Flexible layouts for the mixed-model assembly of heterogeneous vehicles

Andreas Hottenrott; Martin Grunow

doi:10.1007/s00291-019-00556-x

OR Spectrum

December 2019, Volume 41, Issue 4, pp 943–979 | Cite as

Flexible layouts for the mixed-model assembly of heterogeneous vehicles

Authors
Authors and affiliations

Andreas Hottenrott
Martin Grunow

Regular Article

First Online: 13 May 2019

196 Downloads

Abstract

The increasing vehicle heterogeneity is pushing the widespread mixed-model assembly line to its limit. The paced, serial design is incapable of coping with the diversity in workloads and task requirements. As an alternative, the automotive industry has started to introduce flexible layouts for segments of the assembly. In flexible layouts, the stations are no longer arranged serially and no longer linked by a paced transportation system but by automated guided vehicles. This paper investigates the initial configuration of such systems. The flexible layout design problem (FLDP) is the problem of designing a flexible layout for a segment of the assembly of heterogeneous vehicles. It comprises an integrated station formation and station location problem. Moreover, the FLDP anticipates the operational flow allocation of the automated guided vehicles. We formalize the FLDP in a mixed-integer linear program and develop a decomposition-based solution approach that can optimally solve small- to mid-sized instances. In addition, we transform this solution approach to a matheuristic that generates high-quality solutions in acceptable time for large-sized instances. We compare the efficiency of flexible layouts to mixed-model assembly lines and quantify the benefits of flexible layouts which increase with vehicle heterogeneity.

Keywords

Product variety Automotive industry Job shop configuration Cellular design Classification of decision problems

This is a preview of subscription content, to check access.

Notes

Appendix B

Benchmark mixed-model assembly line balancing model adapted from Bukchin and Rabinowitch (2006)

We adapt the mixed-model assembly line balancing model formulation by Bukchin and Rabinowitch (2006). Table 10 shows the required additional notation. We introduce a new index set $s\in S$ that represents the stations on the line. Parameter c denotes the cycle time. We add parameter $\alpha \ge 0$ to vary between closed and open stations. $\alpha $ represents the percentage of cycle time that workers are allowed to drift out into downstream stations. Next, we denote three sets of decision variables. The binary variable ${\bar{X}}_{t,m,s}$ shows whether task t for model m is assigned to station s. ${\bar{Y}}_{t,s}$ is a binary variable as well. It indicates whether task t is assigned to station s for any model. Last, the continuous variable ${\bar{Z}}$ represents the number of stations used and is to be minimized (23).

Table 10

Additional notation for mixed-model assembly line balancing problem

Index sets
$s\in S$	Stations ($s=1,\ldots ,\|S\|$)

Parameters
c	Cycle time
$\alpha $	Drift factor: percentage of cycle time that workers are allowed to drift out into downstream stations

Decision variables
${\bar{X}}_{t,m,s}$	1 if task t of model m is assigned to station s, else 0
${\bar{Y}}_{t,s}$	1 if task t of any model is assigned to station s, else 0
${\bar{Z}}$	Number of stations to be used in the assembly line

Constraints (24) force the workload of a task for a particular model to be assigned to a single station. Note again that splitting the workload of one model among task duplicates at different stations is not allowed on mixed-model assembly lines. Precedence relations are satisfied by constraints (25). Constraints (26) limit the total processing time for each model at each station. For $\alpha =0$, we evaluate closed stations, in which workers are not allowed to drift out into downstream stations. For $\alpha >0$, workers are allowed to drift out into the neighboring stations by $\alpha \%$ of the cycle time. In order to make sure that the overall capacity of the station is not violated, we add constraints (27) to the model by Bukchin and Rabinowitch (2006). The number of stations used is derived in constraints (28). Constraints (29) link the two binary variables by checking whether a task is performed for any model at a certain station. As an extension to the model by Bukchin and Rabinowitch (2006), we introduce constraints (30) that limit the maximum number of task duplicates. Without these constraints, the mixed-model assembly line solution would not be comparable to the flexible layout solution. Finally, in constraints (31)–(33), we restrict the domains of the decision variables.

$$\begin{aligned} min~Z^L&= {\bar{Z}} \end{aligned}$$

(23)

s.t.

$$\begin{aligned} \sum \limits _{s{\in }S}{\bar{X}}_{t,m,s}&=1&\forall m{\in }M,t{\in }T_m \end{aligned}$$

(24)

$$\begin{aligned} \sum \limits _{s_1{\in }S}s_1\cdot {\bar{X}}_{t_1,m,s_1}&\le \sum \limits _{s_2{\in }S}s_2\cdot {\bar{X}}_{t_2,m,s_2}&\forall m{\in }M,t_1{\in }T_m,t_2{\in }V_{m,t_1} \end{aligned}$$

(25)

$$\begin{aligned} \sum \limits _{t{\in }T_m}q_{m,t}\cdot {\bar{X}}_{t,m,s}&\le c\cdot (1+\alpha )&\forall m{\in }M,s{\in }S \end{aligned}$$

