# THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers

### Andreas Stenger

#### Abstract

In this paper, we propose a new routing problem to model a highly relevant planning problem in small package shipping. The problem, called Prize-Collecting Vehicle Routing Problem with Non-Linear cost (PCVRPNL), allows for each customer the choice of being serviced by a vehicle of the private fleet or being outsourced to a subcontractor. A lower bound on the total customer demand serviced by the private fleet ensures a constant capacity utilization. The subcontracting costs follow a non-linear function representing the discount given by a subcontractor if larger amounts of packages are assigned. To solve the NP-hard problem, we propose a Variable Neighborhood Search algorithm. In numerical studies performed on benchmark instances adapted from classical VRP, we demonstrate the strong performance of our algorithm and study the effect of different cost functions on the routing solution.

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#### Paper Citation

#### in Harvard Style

Stenger A. (2012). **THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers** . In *Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-8425-97-3, pages 265-273. DOI: 10.5220/0003740002650273

#### in Bibtex Style

@conference{icores12,

author={Andreas Stenger},

title={THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers},

booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2012},

pages={265-273},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003740002650273},

isbn={978-989-8425-97-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers

SN - 978-989-8425-97-3

AU - Stenger A.

PY - 2012

SP - 265

EP - 273

DO - 10.5220/0003740002650273