Two approaches to car sequencing in the paint shop
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Journal of Physics: Conference Series
PAPER • OPEN ACCESS
Two approaches to car sequencing in the paint shop
To cite this article: Sara Bysko et al 2021 J. Phys.: Conf. Ser. 1780 012028
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This content was downloaded from IP address 46.4.80.155 on 01/05/2021 at 21:32SAMDE 2020 IOP Publishing
Journal of Physics: Conference Series 1780 (2021) 012028 doi:10.1088/1742-6596/1780/1/012028
Two approaches to car sequencing in the paint shop
Sara Bysko1,*, Jolanta Krystek1 and Szymon Bysko1
1
Faculty of Automatic Control, Electronics and Computer Science, Silesian University
of Technology, Gliwice, Poland
*Email: sara.bysko@polsl.pl
Abstract. 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.
1. Introduction
The impact of strong market competition and dynamically changing customer requirements have
contributed to the evolution of production systems. Mass production system of one-assortment have
been replaced by systems of multi-assortment and multi-version production, characterized by the
simultaneous implementation of many products (assortments) or their variants (versions). An example
illustrating the issue of multi-version production is the multistage process of car production. It begins
at the body shop, where sheet metal is first cut, followed by pressing of individual components of car
bodies. The body parts obtained in this way are connected in the correct order in the welding shop.
Complete bodies are transported to the paint shop, where painting process is carried out. After its
completion, the finished bodies are dried and transferred to the assembly line. Along this line there are
several dozen stands on which all parts of the car equipment are assembled, including seats,
dashboards etc.
Between each production department warehouses or buffers are used to ensure continuity of
production. In recent years, these solutions have gained a new meaning. Due to variety of restrictions
and requirements occurring at individual production departments, each of the process stages has
different optimization criteria. This contributed to a change in the perception of the possibility of using
warehouses and buffers. These areas were included in the process of changing the order of products
between subsequent stages of production, which results in improved production indicators.
The problem of car sequencing has become one of the main aspects of production optimization in
the automotive industry, in particular in painting process. From the economic indicators point of view,
painting process is today a complex, multistage, extremely energy consuming and cost intensive
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Published under licence by IOP Publishing Ltd 1SAMDE 2020 IOP Publishing
Journal of Physics: Conference Series 1780 (2021) 012028 doi:10.1088/1742-6596/1780/1/012028
operation, which has an adverse effect on the environment. It generates one of the higher production
costs, and therefore its optimization plays a key role. In addition, painting process is the primary
source for air emissions of regulated chemicals, including volatile organic compounds (VOCs) and
hazardous air pollutants (HAPs). Solid and hazardous wastes arise especially as a result of too frequent
changeovers of painting guns, and are created in the painting process, e.g. waste paint through
overspray, chemicals used to clean the paint lines and application equipment.
There is no doubt that the control of car body flow through the paint shop is necessary. The key
element of the painting process, which has a direct impact on the optimization indicators of this
process, is sequencing of cars transported from the body shop to the paint shop. This problem is
presented and discussed in details in the paper.
The article is organized as follows. Section 2 presents considered in the literature similar
sequencing problem and methods to solve it. Section 3 described proposed by the authors Car
Sequencing Problem 4.0. (CSP 4.0). Section 4 presents approach to solve CSP 4.0 based on priority
rules. Section 5 contains description of game theoretic approach. Section 6 presents experimental
research and discussion of obtained results. The final Section concludes the paper.
2. Literature review
In the literature, the issue of sequencing in the production of cars was considered in the context of the
requirements and limitations of various production departments, in particular the paint shop and
assembly line. Research on scheduling car production processes focused mainly on the problem of car
sequencing. For the first time this issue was presented and described in [1]. The Car Sequencing
Problem (CSP) concerns the sequencing of cars in the assembly shop, in which various options (e.g.
sunroof, air conditioning) are to be installed in cars by appropriate work stations located along the
assembly line. The modified problem became subject in ROADEF'2005 Challenge, organized by the
French Society of Operations Research and Decision Analysis [2]. In the literature the Car Sequencing
Problem were solved using different exact approaches: Constraint Programming (CP) [3], Integer
Programming (IP) [4] and Branch and Bound (B&B) [5]. Among approximate methods it can be
distinguished: the Local Search [6], very fast local search method [7] which won the ROADEF’2005
Challenge. The Beam Search procedure was used in [8], tabu search [9], simulated annealing [10],
genetic algorithm [11] and ant colony optimization [12]. The research, which is closer to the one
considered in the paper concerned the Color Batching Problem (CBP) [13, 14, 15].