(26)

$$\begin{aligned} \sum \limits _{m{\in }M}d_{m}\cdot \sum \limits _{t{\in }T_m}q_{m,t}\cdot {\bar{X}}_{t,m,s}&\le \tau&\forall s{\in }S \end{aligned}$$

(27)

$$\begin{aligned} {\bar{Z}}&\ge \sum \limits _{s{\in }S}s\cdot {\bar{X}}_{t,m,s}&\forall m{\in }M,t{\in }T_m \end{aligned}$$

(28)

$$\begin{aligned} {\bar{Y}}_{t,s}&\ge \frac{1}{|M|}\cdot \sum \limits _{m{\in }M|t{\in }T_m}{\bar{X}}_{t,m,s}&\forall t{\in }T,s{\in }S \end{aligned}$$

(29)

$$\begin{aligned} \sum \limits _{s{\in }S}{\bar{Y}}_{t,s}&\le n_t&\forall t{\in }T \end{aligned}$$

(30)

$$\begin{aligned} {\bar{X}}_{t,m,s}&\in \lbrace 0,1 \rbrace&\forall m{\in }M,t{\in }T_m,s{\in }S \end{aligned}$$

(31)

$$\begin{aligned} {\bar{Y}}_{t,s}&\in \lbrace 0,1 \rbrace&\forall t{\in }T,s{\in }S \end{aligned}$$

(32)

$$\begin{aligned} {\bar{Z}}&\ge 0 \end{aligned}$$

(33)

