•We provide a comprehensive and relevant taxonomy for the literature devoted to Rich Vehicle Routing Problems (RVRPs).•We analyze 41 articles devoted to “rich” vehicle routing problems in detail.•We ...propose an elaborate definition of RVRPs.
Over the last years, several variants of multi-constrained Vehicle Routing Problems (VRPs) have been studied, forming a class of problems known as Rich Vehicle Routing Problems (RVRPs). The purpose of the paper is twofold: (i) to provide a comprehensive and relevant taxonomy for the RVRP literature and (ii) to propose an elaborate definition of RVRPs. To this end, selected papers addressing various cases are classified using the proposed taxonomy. Once the articles have been classified, a cluster analysis based on two discriminating criteria is performed and leads to the definition of RVRPs.
In this paper, we address a rich Traveling Salesman Problem with Profits encountered in several real-life cases. We propose a unified solution approach based on variable neighborhood search. Our ...approach combines several removal and insertion routing neighborhoods and efficient constraint checking procedures. The loading problem related to the use of a multi-compartment vehicle is addressed carefully. Two loading neighborhoods based on the solution of mathematical programs are proposed to intensify the search. They interact with the routing neighborhoods as it is commonly done in matheuristics. The performance of the proposed matheuristic is assessed on various instances proposed for the Orienteering Problem and the Orienteering Problem with Time Window including up to 288 customers. The computational results show that the proposed matheuristic is very competitive compared with the state-of-the-art methods. To better evaluate its performance, we generate a new testbed including instances with various attributes. Extensive computational experiments on the new testbed confirm the efficiency of the matheuristic. A sensitivity analysis highlights which components of the matheuristic contribute most to the solution quality.
•Studied the generalized traveling salesman problem with time windows (GTSPTW).•Proposed two MILP formulations and several valid inequalities for the GTSPTW.•Proposed the first exact algorithm ...(branch-and-cut) for the GTSPTW.•Developed a simple and fast heuristic for the GTSPTW.•Solved instances with up to 30 clusters to optimality within one hour.
The generalized traveling salesman problem with time windows (GTSPTW) is defined on a directed graph where the vertex set is partitioned into clusters. One cluster contains only the depot. Each vertex is associated with a time interval, the time window, during which the visit must take place if the vertex is visited. The objective is to find a minimum cost tour starting and ending at the depot such that each cluster is visited exactly once and time constraints are respected, i.e., for each cluster, one vertex is visited during its time window. In this paper, two integer linear programming formulations for GTSPTW are provided as well as several problem-specific valid inequalities. A branch-and-cut algorithm is developed in which the inequalities are separated dynamically. To reduce the computation times, an initial upper bound is provided by a simple and fast heuristic. We propose different sets of instances characterized by their time window structures. Experimental results show that our algorithm is effective and instances including up to 30 clusters can be solved to optimality within one hour.
•We study the logistics service network design problem.•We propose a new algorithmic strategy based on the partial Benders decomposition technique.•Our approach varies the subproblem information used ...to formulate the Benders master problem.•We provide theoretical results for aggregating subproblem information in network design problems.•Computational results are reported on both random and real-world instances.
Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service provider seeks to cost-effectively source and fulfill customer demands of products within a multi-echelon distribution network. However, many industrial settings yield instances of the LSNDP that are too large to be solved in reasonable run-times by off-the-shelf optimization solvers. We introduce an exact Benders decomposition algorithm based on partial decompositions that strengthens the master problem with information derived from aggregated subproblem data. More specifically, the proposed Meta Partial Benders Decomposition intelligently switches from one master problem to another by changing both the amount of subproblem information to include in the master as well as how it is aggregated. Through an extensive computational study, we show that the approach outperforms existing benchmark methods and demonstrate the benefits of dynamically refining the master problem in the course of a partial Benders decomposition-based scheme.
•Benders master problem based on an aggregated product yields an improved lower bound.•Aggregated information enables new valid inequalities that strengthen lower bounds.•New primal heuristic enables ...Benders approach to produce high-quality solutions.
We propose an exact solution method for a Logistics Service Network Design Problem (LSNDP) inspired by the management of restaurant supply chains. In this problem, a distributor seeks to source and fulfill customer orders of products (fruits, meat, napkins, etc.) through a multi-echelon distribution network consisting of supplier locations, warehouses, and customer locations in a cost-effective manner. As these products are small relative to vehicle capacity, an effective strategy for achieving low transportation costs is consolidation. Specifically, routing products so that vehicles transport multiple products at a time, with each product potentially sourced by a different supplier and destined for a different customer. As instances of this problem of sizes relevant to the operations of an industrial partner are too large for off-the-shelf optimization solvers, we propose a suite of techniques for enhancing a Benders decomposition-based algorithm, including a strengthened master problem, valid inequalities, and a heuristic. Together, these enhancements enable the resulting method to produce provably high-quality solutions to multiple variants of the problem in reasonable run-times.
•Provide the first dedicated heuristic algorithm for the commodity constrained split delivery vehicle routing problem (C-SDVRP) based on an adaptive large neighborhood search framework.•Adapt some ...classical local search moves taking into account the main feature of the C-SDVRP.•A mathematical programming based operator to intensify the search and further improve the best solutions.•High-quality solutions for medium and large size instances.
