Car Sequencing Problem con flotas de vehículos especiales. Presentación

Car Sequencing Problem con demanda parcial incierta. Robustez en una multi-secuencia de vehículos mixtos.Partiendo del Car Sequencing Problem (CSP), introducimos el concepto demanda parcial incierta a través de la incorporación de Flotas de vehículos especiales en un plan de demanda. Tras resaltar las peculiaridades de una Flota y establecer las hipótesis de trabajo, proponemos un modelo de programación lineal entera mixta orientado a satisfacer el máximo número de restricciones CSP. Posteriormente, introducimos el concepto multi-secuencia de producción y proponemos funciones para medir su robustez. La versión robusta del CSP considera un conjunto de escenarios de la demanda para las Flotas y presenta funciones que miden el exceso sobre el requerimiento estándar de las opciones del CSP en planes de demanda, opciones concretas y ciclos de fabricación. Dichas funciones pueden emplearse como función objetivo en problemas de optimización y como métricas ante una muli-secuencia de producción concreta.Preprin

Modelos y métricas para la versión robusta del Car Sequencing Problem con flotas de vehículos especiales

Partiendo del Car Sequencing Problem (CSP), introducimos el concepto de demanda parcial incierta, incorporando Flotas de vehículos especiales en un plan de demanda. Tras establecer las hipótesis de trabajo con Flotas, proponemos un modelo de programación lineal entera mixta (r-CSP) para satisfacer el máximo número de restricciones del CSP. Posteriormente, definimos multi-secuencia de producción y algunas métricas para evaluar su robustez. El r-CSP considera diversos escenarios de demanda y funciones para medir el requerimiento excesivo de opciones en programas de producción. Dichas funciones son válidas como objetivo en problemas de optimización y como métricas de robustez de multi-secuencias de producción.Postprint (published version

