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Arabian Journal for Science and Engineering

, Volume 44, Issue 8, pp 7219–7233 | Cite as

A Maximal Covering Problem in Supply Chain Considering Variable Radius and Gradual Coverage with the Choice of Transportation Mode

  • Alireza EydiEmail author
  • Hossein Torabi
Research Article - Systems Engineering
  • 24 Downloads

Abstract

Today, supply chain management is a fundamental principle of business infrastructure implementation in the world. One of the most important pillars of the supply chain management is distribution network design. A distribution network with appropriate structure reduces costs and enhances customer-perceived service level, thereby improving competitive advantages of the company. In supply chain analysis, it is essential to focus on customers, as they greatly affect the formation of chain. This requires a balance between associated costs and the level of service provided. Variable radius and gradual radius maximal covering problem focus on the service levels in relation to the costs incurred to the system. In this study, a bi-objective mixed-integer nonlinear programming model was presented to determine optimal number, location and capacity of factories, distribution centers, and retailers, select transportation modes between the chain elements, and evaluate coverage radius of retailers, in such a way to minimize total transportation costs, maximize the covered demand, and achieve gradual coverage of facilities in a variable radius scheme. The proposed model was validated on a number of sample problems produced and solved by GAMS optimization software. Being NP-Hard, the problem was proposed to be solved via NSGA-II algorithm when its dimensions go large. Analysis of the computational results and respective comparisons indicated good performance of the presented algorithm.

Keywords

Supply chain design Multi-objective Variable radius and gradual covering Transportation mode selection NSGA-II algorithm 

Set of Indexes

I

Set of customers

J

Set of retailers

K

Distribution centers

P

Factories

L

Mode of transportation

V

Set of capacity levels available for factories

H

Set of levels of capacity available for distribution centers

U

Set of levels of capacity for retailers

Model Parameters

\(\hbox {DE}_{{{i}}}\)

The demand of customer i

\(d_{ij}\)

The distance of customer i from the potential location of retailer j

\(d_{kj}\)

The potential location of distribution center k from the potential location of retailer j

\(d_{pk}\)

The potential location of factory p from the potential location of retailer k

\(\upvarphi _{j} (r)\)

The variable establishment cost function of retailer j with radius of r

B

The budget allocated to the establishment of the facility

\(f_{i}(d_{ij})\)

Covering function determined based on the distance (decreasing)

\(F_{kh}\)

The cost of establishing a distribution center of the capacity h at potential location k

\(F_{ju}\)

Fixed cost of establishing a retailer facility of the capacity u at location j

\(F_{pv}\)

The cost of establishing the factory of the capacity m at potential location of p

\(C_{kjl}\)

Shipping cost of a single product from a potential distribution center k to the potential retailer j via the transportation mode i

\(C_{pkl}\)

Shipping cost of a single product from the potential factory at location p to the potential distribution center k via the transportation mode i

\(C_{ij}\)

Shipping cost of a single product from the potential retailer j to customer i

\(\hbox {Cap}_{kh}\)

Capacity of the distribution center k at level h

\(\hbox {Cap}_{pv}\)

Capacity of the factory p at level m

\(\hbox {Cap}_{ju}\)

Capacity of retailer j at level u

Model Variables

\(X_{{{pkl}}}\)

The amount of product transported from factory p to distribution center k via the transportation mode l

\(O_{{{kjl}}}\)

The amount of product transported from distribution center k to retailer j via the transportation mode l

\(W_{{{kh}}}\)

A binary variable, 1 if a distribution center of the capacity h is established at location k, and 0 otherwise

\(E_{{{pv}}}\)

A binary variable, 1 if a factory of the capacity v is constructed at location p, and 0 otherwise

\(S_{{{ju}}}\)

A binary variable, 1 if a retailer is constructed at location j, and 0 otherwise

\(Y_{{{ij}}}\)

A binary variable, 1 if customer i is assigned to retailer j, and 0 otherwise

\(A_{{{pkl}}}\)

A binary variable, 1 if transportation mode i is selected to serve the path between distribution center k and factory p, and 0 otherwise

\(G_{{{kjl}}}\)

A binary variable, 1 if transportation mode i is selected to serve the path between distribution center k and retailer j, and 0 otherwise

