Bibliographic Details
| Title: |
An augmented Lagrangian decomposition method for the single-source capacitated facility location problem. |
| Authors: |
Hong, Deshan1 (AUTHOR), Wang, Rui1 (AUTHOR) ruiwang@bicmr.pku.edu.cn |
| Source: |
Journal of Industrial & Management Optimization. 2026, Vol. 22 Issue 7, p1-26. 26p. |
| Subject Terms: |
Location problems (Programming), Assignment problems (Programming), Combinatorial optimization, Constraint satisfaction, Duality theory (Mathematics) |
| Abstract: |
We studied the single-source capacitated facility location problem (SSCFLP), which can also be viewed as a representative structured binary optimization model with assignment, activation, and capacity constraints. The main difficulty comes from the discrete structure of the model and the coupling constraints, which make large-scale instances hard to solve. To exploit this structure, we introduced a split formulation that separates the original variables into two blocks connected by an equality constraint. For the reformulated model, we proposed an augmented Lagrangian decomposition method with tractable primal subproblems. We further showed that the augmented Lagrangian dual has zero duality gap with the original binary problem when the penalty parameter is sufficiently large. This result provides a theoretical basis for applying the augmented Lagrangian method to this discrete optimization problem. In addition, we used a primal recovery step and a final refinement step to improve feasible solutions. Numerical results demonstrated that the proposed method can produce high-quality feasible solutions on both synthetic and benchmark instances, especially for large instances in time-limited settings. [ABSTRACT FROM AUTHOR] |
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| Database: |
Business Source Index |