The Flexible Periodic Vehicle Routing Problem

•A Mathematical model for the Flexible Periodic Vehicle Routing Problem (FPVRP) is proposed.•A Load-based formulation is developed to solve the FPVRP.•A set of several inequalities are proposed to reinforce the load-based FPVRP formulation.•A Load-based formulation for the Periodic Vehicle Routing P...

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Published in:	Computers & operations research Vol. 85; pp. 58 - 70
Main Authors:	Archetti, Claudia, Fernández, Elena, Huerta-Muñoz, Diana L.
Format:	Journal Article Publication
Language:	English
Published:	New York Elsevier Ltd 01.09.2017 Pergamon Press Inc
Subjects:	65 Numerical analysis 65K Mathematical programming, optimization and variational techniques 90 Operations research, mathematical programming 90C Mathematical programming Anàlisi numèrica Classificació AMS Cost analysis Customers Delivery scheduling Flexibility Inequalities Inventory Routing Investigació operativa Matemàtiques i estadística Modelització matemàtica Numerical analysis Operations research Periodic Vehicle Routing Programació (Matemàtica) Programming (Mathematics) Route planning Routing Schedules Service frequency Traveling salesman problem Vehicle routing Àrees temàtiques de la UPC Periodic Vehicle Routing Inventory Routing Service frequency Flexibility
ISSN:	0305-0548, 1873-765X, 0305-0548
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Abstract	•A Mathematical model for the Flexible Periodic Vehicle Routing Problem (FPVRP) is proposed.•A Load-based formulation is developed to solve the FPVRP.•A set of several inequalities are proposed to reinforce the load-based FPVRP formulation.•A Load-based formulation for the Periodic Vehicle Routing Problem (PVRP) and a load-based formulation for the Flexible Periodic Vehicle Routing Problem with InventoryConstraints (FPVRP-IC) are proposed for a fair comparison in the computational experience.•A computational experience was carried out in order to show that FPVRP formulation outperforms PVRP and FPVRP-IC formulations in terms of solution quality. [Display omitted] This paper introduces the Flexible Periodic Vehicle Routing Problem (FPVRP) where a carrier has to establish a distribution plan to serve his customers over a planning horizon. Each customer has a total demand that must be served within the horizon and a limit on the maximum quantity that can be delivered at each visit. A fleet of homogeneous capacitated vehicles is available to perform the services and the objective is to minimize the total routing cost. The FPVRP can be seen as a generalization of the Periodic Vehicle Routing Problem (PVRP) which instead has fixed service frequencies and schedules and where the quantity delivered at each visit is fixed. Moreover, the FPVRP shares some common characteristics with the Inventory Routing Problem (IRP) where inventory levels are considered at each time period and, typically, an inventory cost is involved in the objective function. We present a worst-case analysis which shows the advantages of the FPVRP with respect to both PVRP and IRP. Moreover, we propose a mathematical formulation for the problem, together with some valid inequalities. Computational results show that adding flexibility improves meaningfully the routing costs in comparison with both PVRP and IRP.