Integrating Tier-1 module suppliers in car sequencing problem

[EN] The objective of this study is to develop a car assembly sequence that is mutually agreed between car manufacturers and Tier-1 module suppliers such that overall modular supply chain efficiency is improved. In the literature so far, only constraints of car manufacturers have been considered in the car sequencing problem. However, an assembly sequence from car manufacturer imposes a module assembly sequence on Tier-1 module suppliers since their assembly activities are synchronous and in sequence with assembly line of that car manufacturer. An imposed assembly sequence defines a certain demand rate for Tier-1 module suppliers and has significant impacts on operational cost of these suppliers which ultimately affects the overall modular supply chain efficiency. In this paper, a heuristic approach has been introduced to generate a supplier cognizant car sequence which does not only provide better operational conditions for Tier-1 module suppliers, but also satisfies constraints of the car manufacturer.Jung, E. (2021). Integrating Tier-1 module suppliers in car sequencing problem. International Journal of Production Management and Engineering. 9(2):113-123. https://doi.org/10.4995/ijpme.2021.14985OJS11312392Benoist, T., Gardi, F., Megel, R., Nouioua, K. 2011. LocalSolver 1.x: a black-box local-search solver for 0-1 programming. 4OR - A Quarterly Journal of Operations Research, 9(299). https://doi.org/10.1007/s10288-011-0165-9Boysen, N., Fliedner, M., Scholl, A. 2009. Sequencing mixed-model assembly lines: survey, classification and model critique. European Journal of Operational Research, 192, 349-373. https://doi.org/10.1016/j.ejor.2007.09.013Doran, D. 2002. Manufacturing for synchronous supply: a case study of Ikeda Hoover Ltd. Integrated Manufacturing Systems, 13(1), 18-24. https://doi.org/10.1108/09576060210411477Drexl, A., Kimms, A. 2001. Sequencing JIT mixed-model assembly lines under station-load and part-usage constraints. Management Science, 47,(3), 480-491. https://doi.org/10.1287/mnsc.47.3.480.9777Estellon, B., Gardi, F. 2006. Car sequencing is NP-hard: a short proof. Journal of the Operational Research Society, 64, 1503-1504. https://doi.org/10.1057/jors.2011.165Estellon, B., Gardi, F., Nouioua, K. 2006. Large neighborhood improvements for solving car sequencing problems. RAIRO - Operations Research, 40(4), 355-379. https://doi.org/10.1051/ro:2007003Estellon, B., Gardi, F., Nouioua, K. 2008. Two local search approaches for solving real-life car sequencing problems. European Journal of Operational Research, 191(3), 928-944. https://doi.org/10.1016/j.ejor.2007.04.043Fredriksson, P., Gadde, L.E. 2005. Flexibility & rigidity in customization and build-to-order production. Science Direct Industrial Marketing Management, 34, 695-705. https://doi.org/10.1016/j.indmarman.2005.05.010Gagne, C., Gravel, M., Price, W. 2006. Solving real car sequencing problems with ant colony optimization. European Journal of Operational Research, 174(3), 1427-1448. https://doi.org/10.1016/j.ejor.2005.02.063Gottlieb, J., Puchta, M., Solnon., C. 2003. A study of greedy, local search and ant colony optimization approaches for car sequencing problems. In Applications of Evolutionary Computing, Lecture Notes in Computer Science, 2611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36605-9_23Hellingrath, B. 2008. Key principles of flexible production and logistics networks. Build to Order: The Road to the 5-Day Car, Springer-Verlag, London, 177-180. https://doi.org/10.1007/978-1-84800-225-8_10Larsson, A. 2002. The development and regional significance of the automotive industry: supplier parks in Western Europe. International Journal of Urban and Regional Research, 26(4), 767-784. https://doi.org/10.1111/1468-2427.00417Monden, Y. 1998. Toyota production systems: an integrated approach to just-in-time, 3rd edition. Industrial Engineering & Management Press, NorcossNiemann, J., Seisenberger, S., Schlegel, A., Putz, M. 2019. Development of a method to increase flexibility and changeability of supply contracts in the automotive industry. 52nd CIRP Conference on Manufacturing Systems, Ljubljana, Slovenia, June 12-14. https://doi.org/10.1016/j.procir.2019.03.045Parrello, B.D., Kabat, W.C., Wos, L. 1986. Job-shop scheduling using automated reasoning: a case study of the car-sequencing problem. Journal of Automated Reasoning, 2(1), 1-42. https://doi.org/10.1007/BF00246021Regin, J.C., Puget, J.F. 1997. A filtering algorithm for global sequencing constraints. In: Smolka G. (eds) Principles and Practice of Constraint Programming-CP97. Lecture Notes in Computer Science, 1330. Springer, Heidelberg. https://doi.org/10.1007/BFb0017428Solnon, C., Cung, V.D., Nguyen A., Artigues, C. 2008. The car sequencing problem: overview of state-of-the-art methods and industrial casestudy of the ROADEEF'2005 challenge problem. European Journal of Operational Research, 191, 912-927. https://doi.org/10.1016/j.ejor.2007.04.03

