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Design of multi-service systems with facilities functioning as open Jackson queueing networks: application to online shopping stores

OR Spectrum (2022)Cite this article

Abstract

This paper considers a realistic multi-service system design problem in which each service type is a stochastic sequence of services provided by different units of facilities where each facility is modeled as a set of open Jackson queueing networks. The problem is first formulated as a mixed-integer nonlinear programming model, which is further simplified to a model with a smaller number of constraints. Three exact solution methods are applied to solve the amended model. The first one is a cutting-plane method, which is based on a piecewise-linear approximation. The second is based on a mixed-integer linear programming formulation, which is enhanced by valid inequalities. The third is to use mixed-integer second-order cone programming. The methods are compared using a numerical study. Finally, an online pharmacy is considered as an example to illustrate the applicability of the problem, and some managerial insights are provided.

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References

  • Ahmadi-Javid A, Ramshe N (2020) Linear formulations and valid inequalities for a classic location problem with congestion: a robust optimization application. Optim Lett 14(5):1265–1285

    Article  Google Scholar 

  • Ahmadi-Javid A, Hoseinpour P (2022) Convexification of queueing formulas by mixed-integer second-order cone programming: an application to a discrete location problem with congestion. INFORMS J Comput. https://doi.org/10.1287/ijoc.2021.1125

    Article  Google Scholar 

  • Ahmadi-Javid A, Seyedi P, Syam SS (2017) A survey of healthcare facility location. Comput Oper Res 79:223–263

    Article  Google Scholar 

  • Ahmadi-Javid A, Berman O, and Hoseinpour P (2018) Location and capacity planning of facilities with general service-time distributions using conic optimization. arXiv preprint arXiv:1809.00080.

  • Bai X, Gopal R, Nunez M, Zhdanov D (2012) On the prevention of fraud and privacy exposure in process information flow. INFORMS J Comput 24(3):416–432

    Article  Google Scholar 

  • Berman O, Krass D (2019) Stochastic location models with congestion. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, Berlin, pp 477–535

    Chapter  Google Scholar 

  • Berman O, Krass D, Wang J (2006) Locating service facilities to reduce lost demand. IIE Trans 38(11):933–946

    Article  Google Scholar 

  • Bitran GR, Dasu S (1992) A review of open queueing network models of manufacturing systems. Queue Syst 12(1):95–133

    Article  Google Scholar 

  • Boffey B, Galvão R, Espejo L (2007) A review of congestion models in the location of facilities with immobile servers. Eur J Oper Res 178(3):643–662

    Article  Google Scholar 

  • Cardoso T, Oliveira MD, Barbosa-Póvoa A, Nickel S (2015) An integrated approach for planning a long-term care network with uncertainty, strategic policy and equity considerations. Eur J Oper Res 247(1):321–334

    Article  Google Scholar 

  • Elhedhli S (2006) Service system design with immobile servers, stochastic demand, and congestion. Manuf Serv Oper Manag 8(1):92–97

    Article  Google Scholar 

  • Fernández E, Landete M (2019) Fixed-charge facility location problems. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, Berlin, pp 47–77

    Google Scholar 

  • Galvão RD, Espejo LGA, Boffey B (2006) Practical aspects associated with location planning for maternal and perinatal assistance in Brazil. Ann Oper Res 143(1):31–44

    Article  Google Scholar 

  • Glover F (1975) Improved linear integer programming formulations of nonlinear integer problems. Manage Sci 22(4):455–460

    Article  Google Scholar 

  • Griffin PM, Scherrer CR, Swann JL (2008) Optimization of community health center locations and service offerings with statistical need estimation. IIE Trans 40(9):880–892

    Article  Google Scholar 

  • Kemeny JG, Snell JL (1983) Finite Markov chains. Springer, Belrin

    Google Scholar 

  • Kleinrock L (1964) Communication nets: Stochastic message flow and delay. Dover Publications, NY

    Google Scholar 

  • Marchand H, Martin A, Weismantel R, Wolsey L (2002) Cutting planes in integer and mixed integer programming. Discret Appl Math 123(1):397–446

    Article  Google Scholar 

  • Mestre AM, Oliveira MD, Barbosa-Póvoa A (2012) Organizing hospitals into networks: A hierarchical and multi-service model to define location, supply and referrals in planned hospital systems. Or Spectrum 34(2):319–348

    Article  Google Scholar 

  • Mestre AM, Oliveira MD, Barbosa-Póvoa AP (2015) Location–allocation approaches for hospital network planning under uncertainty. Eur J Oper Res 240(3):791–806

    Article  Google Scholar 

  • Radman M, Eshghi K (2018) Designing a multi-service healthcare network based on the impact of patients’ flow among medical services. OR Spectrum 40(3):637–678

    Article  Google Scholar 

  • Ramshe N, Ahmadi-Javid A (2018) Socially optimal design of a service network with location-aware multi-services under different delivery policies. Comput Ind Eng 125:490–499

    Article  Google Scholar 

  • Rebuge Á, Ferreira DR (2012) Business process analysis in healthcare environments: A methodology based on process mining. Inf Syst 37(2):99–116

    Article  Google Scholar 

  • Schweikhart SB, Smith-Daniels VL (1993) Location and service mix decisions for a managed health care network. Socioecon Plann Sci 27(4):289–302

    Article  Google Scholar 

  • Shanthikumar JG, Xu SH (1997) Asymptotically optimal routing and service rate allocation in a multiserver queueing system. Oper Res 45(3):464–469

    Article  Google Scholar 

  • Shortle JF, Thompson JM, Gross D, Harris CM (2018) Fundamentals of queueing theory. Wiley, NY

    Book  Google Scholar 

  • Stummer C, Doerner K, Focke A, Heidenberger K (2004) Determining location and size of medical departments in a hospital network: A multi-objective decision support approach. Health Care Manag Sci 7(1):63–71

    Article  Google Scholar 

  • Vidyarthi N, Jayaswal S (2014) Efficient solution of a class of location–allocation problems with stochastic demand and congestion. Comput Oper Res 48:20–30

    Article  Google Scholar 

  • Wein LM (1989) Capacity allocation in generalized Jackson networks. Oper Res Lett 8(3):143–146

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering & Management Systems, Amirkabir University of Technology, Tehran, Iran

    Amir Ahmadi-Javid

  2. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

    Mohammadreza Fathi

Authors
  1. Amir Ahmadi-Javid
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  2. Mohammadreza Fathi
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Correspondence to Amir Ahmadi-Javid.

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Ahmadi-Javid, A., Fathi, M. Design of multi-service systems with facilities functioning as open Jackson queueing networks: application to online shopping stores. OR Spectrum (2022). https://doi.org/10.1007/s00291-022-00668-x

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  • DOI: https://doi.org/10.1007/s00291-022-00668-x

Keywords

  • Location problems with congestion
  • Multi-service network design
  • Online shopping sites
  • Open Jackson queueing networks
  • Mixed-integer nonlinear programming (MINLP)
  • Mixed-integer second-order cone programming (MISOCP)
  • Cutting-plane method