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An improved design for cellular manufacturing system associating scheduling decisions

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Abstract

This paper presents a model for the design of Cellular Manufacturing System (CMS) to evolve simultaneously structural design decisions of Cell Formation (CF) and operational issue decisions of optimal schedule. This integrated decision approach is important for designing a better performing cell. The model allows machine duplication and incorporates cross-flow for scheduling flexibility. The cross-flow is the term introduced to mean the inter-cell movement of parts from parent cell to identical machines in other cells though machines are available in the parent cell. This cross-flow facilitates routing flexibility and paves way for reduced schedule length thereby optimizing resources leading to minimized operational cost. A non-linear integer mathematical programming model is formulated with the objective function of minimizing operating cost which is the sum of Machine Utility Cost (MUC) and inter-cell costs. The MUC is a new cost parameter based on machine utility and it integrates CF, scheduling, and machine duplication decisions. The proposed model belongs to the class of NP-hard problems. A hybrid heuristic (HH) that has “Simulated Annealing Algorithm (SAA) embedded with Genetic Algorithm (GA)” is proposed. A comparison with the mathematical solution reveals that the proposed HH is capable of providing solutions closer to optimal in a computationally efficient manner. The model is validated by studying the effect of integrated decisions, machine duplications, and association of scheduling and cross-flow. The model validation reveals that the proposed CMS model evolves CF, scheduling, and machine duplication decisions with minimum operating cost. Thus, it can be inferred that the proposed model gives optimal integrated decisions for designing an effectively and efficiently performing cells and thus evolves improved CMS design decisions.

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Abbreviations

c,\( {\text{c}}^{\prime} \) :

index for cell (c,\( {\text{c}}^{\prime} \) = 1,2, …, C)

i,p:

index for parts (i = 1,2, …, n)

j:

index for machines (j = 1,2, …, m)

k,q:

index for part processing sequence (k = 1,2, …, Ki)

C:

number of cells

\( {\text{C}}_{{{\text{iK}}_{\text{i}} }} \) :

completion time of the last (K thi ) operation \( {\text{O}}_{{{\text{iK}}_{\text{i}} }} \)

Cik :

completion time of the operation Oik

Cmax :

makespan time of the schedule

\( {\text{CF}}_{{\text{c}}^{\prime}{\text{c}}} \) :

cross-flow inter-cell movement cost per unit part from cell ‘\( {\text{c}}^{\prime} \)’ to cell ‘c’

CFC:

cross-flow inter-cell movement cost

di :

demand for part ‘i’ per period

\( {\text{EF}}_{{\text{c}}^{\prime}{\text{c}}} \) :

exceptional element inter-cell movement cost per unit part from cell ‘\( {\text{c}}^{\prime} \)’ to cell ‘c’

\( {\text{IC}}_{{\text{c}}^{\prime}{\text{c}}} \) :

inter-cell movement cost per unit part from cell ‘\( {\text{c}}^{\prime} \)’ to cell ‘c’

ICC:

inter-cell movement cost

IEC:

exceptional element inter-cell movement cost

jik :

machine ‘j’ required for the operation Oik

Ki :

number of operations of part ‘i’

n:

number of parts

m:

number of machines

MUj :

utility rate of machine-type ‘j’ per unit time

MUC:

machine utility cost

MUR:

total machine utility rate

Oik :

kth operation of part ‘i’

Sik :

start time of operation Oik

tik :

processing time for operation Oik

TC:

total cost of operation

\( {\text{X}}_{{{\text{j}}.{\text{c}}}} \) :

binary integer variable that indicates the assignment of machine ‘j’ to cell ‘c’

\( {\text{Y}}_{{{\text{ik}}.{\text{c}}}} \) :

binary integer variable that indicates operation Oik is assigned to cell ‘c’

Zi.c :

binary integer variable that indicates the assignment of part ‘i’ to cell ‘c’

\( {\text{A}}_{{{\text{ikpq}}.{\text{c}}}} \) :

binary integer variable that indicates the precedence relationship of operations Oik and Opq assigned to cell ‘c’

ΔE:

change in entropy

a:

number of operations with alternate machine choices for a cell configuration

b:

index for machine cell configuration

B:

number of alternate machine cell configurations for a cell formation

cnt:

perturbation counter

CFCi :

cross-flow movement cost for SAA string SAi

IECb :

exceptional element inter-cell movement cost for machine cell configuration b

ITmax :

number of iterations per temperature

Mi :

minimum makespan time for SAA string SAi

MUCi :

machine utility cost for SAA string SAi

MURb :

total machine utility rate for machine cell configuration b

Pr :

acceptance probability of worst solutions

QR :

