A reliability model for facility location design under imperfect information

• Consider the optimal trial-and-error visiting strategy in reliable location design.
• Formulate a compact model for reliable location design under imperfect information.
• Compare imperfect information and perfect information models.
• Propose an efficient customized solution approach based on Lagrangian relaxation.
• Reveal managerial insights into optimal location design and cost tradeoff.

This paper aims to propose a modeling framework for reliable facility location design under imperfect information, i.e., when customers do not know the real-time information of facility disruption states. We consider a realistic “trial-and-error” strategy for a customer to visit facilities without knowing their states until arriving at this facility; i.e., a customer keeps trying a number of pre-assigned facilities until she acquires the service or is forced to give up trying. The research problem is to determine the best facility location that minimizes the total system cost, including initial facility investment and expected long-term operational cost from transportation and loss of service, when facilities are subject to probabilistic disruptions and customers use the trial-and-error strategy. This problem is formulated into a compact integer program (IP), and we develop a Lagrangian relaxation algorithm to solve it. A set of case studies are conducted to test the performance of the proposed algorithm, and illustrate the applicability of the proposed model. The results reveal a number of interesting insights into the system design, including the significance of multi-level customer-facility assignments and the existence of a robust system design against variation of the loss-of-service penalty.