3. Problem formulation
Considering the problem of car sequencing requires not only taking into account the limited access to
information and the requirement to make decisions in real time, but also taking into account the
additional restrictions that results from the type of used painting system. It is a system whose painting
guns must be cleaned after painting a certain number of cars. This limitation determines the optimal
length of sequence composed of cars in the same color. This problem is called Car Sequencing
Problem 4.0. An instance of the considered problem is defined as tuple (V, C, NoRowBuff, NoColBuff,
TPerClean): V ={v1, .., vN} – set of vehicle to be produced, C ={c1, .., cD} – set of available colors and
function c: V→C, that associates color ci to each vehicle vi, NoRowBuff, NoColBuff – buffer size
defined by number of buffer rows and number of buffer columns, TPerClean – periodic cleaning
interval.
4. Approach based on priority rules
In the case of the CSP 4.0 problem, the essence of this approach is to give transport lines priorities
defined on the basis of proposed rules. The highest priority transport lines are selected for loading and
unloading a car. Two loading rules, two unloading rules and two optional rules have been proposed.
The following variants have been distinguished among the loading rules:
2SAMDE 2020 IOP Publishing
Journal of Physics: Conference Series 1780 (2021) 012028 doi:10.1088/1742-6596/1780/1/012028
The Smallest Line Occupancy, SLOcc – the order of loading according to the increasing
occupancy of the line, i.e. the line with the least car body is selected,
The Lowest Color Priority, LCPrio – loading order according to increasing color priority, i.e.
the line that ends with the lowest priority color of car is selected. The following variants have
been distinguished among the unloading rules:
The Smallest Number of Color in Buffer, SNCB – the order of unloading according to the
increasing number of colors in the buffer, i.e. the line that has the car in the unloading column
with the smallest color in the buffer is selected,
The Largest Number of Color in Buffer, LNCB – the order of unloading according to the
decreasing number of colors in the buffer, i.e. the line that has the body with the largest color
in the buffer in the unloading column is selected.
Optional rules include the following options:
Forced Color Change after Periodic Cleaning, FCCaPC – unloading order according to the
proposed rules, except for the time when periodic cleaning occurs. The car colors immediately
before and after the periodic cleaning must be different, if possible.
Color Memory, CM – this rule can be applied on both the loading and unloading side of the
buffer. The application of this rule on the loading side of the buffer means that first the body
in cIn color on the loading conveyor is directed to the transport line ended with the same color
car body (cIn). If this is not possible, then one of the proposed loading rules is used. On the
other hand, on the unloading side of the buffer, the CM rule determines that in the first place
the cOut body is removed from the unloading column, i.e. in the color of the body previously
directed for painting. If this is not possible, then one of the proposed unloading rules is used.
5. Game theory approach
The paper presents the main assumptions of the considered game theory approach. This concept is
described in details in [16].
Buffer Slot Assignment Game: On the buffer loading side, the decision problem can be defined
analogously to the concept presented [17]. In the general concept, it can be considered that the buffer
is a set of parking spaces (slots) for cars that are on its entrance side. Each of the entering cars can be
treated as an independent decision-making agent. Such a formulation of car sequencing problem – as
an allocation problem of assigning a parking space – allows considering the CSP 4.0 as a game. It is
assumed that vehicles entering the paint shop are players and they compete for parking spaces and
want at the same time to maximize profit. Their payment depends on their own choices and choices of
other players. Taking into account incomplete access to information and the considered structure of
the buffer, the Buffer Slot Assignment Game (BSAG) can be defined as follows: the set of players: V =
{vI, vII} (vI – vehicle located on the loading conveyor, vII – vehicle located on the buffer input), the set
of available strategies: S = {s1, s2, s3, s4, s5} (transport lines), the payoff function Fvehicle is defined as a
weighted objective function.
Buffer-OutShuttle Game: On the buffer unloading side, the game takes place between the buffer
and the unloading shuttle. The proposed approach was motivated by the need to make the decisions
dependent on the buffer entry and exit situation. In this case, the buffer as a player seeks to obtain a fill
state, which is the most advantageous from the perspective of the entry situation. This is case when the
buffer wants to remove a car from a completely loaded line, which ends with a car in the same color as
the color of car located on the loading shuttle. In turn, the purpose of the unloading shuttle is to
optimize the proposed quality indicators. The proposed Buffer-OutShuttle Game (BOSG) can be
defined as follows: the set of players: P = {pI, pII}, where pI buffer, pII unloading shuttle, the set of
available strategies: S = {s1, s2, s3, s4, s5} (transport lines), the payoff function for player I is
determined by the Fbuffer function the payoff function for player II is determined by the Fout-shuttle
function.
3SAMDE 2020 IOP Publishing
Journal of Physics: Conference Series 1780 (2021) 012028 doi:10.1088/1742-6596/1780/1/012028
An equilibrium strategy: The Nash equilibrium [18] stated in the literature as a standard desired
strategy is proposed in this paper to model the individual choices of players in a game. It defines a
situation where each player's strategy is optimal given the strategies of all other players.