Definition and Evaluation of the difficulty of the Car Sequencing Problem

[EN] The Car Sequencing Problem is a relevant topic both in the literature and in practice. Typ-ically, the objective is to propose exact or heuristic procedures that calculate, in a reduced computational time, a solution that minimizes the number of violated sequencing rules. However, reaching a solution that does not violate any sequencing rule is not always pos-sible because although sequencing rules should be defined to smooth the workload, the evo-lution of the production mix or some other characteristics can influence the quality of the solutions. In this paper, a first definition of a sequencing rule difficulty is proposed and a statistical study is performed, which allow us to determine the impact of the number of rules, as well as to evaluate how difficult an instance is.[ES] El problema de secuenciación de unidades homogéneas es un caso muy tratado en la literatura donde en la mayor parte de los casos se intenta encontrar procedimientos exactos o heurísticos que permitan calcular en un tiempo computacional reducido una solución de la mejor calidad posible. La calidad de la solución se mide en función de las reglas de secuenciación violadas. Sin embargo, llegar a una solución que no viole ninguna restricción no siempre es posible ya que aunque las reglas de secuenciación se deberían definir para alisar la carga de trabajo, la evolución del mix de producción o las características de las reglas influyen sobre la calidad de las soluciones. En este articulo, se propone una medida para la dificultad de una regla de secuenciación cualquiera y determinar como el número de reglas de secuenciación y sus dificultades pueden servir para predecir en un conjunto de unidades a secuenciar como de difícil es conseguir una buena solución, y detectar los factores que hacen que un conjunto de productos sea más difícil de secuenciar.Maheut, J.; García Sabater, JP.; Morant Llorca, J.; Perea, F. (2016). Definición y Evaluación de la dificultad del problema de secuenciación de unidades homogéneas. Working Papers on Operations Management. 7(1):31-42. https://doi.org/10.4995/wpom.v7i1.5173SWORD314271Benoist, T. (2008). Soft car sequencing with colors: Lower bounds and optimality proofs. European Journal of Operational Research, 191(3), 957-971. doi:10.1016/j.ejor.2007.04.035Bergen, M. E., van Beek, P., & Carchrae, T. (2001). Constraint-Based Vehicle Assembly Line Sequencing. Lecture Notes in Computer Science, 88-99. doi:10.1007/3-540-45153-6_9Briant, O., Naddef, D., & Mounié, G. (2008). Greedy approach and multi-criteria simulated annealing for the car sequencing problem. European Journal of Operational Research, 191(3), 993-1003. doi:10.1016/j.ejor.2007.04.052Drexl, A., & Kimms, A. (2001). Sequencing JIT Mixed-Model Assembly Lines Under Station-Load and Part-Usage Constraints. Management Science, 47(3), 480-491. doi:10.1287/mnsc.47.3.480.9777Drexl, A., Kimms, A., & Matthießen, L. (2006). Algorithms for the car sequencing and the level scheduling problem. Journal of Scheduling, 9(2), 153-176. doi:10.1007/s10951-006-7186-9Fisher, M. L., & Ittner, C. D. (1999). The Impact of Product Variety on Automobile Assembly Operations: Empirical Evidence and Simulation Analysis. Management Science, 45(6), 771-786. doi:10.1287/mnsc.45.6.771Fliedner, M., & Boysen, N. (2008). Solving the car sequencing problem via Branch & Bound. European Journal of Operational Research, 191(3), 1023-1042. doi:10.1016/j.ejor.2007.04.045Gent, I. P., & Walsh, T. (1999). CSPlib: A Benchmark Library for Constraints. Lecture Notes in Computer Science, 480-481. doi:10.1007/978-3-540-48085-3_36Golle, U., Boysen, N., & Rothlauf, F. (2010). Analysis and design of sequencing rules for car sequencing. European Journal of Operational Research, 206(3), 579-585. doi:10.1016/j.ejor.2010.03.019Gottlieb, J., Puchta, M., & Solnon, C. (2003). A Study of Greedy, Local Search, and Ant Colony Optimization Approaches for Car Sequencing Problems. Applications of Evolutionary Computing, 246-257. doi:10.1007/3-540-36605-9_23Gravel, M., Gagné, C., & Price, W. L. (2005). Review and comparison of three methods for the solution of the car sequencing problem. Journal of the Operational Research Society, 56(11), 1287-1295. doi:10.1057/palgrave.jors.2601955Kis, T. (2004). On the complexity of the car sequencing problem. Operations Research Letters, 32(4), 331-335. doi:10.1016/j.orl.2003.09.003Maheut, J., & Garcia-Sabater, J. P. (2015). Reglas de secuenciación en el problema de secuenciación en línea de montaje con mezcla de modelos. WPOM-Working Papers on Operations Management, 6(2), 39. doi:10.4995/wpom.v6i2.3525Parrello, B., Kabat, W., & Wos, L. (1986). Job-shop scheduling using automated reasoning: A case study of the car-sequencing problem. Journal of Automated Reasoning, 2(1). doi:10.1007/bf00246021Puchta, M., & Gottlieb, J. (2002). Solving Car Sequencing Problems by Local Optimization. Applications of Evolutionary Computing, 132-142. doi:10.1007/3-540-46004-7_14Solnon, C. (2000). Solving permutation constraint satisfaction problems with artificial ants. In ECAI (Vol. 2000, pp. 118–122)