SAA quenching rate

r:

random number where 0<r<1

Sg :

SAA global best solution

Sp :

SAA perturbed solution

Si :

SAA solution at any instant

SAg :

SAA global best string

SAp :

SAA perturbed string

SAi :

SAA string at any instant

schg :

best optimal schedule

schi :

optimal schedule at any instant

T0 :

SAA initial temperature

Tf :

SAA final temperature

Ti :

SAA temperature at any instant

References

  1. Edwards J D 2013 World Product Data Management - Discrete Guide Release A9.3, E21777-04, Copyright © 2013, Oracle and/or its affiliates

  2. Askin R G 2013 Contributions to the design and analysis of cellular manufacturing systems. International Journal of Production Research 51:23–24: 6778–6787

    Article  Google Scholar 

  3. Caux C, Bruniaux R and Pierreval H 2000 Cell formation with alternative process plans and machine capacity constraints: A new combined approach. International Journal of Production Economics 64: 279–284

    Article  Google Scholar 

  4. Uddin M K and Shanker K 2002 Grouping of parts and machines in presence of alternative process routes by genetic algorithm. International Journal of Production Economics 76: 219–228

    Article  Google Scholar 

  5. Brown J R 2015 A capacity constrained mathematical programming model for cellular manufacturing with exceptional elements. Journal of Manufacturing Systems 37/1: 227–232

    Article  MathSciNet  Google Scholar 

  6. Papaioannou G and Wilson J M 2010 The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research. European Journal of Operational Research 20: 509–521

    Article  Google Scholar 

  7. Tavakkoli-Moghaddam R, Ranjbar-Bourani M, Amin G R and Siada A 2010 A cell formation problem considering machine utilization and alternative process routes by scatter search. Journal of Intelligent Manufacturing 23/4: 1127–1139

    Article  Google Scholar 

  8. Hassan Zadeh A, Hamid Afshari and Reza Ramazani Khorshid-Doust 2014 Integration of process planning and production planning and control in cellular manufacturing. Production Planning and Control: The Management of Operations 25/10: 840–857

    Article  Google Scholar 

  9. Chattopadhyay M, Sengupta S, Ghosh T, Pranab K Dan and Sitanath Mazumdar 2013 Neuro-genetic impact on cell formation methods of Cellular Manufacturing System design: A quantitative review and analysis. Computers and Industrial Engineering 64: 256–272

    Article  Google Scholar 

  10. Li D, Wang Y, Xiao Guangxue and Tang Jiafu 2013 Dynamic parts scheduling in multiple job shop cells considering intercell moves and flexible routes. Computers and Operations Research 40: 1207–1223

    Article  MathSciNet  Google Scholar 

  11. Wemmerlov U and Hyer N L 1986 Procedures for the Part Family/Machine Group Identification Problem in Cellular Manufacturing. Journal of Operations Management 6–2: 125–147

    Article  Google Scholar 

  12. Arkat J, Mehdi Hosseinabadi Farahani and Fardin Ahmadizar 2012 Multi-objective genetic algorithm for cell formation problem considering cellular layout and operations scheduling. International Journal of Computer Integrated Manufacturing 25–7: 625–635

    Article  Google Scholar 

  13. Mak K L, Lau J S K and Wang X X 2005 A genetic scheduling methodology for virtual cellular manufacturing systems: an industrial application. International Journal of Production Research 43–12: 2423–2450

    Article  Google Scholar 

  14. Kesen S E, Das S K and Gung Z 2010 A genetic algorithm based heuristic for scheduling of virtual manufacturing cells (VMCs). Computers and Operations Research 37: 1148–1156

    Article  Google Scholar 

  15. Jeon G and Leep H R 2006 Forming part families by using the genetic algorithm and designing machine cells under demand changes. Computers and Operations Research 33: 263–283

    Article  Google Scholar 

  16. Egilmez Gokhan and Süer Gürsel 2014 The impact of risk on the integrated cellular design and control. International Journal of Production Research 52(5): 1455–1478

