Car Sequencing Problem Research Articles

Modélisation du problème général d'ordonnancement de véhicules sur une ligne de production et d'assemblage

Plusieurs formulations du probleme d'ordonnancement sur une ligne de fabrication multimodele ont ete proposees. L'exemple le plus cite d'une production de masse fortement diversifiee est celui des vehicules. Les hypotheses sur lesquelles ces formulations reposent sont souvent restrictives, limitant ainsi leur portee. Nous proposons ici une formulation generale du probleme d'ordonnancement qui integre le cout resultant d'un appel ponctuel a des operateurs venant en renfort d'une equipe (et donc presents en meme temps qu'elle), et certains couts de lancement (cout des purges dans l'atelier de peinture, par exemple). Le modele lineaire obtenu permet une description explicite et complete de ce probleme complexe.

Algorithms for the car sequencing and the level scheduling problem

This paper deals with two most important problems arising in sequencing mixed-model assembly lines. One problem is to keep the line's workstations loads as constant as possible (the 'car sequencing problem') while the other is to keep the usage rate of all parts fed into the final assembly as constant as possible (the 'level scheduling problem'). The first problem is a difficult constraint-satisfaction problem while the second requires to optimize a nonlinear objective function. The contribution of this paper is twofold: First, we describe a branching scheme and bounding algorithms for the computation of feasible sequences for the car sequencing problem. Second, we present an algorithm which can optimize a level scheduling objective while taking care of the car sequencing constraints. Computational results are presented which show that feasible sequences can be obtained quickly for large problem instances.

Review and comparison of three methods for the solution of the car sequencing problem

The car sequencing problem is the ordering of the production of a list of vehicles which are of the same type, but which may have options or variations that require higher work content and longer operation times for at least one assembly workstation. A feasible production sequence is one that does not schedule vehicles with options in such a way that one or more workstations are overloaded. In variations of the problem, other constraints may apply. We describe and compare three approaches to the modeling and solution of this problem. The first uses integer programming to model and solve the problem. The second approaches the question as a constraint satisfaction problem (CSP). The third method proposes an adaptation of the Ant Colony Optimization for the car sequencing problem. Test-problems are drawn from CSPLib, a publicly available set of problems available through the Internet. We quote results drawn both from our own work and from other research. The literature review is not intended to be exhaustive but we have sought to include representative examples and the more recent work. Our conclusions bear on likely research avenues for the solution of problems of practical size and complexity. A new set of larger benchmark problems was generated and solved. These problems are available to other researchers who may wish to solve them using their own methods.

On the complexity of the car sequencing problem

In this note we give an easier proof of the known result that the car sequencing problem is NP-hard, and point out that it is NP-hard in the strong sense. We show that a previous claim of NP-completeness is incorrect, and instead we give a sufficient condition of membership of NP. We also provide a pseudo-polynomial algorithm for a special case.

Sequencing JIT Mixed-Model Assembly Lines Under Station-Load and Part-Usage Constraints

This paper deals with two most important problems, from both practical and theoretical standpoints, arising in sequencing mixed-model assembly lines. Such lines have become core components of modern repetitive manufacturing, and just-in-time (JIT) manufacturing in particular. One problem is to keep the usage rate of all parts fed into the final assembly as constant as possible (the “level-scheduling problem”), while the other is to keep the line's workstation loads as constant as possible (the “car-sequencing problem”). In this paper the combined problem is formulated as a single-integer programming model. The LP-relaxation of this model is solved by column-generation techniques. The results of an experimental evaluation show that the lower bounds are tight.

Traditional heuristic versus Hopfield neural network approaches to a car sequencing problem

This paper considers the problem of optimally sequencing different car models along an assembly line according to some contiguity constraints, while ensuring that the demands for each of the models are satisfied. This car sequencing problem (CSP) is a practical NP-hard combinatorial optimisation problem. The CSP is formulated as a nonlinear integer programming problem and it is shown that exact solutions to the problem are difficult to obtain due to the indefinite quadratic form of the CSP objective function. Two traditional heuristics (steepest descent and simulated annealing) are employed to solve the CSP approximately. Several Hopfield neural network (HNN) approaches are also presented. The process of mapping an optimisation problem onto a HNN is demonstrated explicitly, and modifications to the existing neural approaches are presented which guarantee feasibility of solutions. Further modifications are proposed to improve the solution quality by permitting escape from local minima in an attempt to locate the global optimum. Results from all solutions techniques are compared on a set of instances of the CSP, and conclusions drawn.

Sequencing Mixed-Model Assembly Lines: A Multi-Criteria and Flexible Approach

Abstract This paper presents a flexible and multi-criteria approach to sequence Mixed-Model Assembly Lines according to two kinds of goals : smoothing the flow of work for resources and other sequencing goals (Part Usage Goal, Car Sequencing Problem.). This can be achieved thanks to several iterating and interactive optimization methods. These methods use an integrated data model which includes multi-station resources, any assembly line where products move simultaneously, and potential goals. By this way, release and due dates for jobs can be computed, and optimization criteria can be defined and dynamically linked to products or resources, according to circumstances.

Tackling Car Sequencing Problems Using a Generic Genetic Algorithm

The car sequencing problem (CarSP) was seen as a challenge to artificial intelligence. The CarSP is a version of the job-shop scheduling problem, which is known to be NP-complete. The task in the CarSP is to schedule a given number of cars (of different types) in a sequence to allow the teams in each workstation on the assembly line to fit the required options (e.g. radio, sunroof) on the cars within the capacity of that workstation. In unsolvable problems, one would like to minimize the penalties associated with the violation of the capacity constraints. Previous attempts to tackle the problem either have been unsuccessful or have been restricted to solvable CarSPs only. In this paper, we report on promising results in applying a generic genetic algorithm, which we call GAcSP, to tackle both solvable and unsolvable CarSPs.

Job-shop scheduling using automated reasoning: A case study of the car-sequencing problem

The ‘job-shop scheduling problem’ is known to be NP-complete. The version of interest in this paper concerns an assembly line designed to produce various cars, each of which requires a (possibly different) set of options. The combinatorics of the problem preclude seeking a maximal solution. Nevertheless, because of the underlying economic considerations, an approach that yields a ‘good’ sequence of cars, given the specific required options for each, would be most valuable. In this paper, we focus on an environment for seeking, studying, and evaluating approaches for yielding good sequences. The environment we discuss relies on the automated reasoning program ITP. Automated reasoning programs of this type offer a wide variety of ways to reason, strategies for controlling the reasoning, and auxiliary procedures that contribute to the effective study of problems of this kind. We view the study presented in this paper as a prototype of what can be accomplished with the assistance of an automated reasoning program.