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In the classical Vehicle Routing Problem (VRP), it is assumed that each worker moves using an individually assigned vehicle. Removing this core hypothesis opens the door for a brand new set of solutions, where workers are seen as transportable resources that can also move without the help of a vehicle. In this context, motivated by a major European energy provider, we consider a situation where workers can either walk or drive to reach a job and where carpooling is enabled. In order to quantify the potential benefits o↵ered by this new framework, a dedicated Variable Neighborhood Search is proposed to e ciently tackle the underlying synchronization and precedence constraints that arise in this extension of the VRP. Considering a set of instances in an urban context, extensive computational experiments show that, despite conservative scenarios favoring car mobility, significant savings are achieved when compared to the solutions currently obtained by the involved company. This innovative formulation allows managers to reduce the size of the vehicle fleet while keeping the number of workers stable and, surprisingly, decreasing the overall driving distance simultaneously.

We propose a model for solving a parcel delivery problem with a fleet of trucks embedded with drones. When appropriate, drones are loaded with a parcel, launched directly from the truck, and sent to a client. Afterward, the drones autonomously return to the truck to be replenished and recharged. Inspired by the case of a large European logistics provider, the proposed modeling framework confronts realistic delivery problems involving time windows, limited drone autonomy, and the eligibility of clients to be served by drones. The considered global cost function includes fixed daily vehicle fares, driver wages, and the fuel and electricity consumption to power trucks and drones. To solve the problems at hand, we propose a mixed-integer linear programming formulation and an adaptive large neighborhood search. Moreover, we introduce an efficient modeling framework to manage the numerous synchronization constraints induced by the simultaneous use of trucks and drones. We analyze the benefits of this new transportation concept for delivery problems involving up to 100 parcels. Results show that truck-and-drone solutions can reduce costs up to 34% compared to traditional truck-only delivery. From a managerial perspective, we show that a certain percentage of client locations must be reachable by drone to make truck-and-drone solutions competitive (i.e., if the fixed costs of the drones are compensated for by the savings on truck routes) and compare the cost structures of truck-and-drone versus truck-only solutions.

The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the agents interaction range and (b) a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.

a b s t r a c tToday's supply networks consist of a certain amount of logistics objects that are enabled to interact with each other and to decide autonomously upon their next steps; in other words, they exhibit a certain degree of autonomous cooperation. Therefore, modern logistics research regards them as complex adaptive logistics systems. In order to analyze evolving dynamics and underlying implications for the respective systems' behavior as well as the potential outcomes resulting from the interaction between autonomous decisionmaking ''smart parts'', we propose in this contribution a fully solvable stylized model. We consider a population of homogeneous, autonomous interacting agents traveling on R with a given velocity that is itself corrupted by White Gaussian Noise. Based on real time observations of the positions of his neighbors, each agent is allowed to adapt his traveling velocity. These agent interactions are restricted to neighboring entities confined in finite spatial clusters (i.e. we have range-limited interactions). In the limit of a large population of neighboring agents, a mean-field dynamics can be derived and, for small interaction range, the resulting dynamics coincides with the exactly solvable Burgers' nonlinear field equation. Explicit Burgers' solution enables to explicitly appreciate the emergent structure due to the local and individual agent interactions. In particular, for strongly interactive regimes in the present model, the resulting spatial distribution of agents converges to a shock wave pattern. To compare performances of centralized versus decentralized organization, we assign cost functions incurred when velocity adaptations are triggered either by multi-agent interactions or by central control. The multi-agent cumulative costs are then compared with the costs that would be incurred by implementing an effective optimal central controller able, for a given time horizon, to reproduce an identical spatial probability distribution of agents. The resulting optimal control problem can be solved exactly and the corresponding costs can be expressed as the Kullback-Leibler relative entropy between the free and the controlled probability measures. This enables one to conclude that for time horizons shorter than a critical value, multi-agent interactions generate smaller cumulative costs than an optimal effective central controller.

a b s t r a c tThe inherent complexity characterizing production and/or service networks strongly favors decentralized and self-organizing mechanisms to regulate the flows of matter and information in circulation. This basic observation motivates us to study the flow dynamics in queueing networks roamed by autonomous agents which, at a given time and at a given vertex location, select their routing according to (individual) historical data (such as waiting times) collected during their past progression in the network. For several simple network configurations and despite the intrinsically non-Markovian character of the dynamics, we are able to discuss analytically the emerging collective dynamics that such a circulation of autonomous agents generates. Feedback loops in the network topology coupled with the presence of delays in the routing selection mechanisms produce a wealth of dynamical phenomena like self-sustained generically stable oscillations, spatio-temporal patterns, stabilization by noise phenomena and oscillator synchronization that are explicitly discussed in this paper.

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This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. A novel approach to modeling imitation is presented based on range-dependent processes that describe how firms consider proximity when imitating peers who are found in a given neighborhood in terms of productivity. Using a particularly tractable approach, we are able to analyze how drastically different economic growth scenarios emerge from different imitation strategies. These emerging scenarios range from diffusive growth where the variance of productivity grows indefinitely, to balanced growth described by a traveling wave with fixed variance. The latter scenario is sustained only when imitation strength among firms exceeds a critical bifurcation threshold.