Showing papers on "Vehicle routing problem published in 2013"

Vehicle Routing Problem: Simultaneous Deliveries and Pickups with Split Loads and Time Windows

Abstract: The vehicle routing problem with simultaneous deliveries and pickups (VRPSDP) has attracted much research interest because of the potential to provide cost savings to transportation and logistics operators. Several extensions of VRPSDP exist. Of these extensions, the simultaneous deliveries and pickups with split loads problem (SDPSLP) has been proposed to eliminate vehicle capacity constraints, as well as allow the deliveries or pickups for a customer to be split into multiple visits. Although delivery and pickup activities are often constrained by time windows, few studies have considered such constraints when SDPSLP has been addressed. To fill the gap, this paper formulates the vehicle routing problem of simultaneous deliveries and pickups with split loads and time windows (VRPSDPSLTW) as a mixed-integer programming problem. A hybrid heuristic algorithm was developed to solve this problem. Solomon data sets with minor modifications were applied to test the effectiveness of the solution algorithm. The r...

The time-dependent pollution-routing problem

Abstract: The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.

An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem

Abstract: This paper deals with the Heterogeneous Fleet Vehicle Routing Problem (HFVRP). The HFVRP is $\mathcal{NP}$ -hard since it is a generalization of the classical Vehicle Routing Problem (VRP), in which clients are served by a heterogeneous fleet of vehicles with distinct capacities and costs. The objective is to design a set of routes in such a way that the sum of the costs is minimized. The proposed algorithm is based on the Iterated Local Search (ILS) metaheuristic which uses a Variable Neighborhood Descent procedure, with a random neighborhood ordering (RVND), in the local search phase. To the best of our knowledge, this is the first ILS approach for the HFVRP. The developed heuristic was tested on well-known benchmark instances involving 20, 50, 75 and 100 customers. These test-problems also include dependent and/or fixed costs according to the vehicle type. The results obtained are quite competitive when compared to other algorithms found in the literature.

The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty

Abstract: The robust capacitated vehicle routing problem (CVRP) under demand uncertainty is studied to address the minimum cost delivery of a product to geographically dispersed customers using capacity-constrained vehicles. Contrary to the deterministic CVRP, which postulates that the customer demands for the product are deterministic and known, the robust CVRP models the customer demands as random variables, and it determines a minimum cost delivery plan that is feasible for all anticipated demand realizations. Robust optimization counterparts of several deterministic CVRP formulations are derived and compared numerically. Robust rounded capacity inequalities are developed, and it is shown how they can be separated efficiently for two broad classes of demand supports. Finally, it is analyzed how the robust CVRP relates to the chance-constrained CVRP, which allows a controlled degree of supply shortfall to decrease delivery costs.

An Adaptive Large Neighborhood Search for the Pickup and Delivery Problem with Transfers

Abstract: The pickup and delivery problem PDP consists in defining a set of routes that satisfy transportation requests between a set of pickup points and a set of delivery points. This paper addresses a variant of the PDP where requests can change vehicle during their trip. The transfer is made at specific locations called “transfer points.” The corresponding problem is called the pickup and delivery problem with transfers PDPT. Solving the PDPT leads to new modeling and algorithmic difficulties. We propose new heuristics capable of efficiently inserting requests through transfer points. These heuristics are embedded into an adaptive large neighborhood search. We evaluate the method on generated instances and apply it to the transportation of people with disabilities. On these real-life instances we show that the introduction of transfer points can bring significant improvements up to 9% to the value of the objective function.

Dynamic Vehicle Routing Problems.

