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Modeling and solving a capacitated stochastic location-allocation problem using sub-sources

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Abstract

We study a capacitated multi-facility location-allocation problem in which the customers have stochastic demands based on Bernoulli distribution function. We consider the capacitated sub-sources of facilities to satisfy demands of customers. In the discrete stochastic problem, the goal is to find optimal locations of facilities among candidate locations and optimal allocations of existing customers to operating facilities so that the total sum of fixed costs of operating facilities, allocation cost of the customers, expected values of servicing and outsourcing costs is minimized. The model is formulated as a mixed-integer nonlinear programming problem. Since finding an optimal solution may require an excessive amount of time depending on nonlinear constraints, we transform the nonlinear constraints of the problem to linear ones to arrive at a simple formulation of the model. Numerical results show that the LINGO 9.0 software is capable of solving small size problems. For medium and large-size problems, we propose two meta-heuristic algorithms, namely a genetic algorithm and a discrete version of colonial competitive algorithm. Computational results show that the proposed algorithms efficiently obtain effective solutions.

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References

  • Albareda-Sambola M, Van Der Vlerk M, Fernández E (2006) Exact solutions to a class of stochastic generalized assignment problems. Eur J Oper Res 173(2):465–487

    Article  MathSciNet  MATH  Google Scholar 

  • Albareda-Sambola M, Fernández E, Laporte G (2007) Heuristic and lower bounds for a stochastic location routing problem. Eur J Oper Res 179(3):940–955

    Article  MATH  Google Scholar 

  • Albareda-Sambola M, Fernández E, Saldanha-da-Gama F (2011) The facility location problem with Bernoulli demands. Omega 39(3):335–345

    Article  Google Scholar 

  • Alizadeh M, Mahdavi I, Shiripour S, Asadi H (2013) A nonlinear model for a capacitated location–allocation problem with Bernoulli demand using sub-sources. Int J Eng 26(2):1007–1016

    Google Scholar 

  • Amiri-Aref M, Javadian N, Tavakkoli-Moghaddam R, Baboli A, Shiripour S (2013) The center location-dependent relocation problem with a probabilistic line barrier. Appl Soft Comput 13(7):3380–3391

    Article  Google Scholar 

  • Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. Evolutionary computation, CEC, IEEE

  • Atashpaz-Gargari E, Hashemzadeh F, Rajabioun R, Lucas C (2008) Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process. Int J Intell Comput Cybern 1(3):337–355

  • Behnamian J, Zandieh M (2011) A discrete colonial competitive algorithm for hybrid flow shop scheduling to minimize earliness and quadratic tardiness penalties. Expert Syst Appl 38(12):14490–14498

  • Berman O, Simchi-Levi D (1988) Finding the optimal a priori tour and location of a traveling salesman with non-homogeneous customers. Transp Sci 22(10):148–154

    Article  MathSciNet  MATH  Google Scholar 

  • Biabangard-Oskouyi A, Atashpaz-Gargari E, Soltani N, Lucas C (2009) Application of imperialist competitive algorithm for materials property characterization from sharp indentation test. Int J Eng Simul 10(1):11–12

    Google Scholar 

  • Bianchi L, Campbell AM (2007) Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem. Eur J Oper Res 176(1):131–144

    Article  MathSciNet  MATH  Google Scholar 

  • Boukani FH, Moghaddam BF, Pishvaee MS (2014) Robust optimization approach to capacitated single and multiple allocation hub location problems. Comput Appl Math 76(5–8):1091–1110

  • Chan KY, Aydin EM, Fogarty TC (2006) Main effect fine-tuning of the mutation operator and the neighbourhood function for uncapacitated facility location problems. Soft Comput 10(11):1075–1090

    Article  Google Scholar 

  • Cooper L (1963) Location–allocation problems. Oper Res 11(3):331–343

    Article  MathSciNet  MATH  Google Scholar 

  • Cooper L (1964) Heuristic methods for location–allocation problems. SIAM Rev 6(1):37–53

