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

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Introduction Problem Definition and Formulation Solution Methodology Conclusion References Describing Pricing Problem Pricing Problem Branching Improving Branch and Price Algorithm Computational Results Objective To find a pairing (a set of routes) associated with a variable with minimum reduced cost: Ĉ p = C p − X a ip · π i + X a ip · d i · µ j + X a ip · σ ji − ν j ∀p ∈ P j, j ∈ J (11) i∈N i∈N i∈N Subject to All of the routes must start & end at the same facility. Each customer node can be visited at most once. Total demand of each route ≤ vehicle capacity. Total travel time of the pairing ≤ time limit. Akça, Ralphs, Berger LRS PROBLEM
Introduction Problem Definition and Formulation Solution Methodology Conclusion References Pricing Problem as a Network Problem: Cont. Pricing Problem Branching Improving Branch and Price Algorithm Computational Results For each facility, construct a network with source and sink. d1 1 2 d2 0 Source Facility j −VCap Sink Facility j Cost of arc (i, k) in network for facility j: d3 3 ĉ ik = j cik − π k + d kµ j + σ jk c ik if k is a customer node otherwise Elementary (wrt. customer nodes), resource constraint shortest path problem (ESPPRC). Not elementary wrt sink → multiple vehicle routes. Sink is the end of a route and possibly beginning of another one. Akça, Ralphs, Berger LRS PROBLEM
Page 1 and 2: Introduction Problem Definition and
Page 7 and 8: Pairing Concept Introduction Proble
Page 11: 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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