6. Numerical experiments
The buffer model used for the stady consisted of 25 positions (5x5). For the purpose of the research,
10 sets of experimental data were used. Each set consisted of 100 or 1000 cars painted in 6 different
colors. The color distribution in each set was the same and as follows: C1: 6%, C2: 38%, C3: 29%, C4:
14%, C5: 10%, C6: 3%. The aim of the research was to compare quality of the CSP 4.0 solutions
between algorithms based on priority rules and game theory approach. For this purpose proposed
quality indicators NCs and ES were calculated. Two data sets were used for testing – first with 100
cars (tables 1 and 2), second with 1000 cars (tables 3 and 4). For the purposes of comparing the results
obtained for the priority algorithms, the following nomenclature was used: CML_CMU + FCCaPC –
configuring the rules for loading L (Load) and unloading U (Unload) + optional rules FCCaPC. The
color memory rule is applied on loading and unloading buffer side. In order to evaluate the solution of
Car Sequencing Problem 4.0, two quality indicators are proposed: Number of Changeovers (NCs) –
defines the number of color changes excluding the changes occurring during periodic cleaning,
Effectiveness of Synchronization (ES) – determines the total number of color changes occurring
between two subsequences in relation to the number of all color changes.
Table 1. Experimental results – NCs for 100-elements instances.
BSAG- CMLCPrio_CMLNCB CMSLOcc_CMSNCB
Dataset No.
BOSG +FCCaPC +FCCaPC
Data_01 16 26 22
Data_02 15 26 38
Data_03 14 29 37
Data_04 21 30 30
Data_05 15 25 34
Table 2. Experimental results – ES for 100-elements instances.
BSAG- CMLCPrio_CMLNCB CMSLOcc_CMSNCB
Dataset No.
BOSG +FCCaPC +FCCaPC
Data_01 71% 71% 79%
Data_02 71% 86% 86%
Data_03 79% 50% 93%
Data_04 86% 57% 93%
Data_05 64% 86% 93%
Table 3. Experimental results – NCs for 1000-elements instances.
BSAG- CMLCPrio_CMLNCB CMSLOcc_CMSNCB
Dataset No.
BOSG +FCCaPC +FCCaPC
Data_01 149 373 338
Data_02 165 392 329
Data_03 168 426 327
Data_04 171 394 320
Data_05 174 402 324
4SAMDE 2020 IOP Publishing
Journal of Physics: Conference Series 1780 (2021) 012028 doi:10.1088/1742-6596/1780/1/012028
Table 4. Experimental results – ES for 1000-elements instances.
BSAG- CMLCPrio_CMLNCB CMSLOcc_CMSNCB
Dataset No.
BOSG +FCCaPC +FCCaPC
Data_01 73% 100% 94%
Data_02 75% 100% 96%
Data_03 75% 100% 94%
Data_04 67% 100% 94%
Data_05 70% 100% 96%
The results of the experiments presented in tables 1 and 3 indicate that the BSAG-BOSG approach
gives the best results in terms of the number of changeovers. If the ES indicator is analyzed (table 2
and 4), the CMSLOcc_CMSNCB + FCCaPC approach is characterized by the highest effectiveness of
synchronization. Considering both quality indicators, it can be concluded that game theory approach is
the best.
7. Conclusions
In the paper, two car sequencing methods in the paint shop were considered, taking into account the
occurrence of a buffer with a finite capacity and a specific structure on the production line. The main
problem associated with the development of these methods was the need to ensure that the sequencing
procedure operated based on limited current information and a short time horizon for which the
production plan was known. For this reason, the decision making process related to the designation of
the transport line for the car body entering the buffer and selection of the car body transported from
the buffer to the painting station was difficult. It was important that these decisions were taken in real
time. In addition, it was necessary to include in the optimization criteria both the changeovers of the
paint guns resulting from changes in paint colors, and periodic cleaning of the guns ensuring good
quality of the painting process. The literature review carried out in the work showed the existence of a
research gap in the field of effective sequencing methods in the painting process.
The considered problem was analyzed from the game-theoretic and priority rules framework.
Based on the conducted research it was stated that using game theory approach it is possible to get
better solution that using algorithms based on priority rules. Future research will focus on comparison
algorithms based on game theory approach with advanced algorithms, i.e. Follow-Up Sequencing
Algorithms (FuSA) [19,20,21].
Acknowledgments
This work has been supported by Polish Ministry of Science and Higher Education under internal
grants 02/010/BKM18/0136, 02/010/BKM2019/0164 and 02/010/BK19/0143 for Institute of
Automatic Control, Silesian University of Technology, Gliwice, Poland
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