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Designing an integrated multi-echelon agile supply chain network: a hybrid taguchi-particle swarm optimization approach

  • Manish Bachlaus
  • Mayank Kumar Pandey
  • Chetan Mahajan
  • Ravi Shankar
  • M. K. TiwariEmail author
Article

Abstract

The present paper attempts to explore the integration of production, distribution and logistics activities at the strategic decision making level where, the objective is to design a multi-echelon supply chain network considering agility as a key design criterion. The design network conceived here addresses a class of five echelons of supply chains including suppliers, plants, distribution centers, cross-docks and customer zones. The problem has been mathematically formulated as a multi-objective optimization model that aims to minimize the cost (fixed and variable) and maximizes the plant flexibility and volume flexibility. The notion of cross-dock has been introduced as an intermediate level between distribution centers and customer zones to increase the profitability of manufacturing and service industries. In order to solve the underlying problem, a novel algorithm entitled hybrid taguchi-particle swarm optimization (HTPSO) has been proposed that incorporates the characteristics of statistical design of experiments and random search techniques. The main idea is to integrate the fundamentals of taguchi method i.e. orthogonal array and signal to noise ratio (SNR) in the PSO meta-heuristic to minimize the effect of the causes of variations. The proposed model has been authenticated by undertaking problem instances of varying size. Extensive computational experiments are conducted to validate the same and also the efficacy of the proposed HTPSO algorithm. The results obtained reveal that proposed solution methodology is an effective approach to solve the underlying problem.

Keywords

Multi-echelon supply chain Agility Hybrid taguchi-particle swarm optimization 

Notations

Indices

s = 1, 2,..., S

Set of suppliers

p = 1, 2,..., P

Set of plants

k = 1, 2,..., K

Set of possible distribution centers

j = 1, 2,..., J

Set of possible cross-docks

m = 1, 2,..., M

Set of customer zones

i = 1, 2,..., I

Product type

r = 1, 2,..., R

Raw material type

Notations

λip

Quantity of product i produced at plant p

νipk

Quantity of product i transported from plant p to distribution center k

φrsp

Quantity of raw material r transported from supplier s to plant p

AGCDj

Agility level of cross-dock j

AGDCk

Agility level of distribution center k

AGPp

Agility level of plant p

AGSs

Agility level of supplier s

CCDj

Capacity of cross-dock j to handle product families

CDCk

Capacity of distribution center k to handle product families

CDF

Cross-dock flexibility

CSCmj

Cost to supply product i from cross-dock j which would be used by the customer zone m

DCF

Distribution center flexibility

Dmi

Demand from customer zone m for product i

DVFm

Distribution volume flexibility of customer zone m

FCDj

Fixed operating cost to open cross- dock j

FCPp

Fixed cost for plant p

FDCk

Fixed cost for distribution center k

HAGl

Lower bound of high agility performance index (0.8)

HAGu

Upper bound of high agility performance index (1.0)

I

Total number of products to be manufactured

J

Total number of cross-docks

K

Total number of distribution centers

LAGl

Lower bound of low agility performance index (0.4)

LAGu

Upper bound of low agility performance index (0.6)

M

Total number of customer zones

MAGl

Lower bound of medium agility performance index (0.6)

MAGu

Upper bound of medium agility performance index (0.8)

MNPVip

Minimum production volume for product i at plant p

MNTHk

Minimum throughput at distribution center k

MXC

Maximum number of cross-docks to be opened

MXD

Maximum number of distribution centers to be opened

MXPVip

Maximum production volume for product i at plant p

MXTHk

Maximum throughput at distribution center k

norm(.)

Represents normalized objective (.)

Obj

Final integrated objective function

P

Total number of plants

PCPp

Production capacity for each plant p

PCVrs

Production capacity of supplier s for raw material r

PF

Plant flexibility

PVFm

Plant volume flexibility

SUPip

Standard units at plant p per unit of product i

R

Total number of raw material to be supplied

S

Total number of suppliers

SF

Supplier flexibility

SUDCik

Standard units at distribution center k per unit of product i

TCm

Total cost of m customer zone

UCRrs

Unit cost of raw material r for supplier s

UCTik

Unit cost of throughput (handling and inventory) for product i at distribution center k

UPCPip

Unit production cost for product i at plant p

URri

Utilization rate for each raw material r per unit of product i

UTCDikj

Unit transportation cost from distribution center k to cross-dock j for product i