    Article  Google Scholar 

  17. Umit Bilge, Murat Firat and Erinc Albey 2008 A parametric fuzzy logic approach to dynamic part routing under full routing flexibility. Computers and Industrial Engineering 55: 15–33

    Article  Google Scholar 

  18. Chung S-H, Tai-Hsi Wu and Chin-Chih Chang 2011 An efficient tabu search algorithm to the cell formation problem with alternative routings and machine reliability considerations. Computers and Industrial Engineering 60: 7–15

    Article  Google Scholar 

  19. Jeon G, Leep H R and Parsaei H R 1998 A cellular manufacturing system based on new similarity coefficient which considers alternative routes during machine failure. Computers and Industrial Engineering 34(1): 21–36

    Article  Google Scholar 

  20. Solimanpur M and Foroughi A 2011 A new approach to the cell formation problem with alternative processing routes and operation sequence. International Journal of Production Research 49(19): 5833–5849

    Article  Google Scholar 

  21. Jayaswal S and Adil G K 2004 Efficient algorithm for cell formation with sequence data, machine replications and alternative process routings. International Journal of Production Research 42(12): 2419–2433

    Article  Google Scholar 

  22. Ming Zhou and Askin R G 1998 Formation of general GT Cells: An Operation based Approach. Computers and Industrial Engineering 34(1): 147–157

    Article  Google Scholar 

  23. Cao D and Chen M 2004 Using penalty function and Tabu search to solve cell formation problems with fixed cell cost. Computers and Operations Research 31: 21–37

    Article  MathSciNet  Google Scholar 

  24. Özgüven C, LaleÖzbak and Yasemin Yavuz 2010 Mathematical models for job-shop scheduling problems with routing and process plan flexibility. Applied Mathematical Modelling 34: 1539–1548

    Article  MathSciNet  Google Scholar 

  25. Deljoo V, Mirzapour Al-e-hashem S M J, Deljoo F and Aryanezhad M B 2010 Using genetic algorithm to solve dynamic cell formation problem. Applied Mathematical Modeling 34: 1078–1092

    Article  MathSciNet  Google Scholar 

  26. Mahdavi I, Amin Aalaei, Mohammad Mahdi Paydar, and Maghsud Solimanpur 2010 Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment. Computers and Mathematics with Applications 60: 1014–1025

    Article  MathSciNet  Google Scholar 

  27. Defersha F M and Chen M 2006 A comprehensive mathematical model for the design of cellular manufacturing systems. International Journal of Production Economics 103: 767–783

    Article  Google Scholar 

  28. Mathur K and Süer G A 2013 Math modeling and GA approach to simultaneously make overtime decisions, load cells and sequence products. Computers and Industrial Engineering 66: 614–624

    Article  Google Scholar 

  29. King J R 1980 Machine-component grouping in production flow analysis: an approach using a rank order clustering. International Journal of Production Research 18(2): 213–232

    Article  MathSciNet  Google Scholar 

  30. Chandrasekharan M P and Rajagopalan R 1986 MODROC - an extension of rank order clustering for group technology. International Journal of Production Research 24(5): 1221–1233

    Article  Google Scholar 

  31. Chandrasekharan M P and Rajagopalan R 1987 ZODIAC- an algorithm for concurrent formation of part-families and machine-cells. International Journal of Production Research 25(6): 835–850

    Article  Google Scholar 

  32. Jayakrishnan Nair G and Narendran T T 1998 CASE: A clustering algorithm for cell formation with sequence data. International Journal of Production Research 36(1): 157–180

    Article  Google Scholar 

  33. Jayakrishnan Nair G and Narendran T T 1999 Accord: A bi-criterion algorithm for cell formation using ordinal and ratio-level data. International Journal of Production Research 37(3): 539–556

    Article  Google Scholar 

  34. Paydar M M, Iraj Mahdavi, Iman Sharafuddin and Maghsud Solimanpur 2010 Applying simulated annealing for designing cellular manufacturing systems using MDmTSPq. Computers and Industrial Engineering 59: 929–936

    Article  Google Scholar 

  35. Chang C-C, Wu, T-H and Wu C-W 2013 An efficient approach to determine cell formation, cell layout and intracellular machine sequence in cellular manufacturing systems. Computers and Industrial Engineering 66: 438–450

    Article  Google Scholar 

  36. Liu C, Wang J and Leung Joseph Y-T 2018 Integrated bacteria foraging algorithm for cellular manufacturing in supply chain considering facility transfer and production planning. Applied Soft Computing 62: 602–618

