Car Sequencing Problem Research Articles

The maximum length car sequencing problem

This paper introduces the maximum length car sequencing problem to support the assembly operations of a multinational automotive company. We propose an integer linear programming (ILP) formulation to schedule the maximum number of cars without violating the so-called option constraints. In addition, we present valid combinatorial lower and upper bounds, which can be calculated in less than 0.01 s, as well as binary and iterative search algorithms to solve the problem when good primal bounds are not readily available. To quickly obtain high-quality solutions, we devise an effective iterated local search algorithm, and we use the heuristic solutions as warm start to further enhance the performance of the exact methods. Computational results demonstrate that relatively low gaps were achieved for benchmark instances within a time limit of ten minutes. We also conducted an instance space analysis to identify the features that make the problem more difficult to solve. Moreover, the instances reflecting the company’s needs could be solved to optimality in less than a second. Finally, simulations with real-world demands, divided into shifts, were conducted over a period of four months. In this case, we use the proposed ILP model in all shifts except the last one of each month, for which we employ an alternative ILP model to sequence the unscheduled cars, adjusting the pace of the assembly line in an optimal fashion. The results pointed out that the latter was necessary in only one of the months.

Flexible Programming Model for Efficient Workload Control in the Car Sequencing Problem

In the era of increasing product customization, mixed-model assembly lines (MMALs) stand out, enabling the efficient production of diverse products. However, products with work-intensive characteristics may result in work overload when sequenced closely. The Car Sequencing Problem (CSP) utilizes spacing rules to address this challenge in MMALs. This paper presents a flexible CSP mixed-integer programming model within the context of flexible (fuzzy) linear programming. The results demonstrate that the proposed method empowers decision-makers to effectively manage workloads and prevent intolerable work overloads in MMALs through efficient control of sequencing rule violations.

Solving a Real-Life Stochastic Car Batching and Sequencing Problem With Dynamic Programming Approaches

Solving a Real-Life Stochastic Car Batching and Sequencing Problem With Dynamic Programming Approaches

A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers

In this paper, we research the dynamic car sequencing problem with car body buffer (DCSPwB) in automotive mixed-flow assembly. The objective is to reorder the sequence of cars in the paint shop using the post-painted body buffers to minimize the violation of constraint rules and the time cost of sequencing in the general assembly shop. We establish a mathematical model of DCSPwB and propose a decomposition-based algorithm based on the dynamic genetic algorithm (DGA) and greedy algorithm for delayed car release (PGDA). Experiments are conducted based on production orders from actual companies, and the results are compared with the solution results of the underlying genetic algorithm (GA) and greedy algorithm (GDA) to verify the effectiveness of the algorithm. In addition, the effect of buffer capacity on DCSPwB is investigated.

Adaptive local search algorithm for solving car sequencing problem

The global competitive environment leads companies to consider how to produce high-quality products at a lower cost. Mixed-model assembly lines (MMAL) 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 is the 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 mixed-model sequencing problem that minimizes the 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 study, we show that exact solution procedures are insufficient for application in industry. however, we provide five improved lower bounds for CSPLib instances by solving problems optimally with a subset of options. Additionally, we present four local search metaheuristics that are commonly used to solve CSP. The local search algorithms are compared over CSP benchmark instances, including CSPLib and ROADEF Challenge 2005. The computational experiments show that an Adaptive Local Search (ALS) provides a significant advantage by not requiring tuning on the operator weights due to its adaptive control mechanism. Moreover, results show that the algorithmic effort should focus on randomly exploring more non-deteriorated solutions instead of systematic search or spending time visiting deteriorated solutions to escape local optima.

Nash equilibrium as a tool for the Car Sequencing Problem 4.0

This paper introduces a new concept to solve car sequencing problem called the Car Sequencing Problem 4.0, focuses the paint shop. The problem of effective car sequencing in the paint shop is caused by the specifics of the production process itself and the structure of the production line. Sequencing of cars as required by the painting process is justified economically. The main goal is to minimize the number of costly changeovers of the painting guns because of color changes and to synchronize those with periodic cleanings, forced by technological requirements. For this purpose, a buffer located in the paint shop is applied. In this paper a game theoretic framework is presented to analyze the problem. Three games are introduced: Buffer Slot Assignment Game–Buffer-OutShuttle Game called the BSAG-BOSG, In–Out Shuttle Game and its modification called modified In–Out Shuttle Game. Based on the simulations performed the efficiency of the algorithms is verified using several datasets.

Instance space analysis for the car sequencing problem

We investigate an important research question for solving the car sequencing problem, that is, which characteristics make an instance hard to solve? To do so, we carry out an instance space analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance. In order to visualize the instance space, the feature vectors are projected onto a 2-D space using dimensionality reduction techniques. The resulting 2-D visualizations provide new insights into the characteristics of the instances used for testing and how these characteristics influence the behaviours of an optimization algorithm. This analysis guides us in constructing a new set of benchmark instances with a range of instance properties. We demonstrate that these new instances are more diverse than the previous benchmarks, including some instances that are significantly more difficult to solve. We introduce two new algorithms for solving the car sequencing problem and compare them with four existing methods from the literature. Our new algorithms are shown to perform competitively for this problem but no single algorithm can outperform all others over all instances. This observation motivates us to build an algorithm selection model based on machine learning, to identify the niche in the instance space that an algorithm is expected to perform well on. Our analysis helps to understand problem hardness and select an appropriate algorithm for solving a given car sequencing problem instance.