AbstractList	This paper introduces the Flexible Periodic Vehicle Routing Problem (FPVRP) where a carrier has to establish a distribution plan to serve his customers over a planning horizon. Each customer has a total demand that must be served within the horizon and a limit on the maximum quantity that can be delivered at each visit. A fleet of homogeneous capacitated vehicles is available to perform the services and the objective is to minimize the total routing cost. The FPVRP can be seen as a generalization of the Periodic Vehicle Routing Problem (PVRP) which instead has fixed service frequencies and schedules and where the quantity delivered at each visit is fixed. Moreover, the FPVRP shares some common characteristics with the Inventory Routing Problem (IRP) where inventory levels are considered at each time period and, typically, an inventory cost is involved in the objective function. We present a worst-case analysis which shows the advantages of the FPVRP with respect to both PVRP and IRP. Moreover, we propose a mathematical formulation for the problem, together with some valid inequalities. Computational results show that adding flexibility improves meaningfully the routing costs in comparison with both PVRP and IRP. Peer Reviewed This paper introduces the Flexible Periodic Vehicle Routing Problem (FPVRP) where a carrier has to establish a distribution plan to serve his customers over a planning horizon. Each customer has a total demand that must be served within the horizon and a limit on the maximum quantity that can be delivered at each visit A fleet of homogeneous capacitated vehicles is available to perform the services and the objective is to minimize the total routing cost The FPVRP can be seen as a generalization of the Periodic Vehicle Routing Problem (PVRP) which instead has fixed service frequencies and schedules and where the quantity delivered at each visit is fixed. Moreover, the FPVRP shares some common characteristics with the Inventory Routing Problem (IRP) where inventory levels are considered at each time period and, typically, an inventory cost is involved in the objective function. We present a worst-case analysis which shows the advantages of the FPVRP with respect to both PVRP and IRR Moreover, we propose a mathematical formulation for the problem, together with some valid inequalities. Computational results show that adding flexibility improves meaningfully the routing costs in comparison with both PVRP and IRP. •A Mathematical model for the Flexible Periodic Vehicle Routing Problem (FPVRP) is proposed.•A Load-based formulation is developed to solve the FPVRP.•A set of several inequalities are proposed to reinforce the load-based FPVRP formulation.•A Load-based formulation for the Periodic Vehicle Routing Problem (PVRP) and a load-based formulation for the Flexible Periodic Vehicle Routing Problem with InventoryConstraints (FPVRP-IC) are proposed for a fair comparison in the computational experience.•A computational experience was carried out in order to show that FPVRP formulation outperforms PVRP and FPVRP-IC formulations in terms of solution quality. [Display omitted] This paper introduces the Flexible Periodic Vehicle Routing Problem (FPVRP) where a carrier has to establish a distribution plan to serve his customers over a planning horizon. Each customer has a total demand that must be served within the horizon and a limit on the maximum quantity that can be delivered at each visit. A fleet of homogeneous capacitated vehicles is available to perform the services and the objective is to minimize the total routing cost. The FPVRP can be seen as a generalization of the Periodic Vehicle Routing Problem (PVRP) which instead has fixed service frequencies and schedules and where the quantity delivered at each visit is fixed. Moreover, the FPVRP shares some common characteristics with the Inventory Routing Problem (IRP) where inventory levels are considered at each time period and, typically, an inventory cost is involved in the objective function. We present a worst-case analysis which shows the advantages of the FPVRP with respect to both PVRP and IRP. Moreover, we propose a mathematical formulation for the problem, together with some valid inequalities. Computational results show that adding flexibility improves meaningfully the routing costs in comparison with both PVRP and IRP.
Author	Fernández, Elena Huerta-Muñoz, Diana L. Archetti, Claudia
Author_xml	– sequence: 1 givenname: Claudia surname: Archetti fullname: Archetti, Claudia email: claudia.archetti@unibs.it organization: Department of Economics and Management, Università di Brescia, Brescia, Italy – sequence: 2 givenname: Elena surname: Fernández fullname: Fernández, Elena email: e.fernandez@upc.edu organization: Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Barcelona, Spain – sequence: 3 givenname: Diana L. surname: Huerta-Muñoz fullname: Huerta-Muñoz, Diana L. email: diana.huerta@upc.edu organization: Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Barcelona, Spain
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Snippet	•A Mathematical model for the Flexible Periodic Vehicle Routing Problem (FPVRP) is proposed.•A Load-based formulation is developed to solve the FPVRP.•A set of... This paper introduces the Flexible Periodic Vehicle Routing Problem (FPVRP) where a carrier has to establish a distribution plan to serve his customers over a...
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SubjectTerms	65 Numerical analysis 65K Mathematical programming, optimization and variational techniques 90 Operations research, mathematical programming 90C Mathematical programming Anàlisi numèrica Classificació AMS Cost analysis Customers Delivery scheduling Flexibility Inequalities Inventory Routing Investigació operativa Matemàtiques i estadística Modelització matemàtica Numerical analysis Operations research Periodic Vehicle Routing Programació (Matemàtica) Programming (Mathematics) Route planning Routing Schedules Service frequency Traveling salesman problem Vehicle routing Àrees temàtiques de la UPC
Title	The Flexible Periodic Vehicle Routing Problem
URI	https://dx.doi.org/10.1016/j.cor.2017.03.008 https://www.proquest.com/docview/1913317932 https://recercat.cat/handle/2072/304738
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