A cut-and-solve based algorithm for the single-source capacitated facility location problem
► The Single Source Capacitated Facility Location Problem (SSCFLP) is studied. ► A cut-and-solve based exact method is proposed for SSCFLP. ► New Fenchel cutting plane algorithm is proposed to separate 0–1 knapsack polytopes. ► Partial integrality strategy is used to further tighten the lower bound...
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| Published in: | European journal of operational research Vol. 221; no. 3; pp. 521 - 532 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Amsterdam
Elsevier B.V
16.09.2012
Elsevier Elsevier Sequoia S.A |
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | ► The Single Source Capacitated Facility Location Problem (SSCFLP) is studied. ► A cut-and-solve based exact method is proposed for SSCFLP. ► New Fenchel cutting plane algorithm is proposed to separate 0–1 knapsack polytopes. ► Partial integrality strategy is used to further tighten the lower bound of SSCFLP. ► Numerical experiments demonstrate the effectiveness of the proposed method.
In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS’s branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0–1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented. |
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| AbstractList | In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS's branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0-1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented. [PUBLICATION ABSTRACT] ► The Single Source Capacitated Facility Location Problem (SSCFLP) is studied. ► A cut-and-solve based exact method is proposed for SSCFLP. ► New Fenchel cutting plane algorithm is proposed to separate 0–1 knapsack polytopes. ► Partial integrality strategy is used to further tighten the lower bound of SSCFLP. ► Numerical experiments demonstrate the effectiveness of the proposed method. In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS’s branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0–1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented. In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CSas branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0a1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented. n this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS's branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0-1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented. |
| Author | Yang, Zhen Chu, Feng Chen, Haoxun |
| Author_xml | – sequence: 1 givenname: Zhen surname: Yang fullname: Yang, Zhen email: zhenyang.utt@gmail.com organization: Industrial Systems Optimization Laboratory, Charles Delaunay Institute and UMR CNRS STMR 6279, University of Technology of Troyes, 12 rue Marie Curie, BP 2060, Troyes 10010, France – sequence: 2 givenname: Feng surname: Chu fullname: Chu, Feng email: feng.chu@iup.univ-evry.fr organization: Laboratoire d’Informatique, Biologie Intégrative et Systèmes Complexes (IBISC), EA 4526, Université d’Evry Val d’Essonne, 40 Rue du Pelvoux, CE1455 Courcouronnes, 91020 Evry Cedex, France – sequence: 3 givenname: Haoxun surname: Chen fullname: Chen, Haoxun email: haoxun.chen@utt.fr organization: Industrial Systems Optimization Laboratory, Charles Delaunay Institute and UMR CNRS STMR 6279, University of Technology of Troyes, 12 rue Marie Curie, BP 2060, Troyes 10010, France |
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| Keywords | Facility location Cut-and-solve Cutting-plane method Polytope Branching Lower bound Tree(graph) Mixed integer programming Combinatorial optimization Cutting plane method Location problem Knapsack problem Upper bound Zero one programming Experimental design Capacity constraint |
| Language | English |
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| Snippet | ► The Single Source Capacitated Facility Location Problem (SSCFLP) is studied. ► A cut-and-solve based exact method is proposed for SSCFLP. ► New Fenchel... In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of... n this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS's... |
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| SubjectTerms | Algorithms Applied sciences Branch & bound algorithms Computer Science Cut-and-solve Cutting Cutting stock problem Cutting-plane method Exact sciences and technology Facility location Flows in networks. Combinatorial problems Integer programming Logistics Lower bounds Mathematical analysis Mathematical models Mathematical programming Operational research and scientific management Operational research. Management science Operations Research Optimization algorithms Planes Position (location) Strategy Studies |
| Title | A cut-and-solve based algorithm for the single-source capacitated facility location problem |
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