Bi-objective optimization of a queueing model with two-phase heterogeneous service - Wu, Chia-Huang; Yang, Dong-Yuh (Computers & operations research, 2021)
•We consider an M/M/(1 + c) queueing system with two-phase heterogeneous service.•The stability condition is derived using the matrix-geometric method.•We obtain the stationary distribution of the system size.•Sensitivity analysis of system performance measures is conducted.•We outline the single-objective and bi-objective optimization models. 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.