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

Abstract

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.

The Car Resequencing Problem with Pull-Off Tables

“…All algorithms were implemented with VB.Net. Throughout the experiments, violations of instances in the first set are measured using the approach by Fliedner and Boysen (2008) and violations of the second set are counted with the Sliding-Window approach (Gravel, Gagne, and Price 2005). The experiments run on a Pentium 2.5 Ghz processor with 2GB RAM.…”

“…T t=1 (Gravel, Gagne, and Price 2005), to distinguish between hard-and soft-sequencing rules (Solnon, Cung, Nguyen, and Artigues 2008), to pursue alternative resequencing objectives like leveling the required material (Drexl and Kimms 2001) while avoiding rule violations or to minimize the number of material deviations between the resulting sequence and an original planned sequence. An example for such a model extension is presented in section 6.…”

“…Note that our basic graph structure can also be applied for solving related resequencing problems. As the adoptions are truly straightforward, e.g., to incorporate other functions for counting rule violations like the sliding-window technique (Gravel, Gagne, and Price 2005), to distinguish between hard-and softsequencing rules (Solnon, Cung, Nguyen, and Artigues 2008) or to pursue alternative resequencing objectives like leveling the required material (Drexl and Kimms 2001) while avoiding rule violations, we abstain from a detailed description.…”

SAT Encodings for the Car Sequencing Problem

“…Over the years different approaches have been used to solve these instances, among them constraint programming, local search and integer programming [14][10] [11][6] [15].…”

“…Here we will restate this technique to apply the method on all problems from the benchmark in [11]. We start with instance 300-04 as an example.…”