UTCPipk

Unit transportation cost from plant p to distribution center k for product i

UTCRrsp

Unit transportation cost from supplier s to plant p for raw material r

w1m

Weight assigned by manufacturer to cost objective

w2m

Weight assigned by manufacturer to distribution volume flexibility

w2m

Weight assigned by manufacturer to distribution volume flexibility

w3m

Weight assigned by manufacturer to plant flexibility

Decision Variables

Xp
$$ =\left\{ \begin{array}{ll} 1, & {\rm if\, plant}\, p\,{\rm is\, open}\\ 0, & {\rm otherwise} \end{array} \right. $$
Yk
$$=\left\{\begin{array} {ll} 1, & {\rm if\, distribution\, center}\, k\,{\rm is\, open}\\ 0, & {\rm otherwise} \end{array}\right.$$
Zj
$$=\left\{ {\begin{array}{ll} 1, & {\rm if\, cross\, dock}\, j\,{\rm is\, open}\\ 0, & {\rm otherwise} \end{array}} \right.$$
Rjki
$$=\left\{ {\begin{array}{lll} 1, & {if\, cross\, dock}\, j\,{\rm is\, assigned\, to}\\ & {\rm distribution\, center\, k\, for\, product\, i} \\ 0, & {\rm otherwise}\\ \end{array}} \right.$$
Amji
$$=\left\{ {\begin{array}{lll} 1, & {\rm if\, customer\, zone}\, m\,{\rm is assigned}\\ &{\rm to\, cross\, dock\, j\, for\, product\, i}\\ 0, & {\rm otherwise} \end{array}} \right.$$
Ns
$$ =\left\{ {\begin{array} {ll} 1, & {\rm if\, supplier}\, s\,{\rm is\, selected}\\ 0, & {\rm otherwise} \end{array}} \right.$$