    Article  MathSciNet  MATH  Google Scholar 

  • Cooper L (1972) The transportation-location problem. Oper Res 20(1):94–108

    Article  MathSciNet  MATH  Google Scholar 

  • Drezner T, Drezner Z, Goldstein Z (2010) A stochastic gradual cover location problem. Nav Res Logist (NRL) 57(4):367–372

    MathSciNet  MATH  Google Scholar 

  • Francis RL, Mcginnis LF, White JA (1992) Facility layout and location: an analytical approach. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Hillier FS, Lieberman GJ (2001) Introduction to operations research, 8th edn. McGraw-Hill, New York

  • Jasour AM, Atashpaz E, Lucas C (2008) Vehicle fuzzy control using imperialist competitive algorithm. In: Second Iranian joint congress on fuzzy and intelligent systems (IFIS 2008), Tehran, Iran

  • Karimi H, Bashiri M (2011) Hub covering location problems with different coverage types. Sci Iran 18(6):1571–1578

    Article  Google Scholar 

  • Khabbazi A, Atashpaz-Gargari E, Lucas C (2009) Imperialist competitive algorithm for minimum bit error rate beamforming. Int J Bio-Inspired Comput 1(1–2):125–133

    Article  Google Scholar 

  • Laporte G, Louveaux FV, Mercure H (1994) An exact solution for the a priori optimization of the probabilistic traveling salesman problem. Oper Res 42(3):543–549

    Article  MathSciNet  MATH  Google Scholar 

  • Lee KY, Han SN, Roh MI (2003) An improved genetic algorithm for facility layout problems having inner structure walls and passages. Comput Oper Res 30(1):117–138

    Article  MathSciNet  MATH  Google Scholar 

  • Manzini R, Gebennini E (2008) Optimization models for the dynamic facility location and allocation problem. Int J Prod Res 46(8):2061–2086

    Article  MATH  Google Scholar 

  • Marić M, Stanimirović Z, Stanojević P (2013) An efficient memetic algorithm for the uncapacitated single allocation hub location problem. Soft Comput 17(3):445–466

    Article  Google Scholar 

  • Marn A (2011) The discrete facility location problem with balanced allocation of customers. Eur J Oper Res 210(1):27–38

    Article  MathSciNet  Google Scholar 

  • Mehdizadeh E, Tavarroth MR, Hajipour V (2011a) A new hybrid algorithm to optimize stochastic-fuzzy capacitated multi-facility location–allocation problem. J Optim Ind Eng 7:71–80

    Google Scholar 

  • Mehdizadeh E, Tavarroth MR, Mousavi SM (2010b) Solving the stochastic capacitated location–allocation problem by using a new hybrid algorithm, MATH’ 10 proceedings of the 15\(^{th}\) WSEAS international conference on applied mathematics, Athens, Greece, December 29–31, 2010, pp 27–32

  • Mousavi M, Niaki T (2013) Capacitated location allocation problem with stochastic location and fuzzy demand: a hybrid algorithm. Appl Math Model 37(7):5109–5119

    Article  MathSciNet  Google Scholar 

  • Mousavi M, Niaki T, Mehdizadeh E, Tavarroth M (2013) The capacitated multi-facility location–allocation problem with probabilistic customer location and demand: two hybrid meta-heuristic algorithms. Int J Syst Sci 44(10): 1897–1912

    Article  MathSciNet  MATH  Google Scholar 

  • Mozafari H, Abdi B, Ayob A (2012) Optimization of adhesive-bonded fiber glass strip using imperialist competitive algorithm. Procedia Technol 1:194–198

    Article  Google Scholar 

  • Nazari-Shirkouhi S, Eivazy H, Ghodsi R, Rezaie K, Atashpaz-Gargari E (2010) Solving the integrated product mix outsourcing problem using the imperialist competitive algorithm. Expert Syst Appl 37(12):7615–7626