This paper addresses the commodity constrained split delivery vehicle routing problem (C-SDVRP) where customers require multiple commodities. This problem arises when customers accept to be delivered separately. All commodities can be mixed in a vehicle as long as the vehicle capacity is satisfied. Multiple visits to a customer are allowed, but a given commodity must be delivered in one delivery.
In this paper, we propose a heuristic based on the adaptive large neighborhood search (ALNS) to solve the C-SDVRP, with the objective of efficiently tackling medium and large sized instances. We take into account the distinctive features of the C-SDVRP and adapt several local search moves to improve a solution. Moreover, a mathematical programming based operator (MPO) that reassigns commodities to routes is used to improve a new global best solution.
Computational experiments have been performed on benchmark instances from the literature. The results assess the efficiency of the algorithm, which can provide a large number of new best-known solutions in short computational times.
•Studied the generalized vehicle routing problem with time windows (GVRPTW).•Proposed a column generation based heuristic for the GVRPTW.•Several types of benchmark instances can be solved ...efficiently and effectively.
The generalized vehicle routing problem with time windows (GVRPTW) is defined on a directed graph G=(V,A) where the vertex set V is partitioned into clusters. One cluster contains only the depot, where is located a homogeneous fleet of vehicles, each with a limited capacity. The other clusters represent customers. A demand is associated with each cluster. Inside a cluster, the vertices represent the possible locations of the customer. A time window is associated with each vertex, during which the visit must take place if the vertex is visited. The objective is to find a set of routes such that the total traveling cost is minimized, exactly one vertex per cluster is visited, and all the capacity and time constraints are respected. This paper presents a set covering formulation for the GVRPTW which is used to provide a column generation based heuristic to solve it. The proposed solving method combines several components including a construction heuristic, a route optimization procedure, local search operators and the generation of negative reduced cost routes. Experimental results on benchmark instances show that the proposed algorithm is efficient and high-quality solutions for instances with up to 120 clusters are obtained within short computation times.
In this paper, we present a survey on vehicle routing problems with multiple commodities. In most routing problems, only one commodity is explicitly considered. This may be due to the fact that, ...indeed, a single commodity is involved, or multiple commodities are transported, but they are aggregated and modeled as a single commodity, as no specific requirement imposes their explicit consideration. However, there exist cases in which this aggregation is not possible due to the characteristics of the commodities or to the fact that it would lead to sub-optimal routing plans.
This survey focuses on the analysis of the settings of the problems and the features of the commodities that require explicit consideration of disaggregated commodities in routing problems. We show that problem settings are inherently different with respect to the single commodity problems, and this has a consequence on both models and solution approaches, which cannot be straightforwardly adapted from the single commodity cases. We propose a classification of the routing problems with multiple commodities and discuss the motivations that force considering the presence of multiple commodities explicitly. Specifically, we focus on the modeling perspective by proposing a general formulation for routing problems with multiple commodities and showing how this formulation can be adapted to the different features that characterize the problem classes discussed in the survey. Also, for each major class of problems, promising future research directions are discussed by analyzing what has been studied in the current literature and focusing on challenging topics not covered yet.
•This is a review paper on routing problems with multiple commodities.•We provide a classification of scientific contributions.•We show problem formulations.•We discuss issues in modeling different problem features.•We provide insights and discuss future research directions.
This paper addresses challenges in agricultural cooperative autonomous fleet routing through the proposition, modeling, and resolution of the Dynamic Vehicle Routing Problem with Fair Profits and ...Time Windows (DVRP-FPTW). The aim is to dynamically optimize routes for a vehicle fleet serving tasks within assigned time windows, emphasizing fair and efficient solutions. Our DVRP-FPTW accommodates unforeseen events like task modifications or vehicle breakdowns, ensuring adherence to task demand, vehicle capacities, and autonomies. The proposed model incorporates mandatory and optional tasks, including optional ones in operational vehicle routes if not compromising the vehicles’ profits. Including asynchronous and distributed column generation heuristics, the proposed Multi-Agent-based architecture DIMASA for the DVRP-FPTW dynamically adapts to unforeseen events. Systematic Egalitarian social welfare optimization is used to iteratively maximize the profit of the least profitable vehicle, prioritizing fairness across the fleet in light of unforeseen events. This improves upon existing dynamic and multi-period VRP models that rely on prior knowledge of demand changes. Our approach allows vehicle agents to maintain privacy while sharing minimal local data with a fleet coordinator agent. We propose publicly available benchmark instances for both static and dynamic VRP-FPTW. Simulation results demonstrate the effectiveness of our DVRP-FPTW model and our multi-agent system solution approach in coordinating large, dynamically evolving cooperative autonomous fleets fairly and efficiently in close to real-time.
•DVRP-FPTW: New dynamic routing problem with fair profits and time windows.•Fair profits in agri-coops: Dynamic and distributed route optimization for equity.•Egalitarian optimization for fairness and efficiency amid unforeseen events.•Adaptive and distributed DIMASA architecture copes with disruptions in real-time.•Scalable, computationally efficient DIMASA architecture protects vehicle privacy.
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