Nash equilibrium as a tool for the Car Sequencing Problem 4.0
Authors: 
Sara Bysko, Jolanta Krystek, and Andrzej ŚwierniakAuthors Info & Claims
Sara Bysko, Jolanta Krystek, and Andrzej ŚwierniakAuthors Info & ClaimsPages 1037 - 1053
Abstract
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.
References
[1]
Amini H, Meunier F, Michel H, and Mohajeri A Greedy colorings for the binary paintshop problem Journal of Discrete Algorithms 2010 8 8-14
[2]
Andres SD and Hochstättler W Some heuristics for the binary paint shop problem and their expected number of colour changes Journal of Discrete Algorithms 2011 9 203-211
[3]
Ayala, D., Wolfson, O., Xu, B., Dasgupta, B., & Lin, J. (2011). Parking slot assignment games. In Proc. ACM SIGSPATIAL international conference on advances in geographic information systems (GIS 2011) (pp. 299–308). ACM Press.
[4]
Bysko, S., & Krystek, J. (2018). A game theory approach for solving the new concept of car sequencing problem. In Proc. international conference on control, automation and robotics (ICCAR) ( pp. 531–535).
[5]
Bysko, S., & Krystek, J. (2019). Follow-up sequencing algorithm for car sequencing problem 4.0. In Proc. automation 2019. Advances in intelligent systems and computing (pp. 145–154). Springer.
[6]
Bysko S and Krystek J Automotive paint shop 4.0 Computers & Industrial Engineering 2020 139 105546
[7]
Cheng J, Lu Y, Puskorius G, Bergeon S, and Xiao J Vehicle sequencing based on evolutionary computation Evolutionary Computation 1999 2 1207-1214
[8]
Chew, T. L., David, J. M., Nguyen, A., & Tourbier, Y. (1992). Solving constraint satisfaction problems with simulated annealing: The car sequencing problem revisited. In Proc. international workshop on expert system & their applications (pp. 405–416).
[9]
Codognet Ph and Diaz D Compiling constraints in clp(FD) Journal of Logic Programming 1996 27 3 185-226
[10]
Epping T, Hochstättler W, and Oertel P Complexity results on a paint shop problem Discrete Applied Mathematics 2004 136 217-226
[11]
Estellon B, Gardi F, and Nouioua K Large neighborhood improvements for solving car sequencing problems RAIRO Operation Research 2004 40 355-379
[12]
Fiat A and Woeginger G Online algorithms—The state of the art 1998 Springer
[13]
Geffen CA and Rothenberg S Suppliers And Environmental Innovation: The automotive paint process International Journal of Operations and Production Management 2000 20 20 166-186
[14]
Giannetti C and Essien A Towards scalable and reusable predictive models for cyber twins in manufacturing systems Journal of Intelligent Manufacturing 2022 33 441-455
[15]
Gravel M, Gagne C, and Price WL Review and comparison of three methods for the solution of the car-sequencing problem Journal of the Operational Research Society 2005 56 11 1287-1295
[16]
Hartmann, S.A., & Runkler, T.A. (2008). Online optimization of a color sorting assembly buffer using ant colony optimization. In Operations research proceedings (pp. 415–420). Springer.
[17]
Jahren E and Achá RA A column generation approach and new bounds for the car sequencing problem Annals of Operations Research 2018 264 1–2 193-211
[18]
Ko SS, Han YH, and Choi JY Paint batching problem on M-to-1 conveyor systems Computers & Operations Research 2016 74 118-126
[19]
Krystek J and Bysko S The follow-up control of the body sequencing process at the paint shop Mechanik 2019 92 7 462-464
[20]
Leonard RJ From parlor games to social science: Von Neumann, Morgenstern, and the creation of game theory 1928–1944 Journal of Economic Literature 1995 33 2 730-761
[21]
Moon DH, Kim HS, and Song C A simulation study for implementing color rescheduling storage in an automotive factory SIMULATION 2005 81 625-635
[22]
Moya I, Chica M, and Bautista J Constructive metaheuristics for solving the Car Sequencing Problem under uncertain partial demand Computers & Industrial Engineering 2019 137 106048
[23]
Nash., J. (1950). Equilibrium points in n-person games. In. Proc. of the national academy of sciences (pp. 48–49), 36(1).
