Optimizing Location, Routing and Scheduling Decisions ... - gerad

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Simple Valid Inequalities Introduction Problem Definition and Formulation Solution Methodology Conclusion References Problem Definition Set Partitioning Formulation X a ipz p ≤ t j ∀i ∈ I, ∀j ∈ J (σ ji ), (6) p∈P j X t j ≥ N F , (7) j∈J X z p = v j ∀j ∈ J (ν j ), (8) p∈P j v j ≥ t j ∀j ∈ J, (9) v j ∈ Z + ∀j ∈ J. (10) N F is the minimum number of facilities required to be open: N F = argmin {l=1..|J|} lX Cj F t ≥ X ! D i t=1 i∈I s.t. Cj F 1 ≥ Cj F 2 ≥ ... ≥ Cj F n Akça, Ralphs, Berger LRS PROBLEM
Introduction Problem Definition and Formulation Solution Methodology Conclusion References Branch and Price Algorithm Pricing Problem Branching Improving Branch and Price Algorithm Computational Results Initial Columns Solve Restricted Master Problem (RMP) Dual Variables Until no new column new columns Optimal Soln. of RMP=LOWER BD IP Soln. of RMP=UPPER BD. Solve Pricing Problem: Find columns with (−) reduced cost ROOT NODE If LP is not integral Branching MODIFIED RPM Constraints + Variable Fixing MODIFIED RPM Constraints + Variable Fixing Solve LP Solve MODIFIED Pricing Problem Solve LP Solve MODIFIED Pricing Problem Akça, Ralphs, Berger LRS PROBLEM
Page 1 and 2: Introduction Problem Definition and
Page 7 and 8: Pairing Concept Introduction Proble
Page 9: Introduction Problem Definition and
Page 15 and 16: Branching Rules Introduction Proble
Page 25 and 26: Conclusions Introduction Problem De

Optimizing Location, Routing and Scheduling Decisions ... - gerad

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