Reliable Facility Location Design Under the Risk of Disruptions

Abstract

Reliable facility location models consider unexpected failures with site-dependent probabilities, as well as possible customer reassignment. This paper proposes a compact mixed integer program (MIP) formulation and a continuum approximation (CA) model to study the reliable uncapacitated fixed charge location problem (RUFL) which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios.The MIP determines the optimal facility locations as well as the optimal customer assignments, and the MIP is solved using a custom-designed Lagrangian Relaxation (LR) algorithm. The CA model predicts the total system cost without details about facility locations and customer assignments, and it provides a fast heuristic to find near-optimum solutions. Our computational results show that the LR algorithm is efficient for mid-sized RUFL problems and that the CA solutions are close to optimal in most of the test instances.For large-scale problems, the CA method is a good alternative to the LR algorithm that avoids prohibitively long running times.

The reliable hub-and-spoke design problem: Models and algorithms

“…[38] seek to minimize the expected transportation cost (and construction cost if fixed cost from construction is included) generated by receiving service from normal and backup facilities under an assumption that all nodes have the same unavailability. [9] relax the assumption of equal facility unavailability. [26] extend this direction by considering correlated unavailability among facilities.…”

“…Nevertheless, those reliable facility location models are difficult discrete optimization problems and state-of-the-art commercial solvers often fail to generate good solutions in a reasonable time for practical instances. To derive optimal solutions, Lagrangian relaxation based algorithms, and their Branch-and-Bound extensions, are the major solution strategies, see [38,26,9,28,25].…”

“…However, when unavailability is node-specific, reliable facility location models will have many nonlinear terms, whose linearizations will introduce enormous number of variables and constraints [9,25] and make Lagrangian relaxation algorithms less efficient. Under this situation, approximation algorithms [26,9] have been developed to efficiently obtain good solutions.…”

“…Under this situation, approximation algorithms [26,9] have been developed to efficiently obtain good solutions.…”

“…able facility location models [9,38,27]. Under some mild conditions, it is easy to prove that once facilities are selected, all customers' assignments, including backup assignments, can be easily derived according to the relative distances between customers and facilities.…”