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References

  1. 1.
    Beamon, B.M.: Supply chain design and analysis: models and methods. Int. J. Prod. Econ. 55, 281–294 (1998)CrossRefGoogle Scholar
  2. 2.
    Jayaraman, V.: An efficient heuristic procedure for practical-sized capacitated warehouse design and management. Decis. Sci. 29, 729–745 (1998)CrossRefGoogle Scholar
  3. 3.
    Nozick, L.K.: The fixed charge facility location problem with coverage restrictions. Transp. Res. E 37, 281–299 (2001)Google Scholar
  4. 4.
    Berman, O.; Krass, D.: The generalized maximal covering location problem. Comput. Oper. Res. 29, 563–591 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Berman, O.; Drezner, Z.; Krass, D.; Wesolowsky, G.O.: The variable radius covering problem. Eur. J. Oper. Res. 196, 516–525 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Jabalameli, M.S.; Bankian Tabrizi, B.: Maximal covering problem considering variable radius and gradual coverage. In: 7th International Conference on Industrial Engineering, Iran (2010)Google Scholar
  7. 7.
    Jabalameli, M.S.; Bankian Tabrizi, B.; Javadi, M.: A simulated Annealing Method to solve a generalized maximal covering location problem. Int. J. Ind. Eng. Comput. 2(1), 439–448 (2011)Google Scholar
  8. 8.
    Bagherinejad, J.; Bashiri, M.; Nikzad, H.: General form of a cooperative gradual maximal covering location problem. J. Ind. Eng. Int. 14, 241–253 (2017)CrossRefGoogle Scholar
  9. 9.
    Eydi, A.; Mohebi, J.: Modeling and solution of maximal covering problem considering gradual coverage with variable radius over multi-periods. Rairo-Oper. Res. (2018).  https://doi.org/10.1051/ro/2018026
  10. 10.
    Syam, S.: A model and methodologies for the location problem with logistical components. Comput. Oper. Res. 29, 1173–1193 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Amiri, A.: Designing a distribution network in a supply chain system: formulation and efficient solution procedure. Eur. J. Oper. Res. 171(2), 567–576 (2006)CrossRefzbMATHGoogle Scholar
  12. 12.
    Truong, T.H.; Azadivar, F.: Optimal design methodologies for configuration of supply chains. Int. J. Prod. Res. 43(11), 2217–2236 (2005)CrossRefGoogle Scholar
  13. 13.
    Sabri, E.H.; Beamon, B.M.: A multi-objective approach to simultaneous strategic and operational planning in SC design. Omega 28, 581–598 (2000)CrossRefGoogle Scholar
  14. 14.
    Erol, I.; Ferrell Jr., W.G.: A methodology to support decision making across the supply chain of an industrial distributor. Int. J. Prod. Econ. 89, 119–129 (2004)CrossRefGoogle Scholar
  15. 15.
    Guillen, G.; Mele, F.D.; Bagajewicz, M.J.; Espuna, A.; Puigjaner, L.: Multi objective supply chain design under uncertainty. Chem. Eng. Sci. 60, 1535–1553 (2006)CrossRefGoogle Scholar
  16. 16.
    Selim, H.; Ozkarahan, I.: A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. Int. J. Adv. Manuf. Technol. 36, 401–418 (2008)CrossRefGoogle Scholar
  17. 17.
    Farahani, R.Z.; SteadieSeifi, M.; Asgari, N.: Multiple criteria facility location problems: a survey. Appl. Math. Model. 34(7), 1689–1709 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Olivares-Benitez, E.; Ríos-Mercado, R.Z.; Luis González Velarde, J.; González-Velarde, J.L.: A metaheuristic algorithm to solve the selection of transportation channel s in supply chain design. Int. J. Prod. Econ. 145, 161–172 (2013)CrossRefGoogle Scholar
  19. 19.
    Jabalameli, M.S.; Bankian Tabrizi, B.; Javadi, Moshref: Capacitated facility location problem with variable coverage radius in distribution system. Int. J. Ind. Eng. Prod. Res. 21, 231–237 (2010)Google Scholar
  20. 20.
    Mastrocinque, E.; Yuce, B.; Lambiase, A.; Packianather, M.S.: A multi-objective optimization for supply chain network using the bees algorithm. Int. J. Eng. Bus. Manag. 38, 1–11 (2013)Google Scholar
  21. 21.
    Ebrahimi Zade, A.; Sadegheih, A.: A modified NSGA-II solution for a new multi-objective hub maximal covering problem under uncertain shipments. J. Ind. Eng. Int. 10, 185–197 (2014)CrossRefGoogle Scholar
  22. 22.
    Bérubé, J.F.; Gendreau, M.; Potvin, J.Y.: An Exact \(\epsilon \)-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur. J. Oper. Res. 194, 39–50 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Krarup,; Pruzan, P.M.: The simple plant location problem: survey and synthesis. Eur. J. Oper. Res. 12, 36–81 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Zarandi, F.; Davari, S.; Haddad Sisakht, A.: The large-scale maximal covering location problem. Sci. Iran. 18(6), 1564–1570 (2011)CrossRefzbMATHGoogle Scholar
  25. 25.
    Srinivas, N.; Deb, K.: Multiobjective optimization using nondominated sorting genetic algorithms. Evol. Comput. 2, 221–248 (1995)CrossRefGoogle Scholar
  26. 26.
    Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T.A.M.T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. Evol. Comput. 6, 182–197 (2002)CrossRefGoogle Scholar
  27. 27.
    Madani, R.; Nookabadi, A.; Hejazi, R.: A bi-objective, reliable single allocation p-hub maximal covering location problem: mathematical formulation and solution approach. J. Air Transp. Manag. 68, 118–136 (2018)CrossRefGoogle Scholar
  28. 28.
    Bhattacharya, R.; Bandyopadhyay, S.: Solving conflicting bi-objective facility location problem by NSGA II evolutionary algorithm. Int. J. Adv. Manuf. Technol. 51, 397–414 (2010)CrossRefGoogle Scholar
  29. 29.
    Niknamfar, A.H.; Niaki, S.T.A.; Niaki, S.A.A.: Opposition-based learning for competitive hub location: a bi-objective biogeography-based optimization algorithm. Knowl. Based Syst. 128, 1–19 (2017)CrossRefGoogle Scholar
  30. 30.
    Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Evol. Comput. 8, 173–195 (2000)CrossRefGoogle Scholar
  31. 31.
    ZeinEldin, R.A.: A hybrid SS-SA approach for solving multi-objective optimization problems. Eur. J. Sci. Res. 121, 310–320 (2014)Google Scholar
  32. 32.
    Sedehzadeh, S.; Tavakkoli-Moghaddam, R.; Jolai, F.: A new multi-mode and multi-product hub covering problem: a priority M/M/c queue approach. Int. J. Ind. Math. 7, 139–148 (2015)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of KurdistanSanandajIran
  2. 2.Master of Industrial Engineering, Faculty of EngineeringUniversity of KurdistanSanandajIran

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