Modeling and Solution Methodologies for Mixed-Model Sequencing in Automobile Industry

The global competitive environment leads companies to consider how to produce high-quality products at a lower cost. Mixed-model assembly lines are often designed such that average station work satisfies the time allocated to each station, but some models with work-intensive options require more than the allocated time. Sequencing varying models in a mixed-model assembly line, mixed-model sequencing (MMS), is a short-term decision problem that has the objective of preventing line stoppage resulting from a station work overload. Accordingly, a good allocation of models is necessary to avoid work overload. The car sequencing problem (CSP) is a specific version of the MMS that minimizes work overload by controlling the sequence of models. In order to do that, CSP restricts the number of work-intensive options by applying capacity rules. Consequently, the objective is to find the sequence with the minimum number of capacity rule violations. In this dissertation, we provide exact and heuristic solution approaches to solve different variants of MMS and CSP. First, we provide five improved lower bounds for benchmark CSP instances by solving problems optimally with a subset of options. We present four local search metaheuristics adapting efficient transformation operators to solve CSP. The computational experiments show that the Adaptive Local Search provides a significant advantage by not requiring tuning on the operator weights due to its adaptive control mechanism. Additionally, we propose a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provide improvements to the second-stage problem. To tackle the exponential number of scenarios, we employ the sample average approximation approach and two solution methodologies. On one hand, we develop an L-shaped decomposition-based algorithm, where the computational experiments show its superiority over solving the deterministic equivalent formulation with an off-the-shelf solver. We also provide a tabu search algorithm in addition to a greedy heuristic to tackle case study instances inspired by our car manufacturer partner. Numerical experiments show that the proposed solution methodologies generate high-quality solutions by utilizing a sample of scenarios. Particularly, a robust sequence that is generated by considering car failures can decrease the expected work overload by more than 20\% for both small- and large-sized instances. To the best of our knowledge, this is the first study that considers stochastic failures of products in MMS. Moreover, we propose a two-stage stochastic program and formulation improvements for a mixed-model sequencing problem with stochastic product failures and integrated reinsertion process. We present a bi-objective evolutionary optimization algorithm, a two-stage bi-objective local search algorithm, and a hybrid local search integrated evolutionary optimization algorithm to tackle the proposed problem. Numerical experiments over a case study show that while the hybrid algorithm provides a better exploration of the Pareto front representation and more reliable solutions in terms of waiting time of failed vehicles, the local search algorithm provides more reliable solutions in terms of work overload objective. Finally, dynamic reinsertion simulations are executed over industry-inspired instances to assess the quality of the solutions. The results show that integrating the reinsertion process in addition to considering vehicle failures can keep reducing the work overload by around 20\% while significantly decreasing the waiting time of the failed vehicles

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)

The Use of Persistent Explorer Artificial Ants to Solve the Car Sequencing Problem

Ant Colony Optimisation is a widely researched meta-heuristic which uses the behaviour and pheromone laying activities of foraging ants to find paths through graphs. Since the early 1990’s this approach has been applied to problems such as the Travelling Salesman Problem, Quadratic Assignment Problem and Car Sequencing Problem to name a few. The ACO is not without its problems it tends to find good local optima and not good global optima. To solve this problem modifications have been made to the original ACO such as the Max Min ant system. Other solutions involve combining it with Evolutionary Algorithms to improve results. These improvements focused on the pheromone structures. Inspired by other swarm intelligence algorithms this work attempts to develop a new type of ant to explore different problem paths and thus improve the algorithm. The exploring ant would persist throughout the running time of the algorithm and explore unused paths. The Car Sequencing problem was chosen as a method to test the Exploring Ants. An existing algorithm was modified to implement the explorers. The results show that for the car sequencing problem the exploring ants did not have any positive impact, as the paths they chose were always sub-optimal

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

Free and regular mixed-model sequences by a linear program-assisted hybrid algorithm GRASP-LP

A linear program-assisted hybrid algorithm (GRASP-LP) is presented to solve a mixed-model sequencing problem in an assembly line. The issue of the problem is to obtain manufacturing sequences of product models with the minimum work overload, allowing the free interruption of operations at workstations and preserving the production mix. The implemented GRASP-LP is compared with other procedures through a case study linked with the Nissan’ Engine Plant from Barcelona.Peer ReviewedPostprint (author's final draft