Application of Strategies on NSGAII for Searching of Optimal Solutions to the Car Sequencing Problem

One of the main conflicts in a car production plant is to deliver the orders received daily in a timely manner, which are not uniform and involve a large amount of human and material resources. The car sequencing problem is a NP-Hard problem that consists of finding the sequence of cars that minimizes the number of constraint violations in an assembly line. The problem can be approached from a mono-objective or multi-objective point of view. The objective of this paper is to treat a case study of this problem, presented at ROADEF 2005, from the multi-objective Pareto approach, taking the NSGAII algorithm as a basis for a proposal scheme and verifying its feasibility. A systematic and general improvement of the quality of the final Pareto fronts is verified, and the results of the implementation of a strategy scheme that consists of the initialization of the population guided by local search, and specialized crossover and mutation operators are reported. These results allow us to give continuity to the generation of an optimization proposal for the vehicle sequencing problem.

Task package division method for the integrated scheduling framework of mixed model car-sequencing problem

Car mixed model production can realize that cars with different models can be produced in a same production line at the same time, which is an effective way to respond the diversified market demand timely. How to design the optimal and feasible car sequences for multi car workshops is a key point for each car manufacturing enterprise. This paper presents an integrated scheduling framework of mixed model car-sequencing problem that includes order sequencing, task package division, and integrated scheduling of mixed model workshops. In this paper, task package division problem as the middle link of the integrated scheduling framework is concerned and investigated, considering the stereo garbage inventory and subsequent scheduling factors of multi workshops. Then, a mathematic model is constructed optimizing three objectives: (1) maximize the proportion of extra inventory cars in buffer; (2) minimize the number of car type changeover and color changeover in the task package; (3) minimize the difference of car type and quantity in the task package. Furthermore, an evolutionary algorithm based on solution information is presented to solve the model. In the proposed algorithm, three strategies adopting domain knowledge and solution information generated on iteration process are utilized to improve the searching ability and efficiency of the algorithm. The validity of the algorithm is verified by a real case. The computational results reveal that the proposed model and algorithm obtain appropriate results and have the potential to be applied to other similar problems.

Heuristic approaches for the car sequencing problems with block batches

Motivated by the practical supply chain management of the automobile industry, we study the car sequencing problem (CSP) that minimizes the conflicts occur when sequentially manufacturing cars on an assembly line. The CSP is a well-established problem, subject to the paint batching constraints to decrease the energy consumption for color changeovers and production rate constraints in the assembly shop to ensure a smooth usage of car options. However, the existing solution algorithms to this problem do not take into account the block batches, which desires a consecutive production batch of cars requiring a certain option. This requirement often occurs when specialized labor time window is short in the customized car production scenario, and renders additional complexities to the traditional car sequencing problem. In this paper, we present a novel model to deal with these constraints and simultaneously generate the sequencing and replenishment decisions. Besides, we develop two math-heuristic algorithms to solve the proposed large-scale CSP. The presented heuristics are on the basis of relax-and-fix procedures, fix-and-optimize procedures and adaptive variable neighborhood search. To solve the large-sized instances (commercial solvers, i.e., Cplex, cannot obtain a feasible result within 1 h), we design and implement a reinforced parameter tuning mechanism to dynamically select the parameter values, so as to speed up the search process. The proposed models and heuristics are tested on representative instances generated from the benchmark in the literature (CSPLib), as well as large-sized instances generated from real-world cases. We report on extensive computational experiments and provide basic managerial insights into the planning process.

Car sequencing problem with cross-ratio constraints: A multi-start parallel local search

Car sequencing is a popular approach to implicitly improve the short-term balancing of a mixed-model assembly line in real-world applications. In this paper, based on a real-world case from a truck final assembly line, we study this problem considering cross-ratio constraints which concern the limitations of some dependent features of products. A mathematical programming model is developed to minimize the total weighted penalty of disrespecting the independent and dependent limitations. Since the problem is NP-hard, a multi-start parallel local search is developed to efficiently solve the problem. A comparison of the results illustrates the effectiveness of using the proposed algorithm.

Integrating Tier-1 module suppliers in car sequencing problem

<p class="Abstract"><span lang="EN-GB">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.</span></p>

Two approaches to car sequencing in the paint shop

The problem of car sequencing has been considered in the literature many times, but very often with the assumption of many simplifications, which meant that the discussed issue was far from the problems occurring in reality. The article presents an attempt to capture the real problem of sequencing, in particular in paint shop, because from the point of view of economic indicators, painting process is today a complex, multistage, extremely energy consuming and cost intensive operation. The main goal is therefore to minimize the number of costly changeovers of painting guns, resulting from color changes and synchronize those with periodic cleanings, forced by technological requirements. For this purpose, a buffer located in the paint shop is applied. In the paper a game-theoretic framework is presented to analyze the considered problem. Two games: Buffer Slot Assignment Game and Buffer-OutShuttle are compared with algorithms based on priority rules. Based on the performed simulations the effectivity of presented algorithms is verified using several datasets.

