Reliable Facility Location Design Under the Risk of Disruptions

Authors:
Tingting Cui;Yanfeng Ouyang;Zuo-Jun Max Shen
Affiliations:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720;Department of Civil and Environmental Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801;Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720
Venue:
Operations Research
Year:
2010

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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 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.