    Article  Google Scholar 

  • Pank K, Lai KK, Liang L, Leung CH (2009) Two-period pricing and ordering policy for the dominant retailer in a two-echelon supply chain with demand uncertainty. Omega 37(4):919–929

    Article  Google Scholar 

  • Pilotta E, Torres G (2011) A projected Weiszfeld algorithm for the box-constrained Weber location problem. Appl Math Comput 218(6):2932–2943

    MathSciNet  MATH  Google Scholar 

  • Rajabioun R, Hashemzadeh F, Atashpaz-Gargari E, Mesgari B, Rajaei Salmasi F (2008a) Identification of a MIMO evaporator and its decentralized PID controller tuning using colonial competitive algorithm. In: Proceedings of the 17th world congress, The International Federation of Automatic Control, Seoul, Korea, July 6–11, 2008, pp 9952–9957

  • Rajabioun R, Atashpaz-Gargari E, Lucas C (2008b) Colonial competitive algorithm as a tool for Nash equilibrium point achievement. Comput Sci Appl-ICCSA 2008 5073:680–695

  • Sha Y, Huang J (2012) The multi-period location–allocation problem of engineering emergency blood supply systems. Syst Eng Procedia 5(1):21–28

    Article  Google Scholar 

  • Shiripour S, Amiri-Aref M, Mahdavi I (2011a) The capacitated location–allocation problem in the presence of \(k\) connections. Appl Math 2:947–952

    Article  MathSciNet  Google Scholar 

  • Shiripour S, Mahdavi I, Amiri-Aref M, Mohammadnia-Otaghsara M, Mahdavi-Amiri N (2011b) Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model. Int J Prod Res 50(15):3988–4008

    Article  Google Scholar 

  • Silva FJF, de la Figuera DS (2007) A capacitated facility location problem with constrained backlogging probabilities. Int J Prod Res 45(21):5117–5134

    Article  MATH  Google Scholar 

  • Wang B, He S, Jaruphongsa W, Tan V, Hui C (2010) Robust optimization model and algorithm for logistics center location and allocation under uncertain environment. J Transp Syst Eng Inf Technol 9(2):69–74

    Google Scholar 

  • Weber A (1909) Über den Standort der Industrien, Tübingen theory of the location of industries. Chicago, University of Chicago Press (English translation by C.J. Friedrich, 1929)

  • Wen M, Kang R (2011) Some optimal models for facility location–allocation problem with random fuzzy demands. Appl Soft Comput 11(1):1202–1207

    Article  Google Scholar 

  • Yang K, Liu Y (2014) Developing equilibrium optimization methods for hub location problems. Soft Comput. doi:10.1007/s00500-014-1427-1

  • Yao Z, Lee L, Jaruphongsa W, Tan V, Hui C (2010) Multi-source facility location–allocation and inventory problem. Eur J Oper Res 207(2):750–762

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou J, Liu B (2003a) New stochastic models for capacitated location–allocation problem. Comput Ind Eng 45(1):111–125

    Article  Google Scholar 

  • Zhou J, Liu B (2007b) Modeling capacitated location-allocation problem with fuzzy demands. Comput Ind Eng 53(3):454–468

    Article  Google Scholar 

Download references

Acknowledgments

The first and third authors acknowledge Mazandaran University of Science and Technology and the second author thanks Sharif University of Technology for supporting this work.

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Authors and Affiliations

  1. Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran

    Morteza Alizadeh & Saber Shiripour

  2. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Nezam Mahdavi-Amiri

Authors
  1. Morteza Alizadeh
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  2. Nezam Mahdavi-Amiri
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  3. Saber Shiripour
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Correspondence to Morteza Alizadeh.

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Communicated by V. Loia.

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Alizadeh, M., Mahdavi-Amiri, N. & Shiripour, S. Modeling and solving a capacitated stochastic location-allocation problem using sub-sources. Soft Comput 20, 2261–2280 (2016). https://doi.org/10.1007/s00500-015-1640-6

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  • DOI: https://doi.org/10.1007/s00500-015-1640-6

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