillard, E. A user’s guide to tabu search. Ann. Oper. Res. 1993, 41, 1–28. [CrossRef] Batista, M.B.M.; Glover, F. Búsqueda Tabú. Intel. Artif. Rev. Iberoam. De Intel. Artif. 2003, 7, 29–48. Chelouah, R.; Siarry, P. Tabu Search applied to global optimization. Eur. J. Oper. Res. 2000, 123, 256–270. [CrossRef] Raza, S.A.; Akgunduz, A.; Chen, M.Y. A tabu search algorithm for solving economic lot scheduling problem. J. Heuristics 2006, 12, 413–426. [CrossRef] Cesaret, B.; Oguz, C.; Sibel Salman, F. A tabu search algorithm for order acceptance and scheduling. ˇ Comput. Oper. Res. 2012, 39, 1197–1205. [CrossRef] Li, X.; Baki, F.; Tian, P.; Chaouch, B.A. A robust block-chain based tabu search algorithm for the dynamic lot sizing problem with product returns and remanufacturing. Omega 2014, 42, 75–87. [CrossRef] Li, J.Q.; Pan, Q.K. Solving the large-scale hybrid flow shop scheduling problem with limited buffers by a hybrid artificial bee colony algorithm. Inf. Sci. 2014, 316, 487–502. [CrossRef] Hindi, K.S. Solving the single-item, capacitated dynamic lot-sizing problem with startup and reservation costs by tabu search. Comput. Ind. Eng. 1995, 28, 701–707. [CrossRef] Hindi, K.S. Solving the CLSP by a Tabu Search Heuristic. J. Oper. Res. Soc. 1996, 47, 151–161. [CrossRef] Gopalakrishnan, M.; Ding, K.; Bourjolly, J.M.; Mohan, S. A Tabu-Search Heuristic for the Capacitated Lot-Sizing Problem with Set-up Carryover. Manag. Sci. 2001, 47, 851–863. [CrossRef] Glover, F. Tabu Search—Part II. ORSA J. Comput. 1990, 2, 4–32. [CrossRef] Orlicky, J. Material Requirements Planning; McGraw-Hill: New York, NY, USA, 1975. Minitab 18. Overview for Create General Full Factorial Design, 2019. Available online: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/doe/howto/factorial/create-factorial-design/create-general-full-factorial/before-you-start/overview/ (accessed on 1 March 2019) Perttunen, J. On the Significance of the Initial Solution in Travelling Salesman Heuristics. J. Oper. Res. Soc. 1994, 45, 1131. [CrossRef] Escobar Z, A.H.; Gallego R, R.A.; Romero L, R.A. Using traditional heuristic algorithms on an initial genetic algorithm population applied to the transmission expansion planning problem. Ing. E Investig. 2011, 31, 127–143. Elaziz, M.A.; Mirjalili, S. A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowl.-Based Syst. 2019, 172, 42–63. [CrossRef] Chen, C.F.; Wu, M.C.; Lin, K.H. Effect of solution representations on Tabu search in scheduling applications. Comput. Oper. Res. 2013, 40, 2817–2825. [CrossRef] Romero-Conrado, A.R. Tabu List Based Algorithm Datasets, 2019. Available online: https://github.com/ alfonsoromeroc/tlba-gmop (accessed on 1 March 2019)
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