Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs.

Vehicle Routing Problems for Drone Delivery

Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

Vehicle routing problems for city logistics

This paper considers a vehicle routing problem where each vehicle performs delivery operations over multiple routes during its workday and where new customer requests occur dynamically. The proposed methodology for addressing the problem is based on an adaptive large neighborhood search heuristic, previously developed for the static version of the problem. In the dynamic case, multiple possible scenarios for the occurrence of future requests are considered to decide about the opportunity to include a new request into the current solution. It is worth noting that the real-time decision is about the acceptance of the new request, not about its service which can only take place in some future routes (a delivery route being closed as soon as a vehicle departs from the depot). In the computational results, a comparison is provided with a myopic approach which does not consider scenarios of future requests.

/pdf/a-dynamic-vehicle-routing-problem-with-multiple-delivery-3zrc6xisix.pdf

A Dynamic Vehicle Routing Problem with Multiple Delivery Routes

A memetic algorithm for the Multi Trip Vehicle Routing Problem

Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows

This article tackles the multi-trip vehicle routing problem with time windows and limited duration. A trip is a timed route such that a succession of trips can be assigned to one vehicle. We provide an exact two-phase algorithm to solve it. The first phase enumerates possible ordered lists of clients which match the maximum trip duration criterion. The second phase uses a Branch and Price scheme to generate and choose a best set of trips so that all customers are visited. We propose a set covering formulation as the column generation master problem, where columns (variables) represent trips. The sub-problem selects appropriate timing for trips and has a pseudo-polynomial complexity. Computational results on Solomon’s benchmarks are presented. The computational times obtained with our new algorithm are much lower than the ones recently obtained in the only two studies published on this problem to date.

/pdf/a-new-exact-algorithm-to-solve-the-multi-trip-vehicle-1b7d05ogoh.pdf

A new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration

The world we live in is an increasingly spatial and temporal data-rich environment, and agriculture is no exception. However, data needs to be processed in order to first get information and then make informed management decisions. The concepts of ‘Precision Agriculture’ and ‘Smart Agriculture’ are and will be fully effective when methods and tools are available to practitioners to support this transformation. An open-source software called GeoFIS has been designed with this objective. It was designed to cover the whole process from spatial data to spatial information and decision support. The purpose of this paper is to evaluate the abilities of GeoFIS along with its embedded algorithms to address the main features required by farmers, advisors, or spatial analysts when dealing with precision agriculture data. Three case studies are investigated in the paper: (i) mapping of the spatial variability in the data, (ii) evaluation and cross-comparison of the opportunity for site-specific management in multiple fields, and (iii) delineation of within-field zones for variable-rate applications when these latter are considered opportune. These case studies were applied to three contrasting crop types, banana, wheat and vineyards. These were chosen to highlight the diversity of applications and data characteristics that might be handled with GeoFIS. For each case-study, up-to-date algorithms arising from research studies and implemented in GeoFIS were used to process these precision agriculture data. Areas for future development and possible relations with existing geographic information systems (GIS) software is also discussed.

https://www.mdpi.com/2077-0472/8/6/73/pdf

GeoFIS: An Open Source, Decision-Support Tool for Precision Agriculture Data

Agricultural Internet of Things and Decision Support for Smart Farming reveals how a set of key enabling technologies (KET) related to agronomic management, remote and proximal sensing, data mining, decision-making and automation can be efficiently integrated in one system. Chapters cover how KETs enable real-time monitoring of soil conditions, determine real-time, site-specific requirements of crop systems, help develop a decision support system (DSS) aimed at maximizing the efficient use of resources, and provide planning for agronomic inputs differentiated in time and space. This book is ideal for researchers, academics, post-graduate students and practitioners who want to embrace new agricultural technologies.

/pdf/agricultural-internet-of-things-and-decision-support-for-2b13casnru.pdf

Agricultural Internet of Things and decision support for precision smart farming

Statecharts were experimented as a mediation tool between multiple experts and a knowledge engineer. After a short survey of knowledge elicitation methods for multiple experts, we present our method for assessing the quality of the elicited model and give critiques on the basis of our case study in vineyards crop protection management.

Olivier Naud

Papers

Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows

A new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration

GeoFIS: An Open Source, Decision-Support Tool for Precision Agriculture Data

Agricultural Internet of Things and decision support for precision smart farming

Experimenting statecharts for multiple experts knowledge elicitation in agriculture