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.
Similar content being viewed by others
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
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
Ahmadi-Javid A, Seyedi P, Syam SS (2017) A survey of healthcare facility location. Comput Oper Res 79:223–263
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
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
Berman O, Krass D, Wang J (2006) Locating service facilities to reduce lost demand. IIE Trans 38(11):933–946
Bitran GR, Dasu S (1992) A review of open queueing network models of manufacturing systems. Queue Syst 12(1):95–133
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
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
Elhedhli S (2006) Service system design with immobile servers, stochastic demand, and congestion. Manuf Serv Oper Manag 8(1):92–97
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
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
Glover F (1975) Improved linear integer programming formulations of nonlinear integer problems. Manage Sci 22(4):455–460
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
Kemeny JG, Snell JL (1983) Finite Markov chains. Springer, Belrin
Kleinrock L (1964) Communication nets: Stochastic message flow and delay. Dover Publications, NY
Marchand H, Martin A, Weismantel R, Wolsey L (2002) Cutting planes in integer and mixed integer programming. Discret Appl Math 123(1):397–446
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
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
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
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
Rebuge Á, Ferreira DR (2012) Business process analysis in healthcare environments: A methodology based on process mining. Inf Syst 37(2):99–116
Schweikhart SB, Smith-Daniels VL (1993) Location and service mix decisions for a managed health care network. Socioecon Plann Sci 27(4):289–302
Shanthikumar JG, Xu SH (1997) Asymptotically optimal routing and service rate allocation in a multiserver queueing system. Oper Res 45(3):464–469
Shortle JF, Thompson JM, Gross D, Harris CM (2018) Fundamentals of queueing theory. Wiley, NY
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
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
Wein LM (1989) Capacity allocation in generalized Jackson networks. Oper Res Lett 8(3):143–146
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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 44, 1255–1286 (2022). https://doi.org/10.1007/s00291-022-00668-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-022-00668-x