    Article  Google Scholar 

  37. Rabbani M, Farrokhi-Asl H and Ravanbakhsh M 2018 Dynamic cellular manufacturing system considering machine failure and workload balance, Journal of Industrial Engineering International, https://doi.org/10.1007/s40092-018-0261-y

    Article  Google Scholar 

  38. Soolaki M and Arkat J 2018 Incorporating dynamic cellular manufacturing into strategic supply chain design. International Journal of Advanced Manufacturing Technology 95(5–8): 2429–2447. https://doi.org/10.1007/s00170-017-1346-2

    Article  Google Scholar 

  39. Solimanpur M and Elmi A 2013 A tabu search approach for cell scheduling problem with makespan criterion. International Journal of Production Economics 141: 639–645.

    Article  Google Scholar 

  40. Liang M and Zolfaghari S 1999 Machine cell formation considering processing times and machine capacities: An ortho-synapse Hopfield neural network approach. Journal of Intelligent Manufacturing 10: 437–447

    Article  Google Scholar 

  41. Vidal T, Teodor Gabriel Crainic, Michel Gendreau and Christian Prins 2013 Heuristics for multi-attribute vehicle routing problems: A survey and synthesis. European Journal of Operational Research 231: 1–21

    Article  MathSciNet  Google Scholar 

  42. Mareda T, Gaudard L and Romerio F 2017 A Parametric Genetic Algorithm Approach to Assess Complementary Options of Large Scale Wind-solar Coupling. IEEE/CAA Journal of Automatica Sinica 4(2): 260–272

    Article  Google Scholar 

  43. Zolfaghari S and Liang M 2002 Comparative study of simulated annealing, genetic algorithms and tabu search for solving binary and comprehensive machine-grouping problems. International Journal of Production Research 40–9: 2141–2158

    Article  Google Scholar 

  44. Yuan H, Bi J, Tan W, Zhou M C, Li B H and Li J 2017 TTSA: An Effective Scheduling Approach for Delay Bounded Tasks in Hybrid Clouds. IEEE Transactions on Cybernetics 47(11): 3658–3668

    Article  Google Scholar 

  45. Moslemipour G 2018 A hybrid CS-SA intelligent approach to solve uncertain dynamic facility layout problems considering dependency of demands. Journal of Industrial Engineering International 14: 429. https://doi.org/10.1007/s40092-017-0222-x

    Article  Google Scholar 

  46. Chibante R 2010 Simulated Annealing Theory with Applications published by Sciyo, Croatia

  47. Jawahar N, Aravindan P and Ponnambalam S G 1998 A genetic algorithm for scheduling flexible manufacturing systems. International Journal of Advanced Manufacturing Technology 14: 588–607

    Article  Google Scholar 

  48. Mak K L, Wong Y S and Wang X X 2000 An adaptive genetic algorithm for manufacturing cell formation. International Journal of Advanced Manufacturing Technology 16: 491–497

    Article  Google Scholar 

  49. James T L, Evelyn C Brown and Kellie B Keeling 2007 A hybrid grouping genetic algorithm for the cell formation problem. Computers and Operations Research 34: 2059–2079.

    Article  Google Scholar 

  50. Albadawi Z, Bashir H and Chen M 2005 A mathematical approach for the formation of manufacturing cells. Computers and Industrial Engineering 48: 3–21

    Article  Google Scholar 

  51. Harhalakis G, Ioannou G, Minis I and Nagi R 1994 Manufacturing cell formation under random product demand. International Journal of Production Research 32(1): 47–64

    Article  Google Scholar 

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Authors and Affiliations

  1. SSM Institute of Engineering and Technology, Dindigul, 624 002, India

    R SUBHAA

  2. Ramco Institute of Technology, Rajapalayam, 626 117, India

    N JAWAHAR

  3. Faculty of Mechanical and Manufacturing Engineering, Universiti Malaysia Pahang, Pekan, Malaysia

    S G PONNAMBALAM

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  1. R SUBHAA
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Correspondence to R SUBHAA.

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SUBHAA, R., JAWAHAR, N. & PONNAMBALAM, S.G. An improved design for cellular manufacturing system associating scheduling decisions. Sādhanā 44, 155 (2019). https://doi.org/10.1007/s12046-019-1135-8

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