Abstract: When a vehicle routing model is cast and solved, it is normally assumed that the values of all input parameters are known with certainty. However, this is hardly the case in reallife applications where parameters such as customer demands, travel and service times, or even the information of whether a particular customer will require service or not are often incomplete, uncertain, or unknown during the route design phase (see Gounaris et al. [60]). As pointed out by Psaraftis [123], there are two important dimensions of input data, namely evolution and quality of information. The former implies that the available information is subject to change even after the routing plan is realized, while the latter reflects the possible uncertainties in the available data. What is common in both cases is that the partially known, uncertain, or unknown input parameters are revealed or updated concurrently with the execution of the routing process. Depending on the availability and quality of a priori information and other characteristics of the problem under consideration, two alternatives emerge for solving the routing problem. Assuming that sufficient information is available (e.g., all input data are known in advance with a predefined degree of uncertainty), the first option is to treat the problem as static and solve it once during the design phase. The goal in this case is to obtain a robust routing plan that will possibly be subject to relatively small changes during the actual execution. This option is named a priori optimization, for which anticipating uncertainty is crucial in order to find realizable routing plans, and to avoid hefty penalties, both economic and reputational, when one fails to provide the required level of service (see Gounaris et al. [60]). The second option is to address the problem in an ongoing and dynamic fashion as new input data arrive or are revealed in real time. While information evolves and decisions must be continuously made in a changing environment, the goal is to react to the new events as well as to anticipate future events, particularly if exploitable stochastic

Particle Swarm Optimization for the Vehicle Routing Problem with Stochastic Demands

Abstract: This paper introduces a new hybrid algorithmic approach based on Particle Swarm Optimization (PSO) for successfully solving one of the most popular supply chain management problems, the Vehicle Routing Problem with Stochastic Demands (VRPSD). The VRPSD is a well known NP-hard problem in which a vehicle with finite capacity leaves from the depot with full load and has to serve a set of customers whose demands are known only when the vehicle arrives to them. A number of different variants of the PSO are tested and the one that performs better is used for solving benchmark instances from the literature.

An Exact Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem

Abstract: In the two-echelon capacitated vehicle routing problem (2E-CVRP), the delivery to customers from a depot uses intermediate depots, called satellites. The 2E-CVRP involves two levels of routing problems. The first level requires a design of the routes for a vehicle fleet located at the depot to transport the customer demands to a subset of the satellites. The second level concerns the routing of a vehicle fleet located at the satellites to serve all customers from the satellites supplied from the depot. The objective is to minimize the sum of routing and handling costs. This paper describes a new mathematical formulation of the 2E-CVRP used to derive valid lower bounds and an exact method that decomposes the 2E-CVRP into a limited set of multidepot capacitated vehicle routing problems with side constraints. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.

A general formal framework for pathfinding problems with multiple agents

Abstract: Pathfinding for a single agent is the problem of planning a route from an initial location to a goal location in an environment, going around obstacles Pathfinding for multiple agents also aims to plan such routes for each agent, subject to different constraints, such as restrictions on the length of each path or on the total length of paths, no self-intersecting paths, no intersection of paths/plans, no crossing/meeting each other It also has variations for finding optimal solutions, eg, with respect to the maximum path length, or the sum of plan lengths These problems are important for many real-life applications, such as motion planning, vehicle routing, environmental monitoring, patrolling, computer games Motivated by such applications, we introduce a formal framework that is general enough to address all these problems: we use the expressive high-level representation formalism and efficient solvers of the declarative programming paradigm Answer Set Programming We also introduce heuristics to improve the computational efficiency and/or solution quality We show the applicability and usefulness of our framework by experiments, with randomly generated problem instances on a grid, on a real-world road network, and on a real computer game terrain

An Adaptive Variable Neighborhood Search Algorithm for a Vehicle Routing Problem Arising in Small Package Shipping

Abstract: In this paper, we investigate a routing problem arising in the last-mile delivery of small packages. The problem, called Multi-Depot Vehicle Routing Problem with Private fleet and Common carriers MDVRPPC, is an extension of the Multi-Depot Vehicle Routing Problem MDVRP where customers can either be served by the private fleet based at self-owned depots or by common carriers, i.e., subcontractors. We develop an effective Variable Neighborhood Search algorithm based on the use of cyclic-exchange neighborhoods that incorporates an adaptive mechanism to bias the random shaking step. The approach is successfully used to solve MDVRPPC as well as closely related problems, such as the MDVRP and the single-depot VRP with Private fleet and Common carriers VRPPC, obtaining high quality solutions within short computing time. Our extensive testing on these problems shows the positive impact of the adaptive mechanism with respect to a standard VNS algorithm.

