The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach

In this paper, we consider a variant of the Location-Routing Problem (LRP), namely the LRP with simultaneous pickup and delivery (LRPSPD). The LRPSPD seeks to minimize total cost by simultaneously locating the depots and designing the vehicle routes that satisfy pickup and delivery demand of each cu...

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Bibliographic Details
Published in:Omega (Oxford) Vol. 40; no. 4; pp. 465 - 477
Main Authors: Karaoglan, Ismail, Altiparmak, Fulya, Kara, Imdat, Dengiz, Berna
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.08.2012
Elsevier
Pergamon Press Inc
Series:Omega
Subjects:
Applied sciences
Deliveries
Exact sciences and technology
Ganzzahlige Optimierung
Heuristic
Heuristik
Integer programming
Linear programming
Location-routing problem
Location-routing problem Simultaneous pickup and delivery Mixed integer programming formulation Simulated annealing
Logistics
Mathematical programming
Mixed integer programming formulation
Operational research and scientific management
Operational research. Management science
Routing
Simulated annealing
Simulation
Simultaneous pickup and delivery
Studies
Tourenplanung
Transportproblem
Location-routing problem
Mixed integer programming formulation
Simultaneous pickup and delivery
Simulated annealing
Lower bound
Costs
Mixed integer programming
Routing
Strong solution
Modeling
Location problem
Computation time
Supply demand balance
Heuristic method
Reverse logistics
Localization
Inequality
ISSN:0305-0483, 1873-5274
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Summary:In this paper, we consider a variant of the Location-Routing Problem (LRP), namely the LRP with simultaneous pickup and delivery (LRPSPD). The LRPSPD seeks to minimize total cost by simultaneously locating the depots and designing the vehicle routes that satisfy pickup and delivery demand of each customer at the same time. We propose two polynomial-size mixed integer linear programming formulations for the problem and a family of valid inequalities to strengthen the formulations. While the first formulation is a node-based formulation, the second one is a flow-based formulation. Furthermore, we propose a two-phase heuristic approach based on simulated annealing, tp_SA, to solve the large-size LRPSPD and two initialization heuristics to generate an initial solution for the tp_SA. We then empirically evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions or strong lower bounds, and investigate the performance of the proposed heuristic approach. Computational results show that the flow-based formulation performs better than the node-based formulation in terms of the solution quality and the computation time on small-size problems. However, the node-based formulation can yield competitive lower bounds in a reasonable amount of time on medium-size problems. Meantime, the proposed heuristic approach is computationally efficient in finding good quality solutions for the LRPSPD. ► We consider a variant of the Location-Routing Problem (LRP), namely the LRP with simultaneous pickup and delivery. ► We propose two polynomial-size mixed integer linear programming formulations, called flow- and node-base formulations, and a family of valid inequalities to strengthen the formulations. ► We also propose a two-phase heuristic approach based on simulated annealing, tp_SA, to solve the large-size problems. ► Computational results show that while the flow-based formulation performs better than the node-based formulation on small-size problems, the node-based formulation can yield competitive lower bounds on medium-size problems. ► The proposed heuristic approach is computationally efficient in finding good quality solutions.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0305-0483
1873-5274
DOI:10.1016/j.omega.2011.09.002