# Exact Solution of the Multi-trip Inventory Routing Problem using a Pseudo-polynomial Model

### Nuno Braga, Cláudio Alves, Rita Macedo

#### Abstract

In this paper, we address an inventory routing problem where a vehicle can perform more than one trip in a working day. This problem was denominated multi-trip vehicle routing problem. In this problem a set of customers with demand for the planning horizon must be satisfied by a supplier. The supplier, with a set of vehicles, delivers the demand using pre-calculated valid routes that define the schedule of the delivery of goods on the planning horizon. The problem is solved with a pseudo-polynomial network flow model that is solved exactly in a set of instances adapted from the literature. An extensive set of computational experiments on these instances were conducted varying a set of parameters of the model. The results obtained with this model show that it is possible to solve instances up to 50 customers and with 15 periods in a reasonable computational time.

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#### Paper Citation

#### in Harvard Style

Braga N., Alves C. and Macedo R. (2017). **Exact Solution of the Multi-trip Inventory Routing Problem using a Pseudo-polynomial Model** . In *Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-218-9, pages 250-257. DOI: 10.5220/0006118502500257

#### in Bibtex Style

@conference{icores17,

author={Nuno Braga and Cláudio Alves and Rita Macedo},

title={Exact Solution of the Multi-trip Inventory Routing Problem using a Pseudo-polynomial Model},

booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2017},

pages={250-257},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006118502500257},

isbn={978-989-758-218-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Exact Solution of the Multi-trip Inventory Routing Problem using a Pseudo-polynomial Model

SN - 978-989-758-218-9

AU - Braga N.

AU - Alves C.

AU - Macedo R.

PY - 2017

SP - 250

EP - 257

DO - 10.5220/0006118502500257