Bi-objective optimization of a queueing model with two-phase heterogeneous service

Chia-Huang Wu, Dong Yuh Yang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper presents a novel queueing model describing the operational process of a semi-attended self-checkout counter for retail stores. Specifically, we consider an M/M/(1 + c) queueing system with two-phase heterogeneous service scheme, where the arrival of customers at the check-out system follows a Poisson process. After using the matrix-geometric method to analyze the queueing system in a steady state, important performance measures are developed. We evaluate a single-objective (i.e., cost minimization) problem based on the expected cost function per unit time, and then apply the canonical particle swarm optimization algorithm to solve it. A bi-objective optimization model used to minimize the expected cost and the expected waiting time of customers is also formulated. The proposed analytical approach makes it possible to achieve an appropriate balance between operational costs and service quality.

Original languageEnglish
Article number105230
Pages (from-to)1-13
Number of pages13
JournalComputers and Operations Research
StatePublished - Jun 2021


  • Bi-objective optimization
  • Canonical particle swarm optimization algorithm
  • Epsilon-constraint algorithm
  • Two-phase heterogeneous service


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