References

  1. Alonso A., Escudero L.F., Garin A., Ortuno M.T., Perz G. (2003) An approach for strategic supply chain planning under uncertainty based on stochastic 0-1 programming. Journal of Global Optimization 26: 97–124CrossRefGoogle Scholar
  2. Amiri A. (2006) Designing a distribution network in a supply chain system: Formulation and efficient solution procedure. European Journal of Operational research 171(2): 567–576CrossRefGoogle Scholar
  3. Chen, C. Y., & Fun, Y. (2004). Particle swarm optimization algorithm and its application to clustering analysis. In Proceedings of IEEE International Conference on Networking, sensing and control, pp. 21–23.Google Scholar
  4. Clerc M., Kennedy J. (2002) The particle swarm—explosion, stability, and convergence in a multi-dimensional complex space. IEEE Transactions on Evolutionary Computations 6: 58–73CrossRefGoogle Scholar
  5. Cohen M.A., Lee H.L. (1978) Manufacturing strategy: Concepts and methods. In: Kleindorfer P.R.(eds) The management of productivity and technology in manufacturing. Plenum Press, New York, pp 153–183Google Scholar
  6. Cohen M.A., Moon S. (1991) An integrated plant loading model with economics of scale and scope. European Journal of Operational Research 50: 266–279CrossRefGoogle Scholar
  7. De Boer L., Vander Weden L., Telgen J. (1998) Outranking methods in support of supplier selection. European Journal of Purchasing and Supply Management 4: 109–118CrossRefGoogle Scholar
  8. Erlebacher S.J., Meller R.D. (2000) The interaction of location and inventory in designing distribution systems. IIE Transactions 32: 155–166Google Scholar
  9. Esmin A., Lambert-Torres G., De Souza A.Z. (2005) A hybrid particle Swarm optimization applied to loss power minimization. IEEE Transactions on power systems 20(2): 859–866CrossRefGoogle Scholar
  10. Francis R.L., McGinnis L.F., White J.A. (1992) Facility location and layout: An analytical approach. Prentice-Hall, Englewoods Cliffs, NJGoogle Scholar
  11. Geoffrion A.M., Graves G.W., Lee S.J. (1978) Strategic distribution system planning: A status report. In: Hax A.C.(eds) Studies in operations management. North Holland, Amsterdam, pp 178–314Google Scholar
  12. Huang W., Romeijn H.E., Geunes J. (2005) The continuous-time single-sourcing problem with production and inventory capacity constraints and expansion opportunities. Naval Research Logistics 52: 193–211CrossRefGoogle Scholar
  13. Jayaraman V. (1998) An efficient heuristic procedure for practical-sized capacitated warehouse design and management. Decision Sciences Journal 29(3): 729–745CrossRefGoogle Scholar
  14. Jayaraman V., Ross A. (2003) A simulated annealing methodology to distribution network design and management. European Journal of Operational Research 144: 629–645CrossRefGoogle Scholar
  15. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948.Google Scholar
  16. Leung Y.W., Wang Y. (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Transactions on Evolutionary Computations 5: 41–53CrossRefGoogle Scholar
  17. Meade L., Sarkis J. (1998) Strategic analysis of logistics and supply chain management systems using the analytical network process. Transportation Research, Part E 34(3): 201–215CrossRefGoogle Scholar
  18. Montgomery D.C. (1991) Design and analysis of experiments. Wiley, New YorkGoogle Scholar
  19. Park S.H. (1996) Robust design and analysis for quality engineering. Chapman & Hall, London, UKGoogle Scholar
  20. Ratnaweera A., Halgamuge S.K. (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation 8(3): 240–255CrossRefGoogle Scholar
  21. Ren, J., Yusuf, Y. Y., & Burns, N. D. (2000). A prototype of measurement system for agile enterprise. The third International Conference of Quality Reliability Maintenance, 29–30 March, Oxford, UK, pp. 274–252.Google Scholar
  22. Revelle C., Laporte G. (1996) The plant location problem: New models and research prospects. Operations Research 44: 864–874Google Scholar
  23. Robinson P.E., Goa L.L., Muggenborg S.T. (1993) Designing an integrated distribution system at Dowbrands, Inc. Interfaces 23(3): 107–117CrossRefGoogle Scholar
  24. Romeijn H.E., Shu J., Teo C.P. (2007) Designing two supply chain echelon networks. European Journal of Operational Research 178: 449–462CrossRefGoogle Scholar
  25. Ross P.J. (1989) Taguchi techniques for quality engineering. McGraw-Hill, New YorkGoogle Scholar
  26. Salman A., Ahmad I., Al-Madani S. (2002) Particle swarm optimization for task assignment problem. Microprocessors and Microsystems 26: 363–371CrossRefGoogle Scholar
  27. Samadhi A.T.M.A., Hoang K. (1998) Partner selection in a shared CIM system. International Journal of Integrated Manufacturing 11(2): 173–182CrossRefGoogle Scholar
  28. Sharp J.M., Irani Z., Desai S. (1999) Working towards agile manufacturing in the UK industry. International Journal of Production Economics 62: 155–169CrossRefGoogle Scholar
  29. Suganthan, N. (1999). Particle swarm optimizer with neighborhood operator. In Proceeding of IEEE International Conference on Evolutionary Computation, Vol. 3, pp. 1958–1962.Google Scholar
  30. Supply Chain Council. (2003). Supply chain operations reference model—Overview of SCOR Version 6.0. Supply Chain Council, Pittsburgh, PA, 2003.Google Scholar
  31. Taguchi G., Chowdhary S., Taguchi S. (2000) Robust engineering. McGraw-Hill, New YorkGoogle Scholar
  32. Talluri S., Baker R.C., Sarkis J. (1999) A framework for designing efficient value chain networks. International Journal of Production Economics 62: 133–144CrossRefGoogle Scholar
  33. Teo C.P., Shu J. (2004) Warehouse-retailer network design problem. Operations Research 52: 396–408CrossRefGoogle Scholar
  34. Tsai J.T., Chou J.H., Liu T.K. (2006) Tuning the structure and parameters of a neural network by using hybrid taguchi-genetic algorithm. IEEE Transactions on Neural Networks 17(1): 69–80CrossRefGoogle Scholar
  35. Van Hoek R.I., Harrison A., Christopher M. (2001) Measuring agile capabilities in the supply chain. International Journal of Operations & Production Management 21(1/2): 126–147CrossRefGoogle Scholar
  36. Wang L., Smith K. (1998) On chaotic simulated annealing. IEEE Transaction Neural Networks 9: 716–718CrossRefGoogle Scholar
  37. Weber M.M. (2002) Measuring supply chain agility in the virtual organization. International Journal of Physical Distribution & Logistical Management 32(7): 577–590CrossRefGoogle Scholar
  38. Yusuf Y.Y., Gunasekaran A., Adeleye E.O., Sivayoganathan K. (2004) Agile supply chain capabilities: Determinants of competitive objectives. European Journal of Operational Research 159: 379–392CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Manish Bachlaus
    • 1
  • Mayank Kumar Pandey
    • 1
  • Chetan Mahajan
    • 2
  • Ravi Shankar
    • 3
  • M. K. Tiwari
    • 4
    Email author
  1. 1.Department of Manufacturing EngineeringNIFFTRanchiIndia
  2. 2.Software EngineerHewlett Packard Global Soft LimitedChennaiIndia
  3. 3.Department of Management StudiesIITDelhiIndia
  4. 4.Department of Industrial Engineering and ManagementIITKharagpurIndia

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