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

Amir Ahmadi-Javid () and Mohammadreza Fathi
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Amir Ahmadi-Javid: Amirkabir University of Technology
Mohammadreza Fathi: Sharif University of Technology

OR Spectrum: Quantitative Approaches in Management, 2022, vol. 44, issue 4, No 8, 1255-1286

Abstract: 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.

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 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00291-022-00668-x

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