A branch and price approach for the Split Pickup and Split Delivery VRP

doi:10.1016/j.endm.2018.07.025

Electronic Notes in Discrete Mathematics

Volume 69, August 2018, Pages 189-196

https://doi.org/10.1016/j.endm.2018.07.025 Get rights and content

Abstract

In this paper we address a Pickup and Delivery Vehicle Routing Problem where the demands of both pickup and delivery nodes can be split between several vehicles. We investigate a new formulation where the route of each vehicle is decomposed into a sequence of simpler substructures called clusters, mitigating the combinatorial explosion of feasible solutions. We implement a branch-and-price algorithm exploiting column generation procedures that dynamically generates clusters to obtain improved dual bounds, and ad hoc branching strategies to achieve integrality.

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Cited by (11)

Solving the vehicle routing problem with drone for delivery services using an ant colony optimization algorithm
2022, Advanced Engineering Informatics
Citation Excerpt :
Conventionally, the VRP obtains the dispatching plan for trucks located at the depot to serve customers. Different VRP variants exist in the literature to accommodate different conditions and requirements such as the pickup and delivery VRP [9], heterogeneous fleet VRP [10], multi-depot VRP [11,12], among others. In recent years, auxiliary vehicles (e.g., motorcycle, trailer, small van, or drone) have been employed to assist primary vehicles (e.g., large trucks) in servicing customers, particularly when encountering poor parking conditions or scarce vehicle accessibility.
E-commerce and logistics companies are facing important challenges to satisfy the rapid growth of customer demands. Unmanned aerial vehicles such as drones are an emerging technology that are very useful to cope with rising customer expectations of fast, flexible, and reliable delivery services. Drones work in tandem with trucks to perform parcel delivery, which have proven to reduce costs, CO2 emissions, and delivery times. This research proposes a mixed integer programming formulation to address the Vehicle Routing Problem with Drone (VRPD) by assigning customers to drone-truck pairs, determining the number of dispatching drone-truck units, and obtaining optimal service routes while the fixed and travel costs of both vehicles are minimized. Given the NP-hard nature of the VRPD, an ant colony optimization (ACO) algorithm is elaborated to solve this problem. Two novel methods are proposed to investigate the efficiency of the drone-truck combination by allowing the drones to perform additional delivery services to only one feasible customer and also multiple feasible customers while the truck waits at a customer location. Experimental results show that the proposed ACO algorithm can effectively solve the VRDP for different size instances and different customer location distributions, and is successful in providing timely solutions for small test instances within 1% of the optimal solutions. Finally, experimentation also reveals that the ACO algorithm outperforms the classical VRP by obtaining cost-savings of over 30% for large instances.
A route decomposition approach for the single commodity Split Pickup and Split Delivery Vehicle Routing Problem
2021, European Journal of Operational Research
Citation Excerpt :
The main idea is to decompose routes into simpler substructures, thereby proving and exploiting a rich set of combinatorial properties on them. A preliminary version of our approach, covering partial results, was presented as Casazza, Ceselli, and Wolfler Calvo (2018). In Section 2 we first formalize the problem and then, in Section 2.1, we describe the way we decompose vehicle routes, obtaining simpler combinatorial substructures that we call clusters, investigating their theoretical properties.
We address a single commodity Pickup and Delivery Vehicle Routing Problem from the literature. A network of customer nodes is given with both travel times and costs. A fleet of vehicles of limited capacity is exploited to satisfy node demands, and a set of routes must be found such that the vehicle capacities are never exceeded, each route does not exceed time resource, and cost is minimized. The demands of both pickup and delivery nodes can be split, and each node can be visited more than once. We provide new theoretical insights. We propose a new formulation where routes are decomposed into sequences of simpler substructures called clusters, mitigating the combinatorial explosion of feasible solutions. We introduce valid inequalities, and design a branch-and-price algorithm, exploiting ad hoc pricing routines and branching strategies, and embedding a rounding heuristic to speed up pruning. An extensive experimental analysis shows our method to offer simultaneously more modelling flexibility and more computational effectiveness than previous attempts from the literature. Our investigation opens also interesting insights into the use of route decomposition strategies.
The bi-objective multi-depot split delivery location routing problems under uncertain conditions
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A Multicommodity, Simultaneous Split Pickup and Split Delivery Vehicle Routing Problem with Demand Allocation
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Decomposition algorithm for the multi-trip single vehicle routing problem with AND-type precedence constraints
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¹: Partially funded by “Piano Sostegno alla Ricerca 2015-17” (Università degli Studi di Milano) and Regione Lombardia, project AD-COM.

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A branch and price approach for the Split Pickup and Split Delivery VRP

Abstract

Discrete Optimization