A literature review on the vehicle routing problem with multiple depots

A widely applied strategy for workload sharing is to equalize the workload assigned to each resource. In mobile multiagent systems, this principle directly leads to equitable partitioning policies whereby: 1) the environment is equitably divided into subregions of equal measure; 2) one agent is assigned to each subregion; and 3) each agent is responsible for service requests originating within its own subregion. The current lack of distributed algorithms for the computation of equitable partitions limits the applicability of equitable partitioning policies to limited-size multiagent systems operating in known, static environments. In this paper, first we design provably correct and spatially distributed algorithms that allow a team of agents to compute a convex and equitable partition of a convex environment. Second, we discuss how these algorithms can be extended so that a team of agents can compute, in a spatially distributed fashion, convex and equitable partitions with additional features, e.g., equitable and median Voronoi diagrams. Finally, we discuss two application domains for our algorithms, namely dynamic vehicle routing for mobile robotic networks and wireless ad hoc networks. Through these examples, we show how one can couple the algorithms presented in this paper with equitable partitioning policies to make these amenable to distributed implementation. More in general, we illustrate a systematic approach to devise spatially distributed control policies for a large variety of multiagent coordination problems. Our approach is related to the classic Lloyd algorithm and exploits the unique features of power diagrams.

/pdf/distributed-algorithms-for-environment-partitioning-in-4lk7q7w3fo.pdf

Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in the context of VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap by providing an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures of equity, and point out important connections between their properties ...

Workload Equity in Vehicle Routing Problems: A Survey and Analysis

We consider an uncapacitated stochastic vehicle routing problem in which vehicle depot locations are fixed, and client locations in a service region are unknown but are assumed to be independent and identically distributed samples from a given probability density function We present an algorithm for partitioning the service region into subregions so as to balance the workloads of all vehicles when the service region is simply connected and point-to-point distances follow some “natural” metric, such as any Lp norm This algorithm can also be applied to load balancing of other combinatorial structures, such as minimum spanning trees and minimum matchings

Dividing a Territory Among Several Vehicles

Distribution of finished goods from depots to predetermined customers and collection of goods and wastes are practical and challengeable optimization and logistics problems; therefore, appropriate ...

The close–open mixed multi depot vehicle routing problem considering internal and external fleet of vehicles

The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of the Single-Depot Vehicle Routing Problem (SDVRP) in which vehicle(s) start from multiple depots and return to their depots of origin at the end of their assigned tours. The traditional objective in MDVRP is to minimize the total length of all the tours, and existing literature handles this problem with a variety of assumptions and constraints. In this paper, we explore the notion of minimizing the maximal length of a tour in MDVRP (“min-max MDVRP”). We also introduce a heuristic method based on region partitioning, which is potentially useful for general network applications. A comparison of the computational implementations for three heuristics is included. Although this model is advantageous for real-world applications, to the best of our knowledge no prior

/pdf/solving-min-max-multi-depot-vehicle-routing-problem-1mt8bb0trk.pdf

Solving Min-Max Multi-Depot Vehicle Routing Problem ⁄

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Solving Min-Max Multi-Depot Vehicle Routing Problem ⁄