[24]
Neveu, B., Trombettoni, G., & Glover, F. (2004). Id walk: A candidate list strategy with a simple diversification device. In Proc. CP’2004 (pp. 423–437). Springer.
[25]
Oluyisola OE, Bhalla S, Sgarbossa F, and Strandhagen JO Designing and developing smart production planning and control systems in the industry 4.0 era: A methodology and case study Journal of Intelligent Manufacturing 2022 33 311-332
[26]
Parello BD, Kabat WC, and Wos LJ Job-shop scheduling using automated reasoning: A case study of the car sequencing problem Journal of Automated Reasoning 1986 2 1 1-42
[27]
Solnon C, Cung VD, Nguyen A, and Artigues C The car sequencing problem: overview of state-of-the-art methods and industrial case-study of the ROADEF 2005 challenge problem European Journal of Operational Research 2008 191 3 912-927
[28]
Solnon, S. (2000). Solving permutation constraint satisfaction problems with artificial ants. In Proc. ECAI’2000 (pp. 118–122). IOS Press.
[29]
Spieckermann S, Gutenschwager K, and Voß S A sequential ordering problem in automotive paint shops International Journal of Production Research 2004 42 1865-1878
[30]
Stutzle T and Hoos HH MAX-MIN ant system Future Generation Computer Systems 2000 16 889-914
[31]
Sun H, Fan S, Shao X, and Zhou J A colour-batching problem using selectivity banks in automobile paint shops International Journal of Production Research 2015 53 1124-1142
[32]
Sun H and Han J A study on implementing color-batching with selectivity banks in automotive paint shops Journal of Manufacturing Systems 2017 44 42-52
[33]
Thiruvady D, Ernst AT, and Wallace M A Lagrangian-ACO Matheuristic for Car Sequencing EURO Journal on Computational Optimization 2014 2 4 279-296
[34]
Thiruvady, D., Meyer, B., & Ernst, A. (2011). Car sequencing with constraint-based ACO. In Proc. of the 13th annual conference on genetic and evolutionary computation (pp. 163–170). New York, USA, ACM.
[35]
Valdondo, J.B., & Gude, J.P. (2007). Sequencing JIT mixed model assembly lines under station-load and part-usage constraints using lagrangean relaxations. In Proc. 3rd multidisciplinary international conference on scheduling: Theory and applications (MISTA 2007) (pp. 550–552).
[36]
von Neumann J and Morgenstern O Theory of games and economic behavior 1944 Princeton University Press
[37]
Xu Y., & Zhou, J. G. (2016). A virtual resequencing problem in automobile paint shops. In Proc. 22nd international conference on industrial engineering and engineering management 2015: Core theory and applications of industrial engineering (pp. 71–80). Atlantis Press.
[38]
Zhang X, Gao L, and Wen L A hybrid algorithm based on tabu search and large neighbourhood search for car sequencing problem Journal of Central South University. 2018 25 315-330
[39]
Zufferey, N., Studer, M., & Silver, E.A. (2006). Tabu search for a car sequencing problem. In Proc. 19th International Florida Artificial Intelligence Research Society conference (FLAIRS 2006) (pp. 457–462). The AAAI Press.
Recommendations
Application of Nash Equilibrium in Two-Person Games
ICIBE '21: Proceedings of the 7th International Conference on Industrial and Business EngineeringGame theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences of those agents. The outcomes in question might have been intended by none of the agents. Here we want to start with ...
Inapproximability of Nash Equilibrium
STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of ComputingWe prove that finding an ε-approximate Nash equilibrium is PPAD-complete for constant ε and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions.
As corollaries, we also prove similar ...
Inapproximability of Nash Equilibrium
We prove that finding an $\epsilon$-approximate Nash equilibrium is $\mathsf{PPAD}$--complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As ...
Comments
Information & Contributors
Information
Published In
© The Author(s) 2023.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 26 February 2023
Accepted: 12 January 2023
Received: 30 July 2020
Author Tags
Qualifiers
- Research-article
Funding Sources
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in