Mathematical modeling and heuristic approaches for a multi-stage car sequencing problem

This paper addresses the scheduling problem in three successive processes in car production including the paint shop, painted body storage (PBS) and the assembly shop. The paint shop, which aims to reduce the costs for color changes, is connected to the final assembly shop, which aims to level the usage of the options. A linear PBS is set in between to change the sequence from the upstream shop to the downstream shop. The joint sequencing problem is formulated as a mixed integer linear programming (MILP) model and some properties including the lower bounds are presented. A structural architecture is designed to solve the large-scale real-life instances, and several meta-heuristic algorithms are embedded in the architecture to enhance the ability of finding good solutions. Numerical experiments validate the quality of the proposed algorithms.

Estudio de factibilidad para la aplicación de algoritmos de estimación de distribución al problema de secuenciación de vehículos

The main objective of an automobile production plant is to deliver on time and form the orders that are received daily. These orders are not homogeneous since they involve large quantities of cars that generally belong to different models and must be painted in different colors. The car sequencing problem that takes these characteristics into account was proposed by the Renault Company in 2005 as part of the ROADEF Challenge. This problem is NP-Hard and various techniques have been proposed to solve it, from exact methods to different heuristic algorithms. This work presents a feasibility study to apply two Distribution Estimation Algorithms (EDAs) to solve this problem. In addition, three important aspects are presented: the adaptation process of the algorithms, a technique for the execution of the algorithms called the "Stepped Approach with Discard" and a methodology that involves tolerance in the substitution of the individuals. The results obtained by the algorithms are also shown. The analysis of the results shows the algorithms adaptation process and the adjustments that can be made to improve their competence with the state of art.

A Multi-Objective Cuckoo Search Algorithm Based on the Record Matrix for a Mixed-Model Assembly Line Car-Sequencing Problem

In the car-sequencing problem of mixed-model assembly lines, a series of cars with different model types will be put into the assembly line in a certain order considering a variety of goals and constraints. In this paper, a multi-objective cuckoo search algorithm based on the record matrix is proposed to solve this problem. In this algorithm, the factors, including the variation of parts usage rates, variation of workstation workload, idle time, overload time, and model switching cost are considered. The record matrix proposed in this paper is utilized to record the characteristic information of the optimal solutions and historical solutions. Meanwhile, two search strategies based on the record matrix are proposed to enhance the ability of local search and global search in the algorithm. The proposed algorithm is verified by a real case. The results show that the proposed model and algorithm have good results, and they have the potential to address other similar problems.

Constructive metaheuristics for solving the Car Sequencing Problem under uncertain partial demand

The car sequencing problem is a well established problem that models the conflicts arising from scheduling cars into an assembly line. However, the existing approaches to this problem do not consider non-regular or out-of-catalog vehicles, which are commonly manufactured in assembly lines. In this paper, we propose a new problem definition that deals with non-regular vehicles. This novel model is called robust Car Sequencing Problem. We model this realistic optimization problem using scenarios defined by different production plans. The problem can be solved by measuring the impact of the plans’ variability and by observing the violations of the problem constraints that appear when switching from one plan to another. In addition to our model formulation, we design and implement a set of constructive metaheuristics to tackle the traditional and the novel robust car sequencing problem. The selected metaheuristics are based on the greedy randomized adaptive search procedure, ant colony optimization, and variable neighborhood search. We have generated compatible instances from the main benchmark in the literature (CSPLib) and we have applied these metaheuristics for solving the new robust problem extension. We complement the experimental study by applying a post hoc statistical analysis for detecting statistically relevant differences between the metaheuristics performance. Our results show that a memetic ant colony optimization with local search is the best method since it performs well for every problem instance regardless of the difficulty of the problem (i.e., constraints and instance size).

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

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

Robust Car Sequencing Problem: Description, models and metrics

The concept of partial demand uncertainty is introduced from the car sequencing problem (CSP) and incorporates special vehicle fleets in a demand plan. After establishing the working hypotheses with fleets, a mixed integer linear programming model, robust car sequencing problem (r-CSP), is proposed to satisfy the maximum number of CSP restrictions. Subsequently, multi-sequence production and metrics to evaluate its robustness are defined. The r-CSP considers various demand scenarios and functions to measure the excess of optional requirements in production programs. These functions are valid as objectives in optimization problems and as multi-sequence pro-duction robustness metrics. Keywords : Assembly lines, Sequencing, Car Sequencing Problem, Vehicle Fleets, Robust Optimization, Production Mix, Demand uncertainty.

Nadążne sterowanie procesem sekwencjonowania karoserii na wydziale lakierni

A modified method of follow-up production control that can be used in a multi-version car body sequencing process at the paint shop department is presented. The actual structure of the paint shop along with the buffer was subjected to tests (Car Sequencing Problem 4.0). The main goals of the research were to minimize the number of changeovers resulting from color changes and to synchronize these changeovers with forced, periodic cleaning of paint guns.