An exact algorithm for the mixed-model level scheduling problem

The Monden Problem, also known as the Output Rate Variation Problem, is one of the original formulations for mixed-model assembly line-level scheduling problems in a just-in-time system. In this paper, we develop a new branch-and-bound procedure for the problem that uses several new and previously proposed lower and upper bounds. The algorithm also includes several dominance rules that leverage the symmetry in the problem as well as a new labelling procedure that avoids repeated exploration of previously examined partial solutions. The branching strategy exploits the capabilities of current multiprocessor computers by exploring the search tree in a parallel fashion. The algorithm has been tested on several sets of instances from the literature and is able to optimally solve problems that are double the size of those addressed by other procedures previously reported in the literature.Preprin

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)

Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table

Balancing and Sequencing of Mixed Model Assembly Lines

Assembly lines are cost efficient production systems that mass produce identical products. Due to customer demand, manufacturers use mixed model assembly lines to produce customized products that are not identical. To stay efficient, management decisions for the line such as number of workers and assembly task assignment to stations need to be optimized to increase throughput and decrease cost. In each station, the work to be done depends on the exact product configuration, and is not consistent across all products. In this dissertation, a mixed model line balancing integer program (IP) that considers parallel workers, zoning, task assignment, and ergonomic constraints with the objective of minimizing the number of workers is proposed. Upon observing the limitation of the IP, a Constraint Programming (CP) model that is based on CPLEX CP Optimizer is developed to solve larger assembly line balancing problems. Data from an automotive OEM are used to assess the performance of both the MIP and CP models. Using the OEM data, we show that the CP model outperforms the IP model for bigger problems. A sensitivity analysis is done to assess the cost of enforcing some of the constraint on the computation complexity and the amount of violations to these constraints once they are disabled. Results show that some of the constraints are helpful in reducing the computation time. Specifically, the assignment constraints in which decision variables are fixed or bounded result in a smaller search space. Finally, since the line balance for mixed model is based on task duration averages, we propose a mixed model sequencing model that minimize the number of overload situation that might occur due to variability in tasks times by providing an optimal production sequence. We consider the skip-policy to manage overload situations and allow interactions between stations via workers swimming. An IP model formulation is proposed and a GRASP solution heuristic is developed to solve the problem. Data from the literature are used to assess the performance of the developed heuristic and to show the benefit of swimming in reducing work overload situations

Mixed-model Sequencing with Stochastic Failures: A Case Study for Automobile Industry

In the automotive industry, the sequence of vehicles to be produced is determined ahead of the production day. However, there are some vehicles, failed vehicles, that cannot be produced due to some reasons such as material shortage or paint failure. These vehicles are pulled out of the sequence, and the vehicles in the succeeding positions are moved forward, potentially resulting in challenges for logistics or other scheduling concerns. This paper proposes a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provides 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. Moreover, we 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.Comment: 30 pages, 9 figure

Applications of simulation and optimization techniques in optimizing room and pillar mining systems

The goal of this research was to apply simulation and optimization techniques in solving mine design and production sequencing problems in room and pillar mines (R&P). The specific objectives were to: (1) apply Discrete Event Simulation (DES) to determine the optimal width of coal R&P panels under specific mining conditions; (2) investigate if the shuttle car fleet size used to mine a particular panel width is optimal in different segments of the panel; (3) test the hypothesis that binary integer linear programming (BILP) can be used to account for mining risk in R&P long range mine production sequencing; and (4) test the hypothesis that heuristic pre-processing can be used to increase the computational efficiency of branch and cut solutions to the BILP problem of R&P mine sequencing. A DES model of an existing R&P mine was built, that is capable of evaluating the effect of variable panel width on the unit cost and productivity of the mining system. For the system and operating conditions evaluated, the result showed that a 17-entry panel is optimal. The result also showed that, for the 17-entry panel studied, four shuttle cars per continuous miner is optimal for 80% of the defined mining segments with three shuttle cars optimal for the other 20%. The research successfully incorporated risk management into the R&P production sequencing problem, modeling the problem as BILP with block aggregation to minimize computational complexity. Three pre-processing algorithms based on generating problem-specific cutting planes were developed and used to investigate whether heuristic pre-processing can increase computational efficiency. Although, in some instances, the implemented pre-processing algorithms improved computational efficiency, the overall computational times were higher due to the high cost of generating the cutting planes --Abstract, page iii

Car Sequencing with respect to Regular Expressions and Linear Bounds

In this paper we introduce a new model and a computational approach for sequencing assembly lines with two types of constraints: (i) patterns described by regular expressions and (ii) linear bounds on the number of certain products that may occur in pre-specified intervals. If we restrict the problem to the second type of constraints only we obtain a generalization of the familiar car sequencing problem, whereas constraints of type (i) may be useful to add extra structure. Constraints of both types may have priorities and can be violated, and a Pareto optimal solution is sought minimizing the violation of constraints in the given priority order. We describe a computational method based on mathematical programming and genetic algorithms for finding suboptimal solutions

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