Reliable facility location design with round-trip transportation under imperfect information part II: A continuous model

Abstract

The Part I paper (Yun et al., 2019) of this study developed a discrete model and a customized Lagrangian relaxation algorithm for the reliable problem of facility locations considering round-trip transportation when customers are not aware of facility states in real time until they visit them on site. Since the investigated problem is an NP-hard problem, large-scale instances of this problem may not be solved efficiently by the discrete model. To address this issue, this paper proposes a counterpart continuous model to solve large-scale instances of the investigated problem. The continuous model assumes that all the settings are continuous and adopts the continuum approximation (CA) technique to obtain a near-optimum solution to this investigated problem. The CA technique also reveals theoretical insights into solution structures of each sub-problem on a customer's pattern of visiting facilities on a homogeneous plane. Numerical experiments find that the continuous model with the CA technique has superior computational efficiency for large-scale instances. The results of the case studies indicate that the proposed continuous model can obtain a near-optimum solution for the investigated location problem with heterogeneous settings and has a robust performance.