References

Aneke NAG, Carrie AS (1986) A design technique for the layout of multi-product flowlines. Int J Prod Res 24(3):471–481. https://doi.org/10.1080/00207548608919743 CrossRefGoogle Scholar
Askin RG, Mitwasi M (1992) Integrating facility layout with process selection and capacity planning. Eur J Oper Res 57(2):162–173. https://doi.org/10.1016/0377-2217(92)90040-G CrossRefGoogle Scholar
Becker C, Scholl A (2006) A survey on problems and methods in generalized assembly line balancing. Eur J Oper Res 168(3):694–715. https://doi.org/10.1016/j.ejor.2004.07.023 CrossRefGoogle Scholar
Benjaafar S, Sheikhzadeh M (2000) Design of flexible plant layouts. IIE Trans 32(4):309–322. https://doi.org/10.1080/07408170008963909 CrossRefGoogle Scholar
Boysen N, Fliedner M, Scholl A (2007) A classification of assembly line balancing problems. Eur J Oper Res 183(2):674–693. https://doi.org/10.1016/j.ejor.2006.10.010 CrossRefGoogle Scholar
Boysen N, Fliedner M, Scholl A (2009) Production planning of mixed-model assembly lines: overview and extensions. Prod Plan Control 20(5):455–471. https://doi.org/10.1080/09537280903011626 CrossRefGoogle Scholar
Browne J, Dubois D, Rathmill K, Sethi SP, Stecke KE (1984) Classification of flexible manufacturing systems. FMS Mag 2(2):114–117Google Scholar
Bukchin J, Dar-El EM, Rubinovitz J (2002) Mixed model assembly line design in a make-to-order environment. Comput Ind Eng 41(4):405–421. https://doi.org/10.1016/S0360-8352(01)00065-1 CrossRefGoogle Scholar
Bukchin Y, Rabinowitch I (2006) A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs. Eur J Oper Res 174(1):492–508. https://doi.org/10.1016/j.ejor.2005.01.055 CrossRefGoogle Scholar
Caux C, Bruniaux R, Pierreval H (2000) Cell formation with alternative process plans and machine capacity constraints: a new combined approach. Int J Prod Econ 64(1–3):279–284. https://doi.org/10.1016/S0925-5273(99)00065-1 CrossRefGoogle Scholar
Chen DS, Wang Q, Chen HC (2001) Linear sequencing for machine layouts by a modified simulated annealing. Int J Prod Res 39(8):1721–1732. https://doi.org/10.1080/00207540010023565 CrossRefGoogle Scholar
Defersha FM, Hodiya A (2017) A mathematical model and a parallel multiple search path simulated annealing for an integrated distributed layout design and machine cell formation. J Manuf Syst 43:195–212. https://doi.org/10.1016/j.jmsy.2017.04.001 CrossRefGoogle Scholar
Drira A, Pierreval H, Hajri-Gabouj S (2007) Facility layout problems: a survey. Ann Rev Control 31(2):255–267. https://doi.org/10.1016/j.arcontrol.2007.04.001 CrossRefGoogle Scholar
Goldengorin B, Krushinsky D, Pardalos PM (2013) Cell Formation in Industrial Engineering, vol 79. Springer, New York, New York, NY. https://doi.org/10.1007/978-1-4614-8002-0 CrossRefGoogle Scholar
Hahn R (1972) Produktionsplanung bei Linienfertigung. De Gruyter, Berlin. https://doi.org/10.1515/9783110835687 CrossRefGoogle Scholar
Handelsblatt (2016) Audi plant eine revolution: Keine fließbänder mehr. Handelsblatt 2016, http://www.handelsblatt.com/unternehmen/industrie/keine-fliessbaender-mehr-audi-plant-eine-revolution/14894190.html
Heragu SS, Chen JS (1998) Optimal solution of cellular manufacturing system design: benders’ decomposition approach. Eur J Oper Res 107(1):175–192. https://doi.org/10.1016/S0377-2217(97)00256-7 CrossRefGoogle Scholar
Heragu SS, Kusiak A (1988) Machine layout problem in flexible manufacturing systems. Oper Res 36(2):258–268. https://doi.org/10.1287/opre.36.2.258 CrossRefGoogle Scholar
Ho YC, Moodie CL (1998) Machine layout with a linear single-row flow path in an automated manufacturing system. J Manuf Syst 17(1):1–22. https://doi.org/10.1016/S0278-6125(98)80006-X CrossRefGoogle Scholar
Hoffmann TR (1992) Eureka: a hybrid system for assembly line balancing. Manag Sci 38(1):39–47. https://doi.org/10.1287/mnsc.38.1.39 CrossRefGoogle Scholar
Jaramillo JR, McKendall AR (2010) The generalised machine layout problem. Int J Prod Res 48(16):4845–4859. https://doi.org/10.1080/00207540903117840 CrossRefGoogle Scholar
Keller B, Buscher U (2015) Single row layout models. Eur J Oper Res 245(3):629–644. https://doi.org/10.1016/j.ejor.2015.03.016 CrossRefGoogle Scholar
Li J, Gao J (2014) Balancing manual mixed-model assembly lines using overtime work in a demand variation environment. Int J Prod Res 52(12):3552–3567. https://doi.org/10.1080/00207543.2013.874603 CrossRefGoogle Scholar
Meyr H (2004) Supply chain planning in the German automotive industry. OR Spectr 26(4):447–470. https://doi.org/10.1007/s00291-004-0168-4 CrossRefGoogle Scholar
Montreuil B (1999) Fractal layout organization for job shop environments. Int J Prod Res 37(3):501–521. https://doi.org/10.1080/002075499191643 CrossRefGoogle Scholar
Nagi R, Harhalakis G, Proth JM (1990) Multiple routeings and capacity considerations in group technology applications. Int J Prod Res 28(12):1243–1257. https://doi.org/10.1080/00207549008942864 CrossRefGoogle Scholar
Papaioannou G, Wilson JM (2010) The evolution of cell formation problem methodologies based on recent studies (1997–2008): review and directions for future research. Eur J Oper Res 206(3):509–521. https://doi.org/10.1016/j.ejor.2009.10.020 CrossRefGoogle Scholar
Pil FK, Holweg M (2004) Linking product variety to order-fulfillment strategies. Interfaces 34(5):394–403. https://doi.org/10.1287/inte.1040.0092 CrossRefGoogle Scholar
Rajamani D, Singh N, Aneja YP (1990) Integrated design of cellular manufacturing systems in the presence of alternative process plans. Int J Prod Res 28(8):1541–1554. https://doi.org/10.1080/00207549008942811 CrossRefGoogle Scholar
Roberts SD, Villa CD (1970) On a multiproduct assembly line-balancing problem. AIIE Trans 2(4):361–364. https://doi.org/10.1080/05695557008974777 CrossRefGoogle Scholar
Scholl A (1993) Data of assembly line balancing problems. Schriften zur Quantitativen Betriebswirtschaftslehre—Technische Hochschule DarmstadtGoogle Scholar
Sofianopoulou S (1999) Manufacturing cells design with alternative process plans and/or replicate machines. Int J Prod Res 37(3):707–720. https://doi.org/10.1080/002075499191742 CrossRefGoogle Scholar
Solimanpur M, Vrat P, Shankar R (2004) A multi-objective genetic algorithm approach to the design of cellular manufacturing systems. Int J Prod Res 42(7):1419–1441. https://doi.org/10.1080/00207540310001638073 CrossRefGoogle Scholar
Urban TL, Chiang WC, Russell RA (2000) The integrated machine allocation and layout problem. Int J Prod Res 38(13):2911–2930. https://doi.org/10.1080/00207540050117369 CrossRefGoogle Scholar

Copyright information

Authors and Affiliations

Andreas Hottenrott
- 1
Email authorView author's OrcID profile
Martin Grunow
- 1
View author's OrcID profile

1.TUM School of ManagementTechnical University of MunichMunichGermany

Flexible layouts for the mixed-model assembly of heterogeneous vehicles

Abstract

Keywords

Notes

References

Copyright information

Authors and Affiliations

Personalised recommendations

Cite article

Parameters
c	Cycle time
\(\alpha \)	Drift factor: percentage of cycle time that workers are allowed to drift out into downstream stations

Decision variables
\({\bar{X}}_{t,m,s}\)	1 if task t of model m is assigned to station s, else 0
\({\bar{Y}}_{t,s}\)	1 if task t of any model is assigned to station s, else 0
\({\bar{Z}}\)	Number of stations to be used in the assembly line