Approximate Submodularity and Its Implications in Discrete Optimization

Submodularity, a discrete analog of convexity, is a key property in discrete optimization that features in the construction of valid inequalities and analysis of the greedy algorithm. In this paper, we broaden the approximate submodularity literature, which so far has largely focused on variants of greedy algorithms and iterative approaches. We define metrics that quantify approximate submodularity and use these metrics to derive properties about approximate submodularity preservation and extensions of set functions. We show that previous analyses of mixed-integer sets, such as the submodular knapsack polytope, can be extended to the approximate submodularity setting. In addition, we demonstrate that greedy algorithm bounds based on our notions of approximate submodularity are competitive with those in the literature, which we illustrate using a generalization of the uncapacitated facility location problem

Heuristic Procedures to Solve Sequencing and Scheduling Problems in Automobile Industry

With the growing trend for greater product variety, mixed-model assembly nowadays is commonly employed in many industries, which can enable just-in-time production for a production system with high variety. Efficient production scheduling and sequencing is important to achieve the overall material supply, production, and distribution efficiency around the mixed-model assembly line. This research addresses production scheduling and sequencing on a mixed-model assembly line for products with multiple product options, considering multiple objectives with regard to material supply, manufacturing, and product distribution. This research also addresses plant assignment for a product with multiple product options as a prior step to scheduling and sequencing for a mixed-model assembly line. This dissertation is organized into three parts based on three papers. Introduction and literature review Part 1. In an automobile assembly plant many product options often need to be considered in sequencing an assembly line with which multiple objectives often need to be considered. A general heuristic procedure is developed for sequencing automobile assembly lines considering multiple options. The procedure uses the construction, swapping, and re-sequencing steps, and a limited search for sequencing automobile assembly lines considering multiple options. Part 2. In a supply chain, production scheduling and finished goods distribution have been increasingly considered in an integrated manner to achieve an overall best efficiency. This research presents a heuristic procedure to achieve an integrated consideration of production scheduling and product distribution with production smoothing for the automobile just-in-time production assembly line. A meta-heuristic procedure is also developed for improving the heuristic solution. Part 3. For a product that can be manufactured in multiple facilities, assigning orders to the facility is a common problem faced by industry considering production, material constraints, and other supply-chain related constraints. This paper addresses products with multiple product options for plant assignment with regard to multiple constraints at individual plants in order to minimize transportation costs and costs of assignment infeasibility. A series of binary- and mixed-integer programming models are presented, and a decision support tool based on optimization models is presented with a case study. Summary and conclusion

Solving Many-Objective Car Sequencing Problems on Two-Sided Assembly Lines Using an Adaptive Differential Evolutionary Algorithm

The car sequencing problem (CSP) is addressed in this paper. The original environment of the CSP is modified to reflect real practices in the automotive industry by replacing the use of single-sided straight assembly lines with two-sided assembly lines. As a result, the problem becomes more complex caused by many additional constraints to be considered. Six objectives (i.e. many objectives) are optimised simultaneously including minimising the number of colour changes, minimising utility work, minimising total idle time, minimising the total number of ratio constraint violations and minimising total production rate variation. The algorithm namely adaptive multi-objective evolutionary algorithm based on decomposition hybridised with differential evolution algorithm (AMOEA/D-DE) is developed to tackle this problem. The performances in Pareto sense of AMOEA/D-DE are compared with COIN-E, MODE, MODE/D and MOEA/D. The results indicate that AMOEA/D-DE outperforms the others in terms of convergence-related metrics

Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints

Cable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring Problem (CTW) as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP) solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and is accepted for inclusion in the MiniZinc challenge 2020