The Multiconstraint Team Orienteering Problem with Multiple Time Windows

Abstract: This paper introduces the multiconstraint team orienteering problem with multiple time windows MC-TOP-MTW. In the MC-TOP-MTW, a set of vertices is given, each with a service time, one or more time windows, and a score. The goal is to maximize the sum of the collected scores, by a fixed number of tours. The tours are limited in length and restricted by the time windows and additional constraints. Next to a mathematical formulation of the MC-TOP-MTW, the main contribution of this paper is a fast and effective algorithm for tackling this problem, by hybridizing iterated local search with a greedy randomized adaptive search procedure. On a large test set, an average run has a score gap of only 5.19% with known high quality solutions, using 1.5 seconds of computational time. For 32% of the test instances, the known high quality solution was found or improved. This solution method also performs well on test instances of the TOPTW, the selective vehicle routing problem with time windows, and the MC-TOP-TW. A sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in the parameter settings.

Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows

Abstract: This paper presents a branch-and-price algorithm for the time-dependent vehicle routing problem with time windows TDVRPTW. We capture road congestion by considering time-dependent travel times, i.e., depending on the departure time to a customer, a different travel time is incurred. We consider the variant of the TDVRPTW where the objective is to minimize total route duration and denote this variant the duration minimizing TDVRPTW DM-TDVRPTW. Because of time dependency, vehicles' dispatch times at the depot are crucial as road congestion might be avoided. Because of its complexity, all known solution methods to the DM-TDVRPTW are based on meta-heuristics. The decomposition of an arc-based formulation leads to a set-partitioning problem as the master problem, and a time-dependent shortest path problem with resource constraints as the pricing problem. The master problem is solved by means of column generation, and a tailored labeling algorithm is used to solve the pricing problem. We introduce new dominance criteria that allow more label dominance. For our numerical results, we modified Solomon's data sets by adding time dependency. Our algorithm is able to solve about 63% of the instances with 25 customers, 38% of the instances with 50 customers, and 15% of the instances with 100 customers.

Heterogeneous fixed fleet vehicle routing considering carbon emission

Abstract: The paper considers heterogeneous fixed fleet vehicle routing with carbon emission to minimizing the sum of variable operation costs. A cost-benefit assessment of the value of purchasing or selling of carbon emission rights, using a mixed integer-programming model to reflect heterogeneous vehicle routing, is incorporated. Essentially, the use of a carbon market as a means of introducing more flexibility into an environmentally constrained network is considered. Tabu search algorithms are used to obtain solutions within a reasonable amount of computation time. In particular, we show the possibility that the amount of carbon emission can be reduced significantly without sacrificing the cost due to the benefit obtained from carbon trading.

A Simulated Annealing-based parallel multi-objective approach to vehicle routing problems with time windows

Abstract: The Capacitated Vehicle Routing Problem with Time Windows (VRPTW) consists in determining the routes of a given number of vehicles with identical capacity stationed at a central depot which are used to supply the demands of a set of customers within certain time windows. This is a complex multi-constrained problem with industrial, economic, and environmental implications that has been widely analyzed in the past. This paper deals with a multi-objective variant of the VRPTW that simultaneously minimizes the travelled distance and the imbalance of the routes. This imbalance is analyzed from two perspectives: the imbalance in the distances travelled by the vehicles, and the imbalance in the loads delivered by them. A multi-objective procedure based on Simulated Annealing, the Multiple Temperature Pareto Simulated Annealing (MT-PSA), is proposed in this paper to cope with these multi-objective formulations of the VRPTW. The procedure MT-PSA and an island-based parallel version of MT-PSA have been evaluated and compared with, respectively, sequential and island-based parallel implementations of SPEA2. Computational results obtained on Solomon's benchmark problems show that the island-based parallelization produces Pareto-fronts of higher quality that those obtained by the sequential versions without increasing the computational cost, while also producing significant reduction in the runtimes while maintaining solution quality. More specifically, for the most part, our procedure MT-PSA outperforms SPEA2 in the benchmarks here considered, with respect to the solution quality and execution time.

A Branch-and-Cut Algorithm for the Symmetric Two-Echelon Capacitated Vehicle Routing Problem

Abstract: This paper presents an exact method for solving the symmetric two-echelon capacitated vehicle routing problem, a transportation problem concerned with the distribution of goods from a depot to a set of customers through a set of satellite locations. The presented method is based on an edge flow model that is a relaxation and provides a valid lower bound. A specialized branching scheme is employed to obtain feasible solutions. Out of a test set of 93 instances the algorithm is able to solve 47 to optimality, surpassing previous exact algorithms.