Showing papers on "Vehicle routing problem published in 1999"

MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows

Abstract: MACS-VRPTW, an Ant Colony Optimization based approach useful to solve vehicle routing problems with time windows is presented. MACS-VRPTW is organized with a hierarchy of artificial ant colonies designed to successively optimize a multiple objective function: the first colony minimizes the number of vehicles while the second colony minimizes the traveled distances. Cooperation between colonies is performed by exchanging information through pheromone updating. We show that MACS-VRPTW is competitive with the best known existing methods both in terms of solution quality and computation time. Moreover, MACS-VRPTW improves some of the best solutions known for a number of problem instances in the literature.

An improved Ant System algorithm for theVehicle Routing Problem

Abstract: The Ant System is a distributed metaheuristic that combines an adaptive memory with alocal heuristic function to repeatedly construct solutions of hard combinatorial optimizationproblems. In this paper, we present an improved ant system algorithm for the Vehicle RoutingProblem with one central depot and identical vehicles. Computational results on fourteenbenchmark problems from the literature are reported and a comparison with five othermetaheuristic approaches for solving Vehicle Routing Problems is given.

Parallel Tabu Search for Real-Time Vehicle Routing and Dispatching

Abstract: An abundant literature about vehicle routing and scheduling problems is available in the scientific community. However, a large fraction of this work deals with static problems where all data are known before the routes are constructed. Recent technological advances now create environments where decisions are taken quickly, using new or updated information about the current routing situation. This paper describes such a dynamic problem, motivated from courier service applications, where customer requests with soft time windows must be dispatched in real time to a fleet of vehicles in movement. A tabu search heuristic, initially designed for the static version of the problem, has been adapted to the dynamic case and implemented on a parallel platform to increase the computational effort. Numerical results are reported using different request arrival rates, and comparisons are established with other heuristic methods.

Applying the ANT System to the Vehicle Routing Problem

Abstract: In this paper we use a recently proposed metaheuristic, the Ant System, to solve the Vehicle Routing Problem in its basic form, i.e., with capacity and distance restrictions, one central depot and identical vehicles. A “hybrid” Ant System algorithm is first presented and then improved using problem-specific information (savings, capacity utilization). Experiments on various aspects of the algorithm and computational results for fourteen benchmark problems are reported and compared to those of other metaheuristic approaches such as Tabu Search, Simulated Annealing and Neural Networks.

The VRP with Time Windows

Abstract: This paper presents a survey of the research on the Vehicle Routing Problem with Time Windows (VRPTW), an extension of the Capacitated Vehicle Routing Problem. In the VRPTW, the service at each customer must start within an associated time window and the vehicle must remain at the customer location during service. Soft time windows can be violated at a cost while hard time windows do not allow for a vehicle to arrive at a customer after the latest time to begin service. We first present a multi-commodity network flow formulation with time and capacity constraints for the VRPTW. Approximation methods proposed in the literature to derive upper bounds are then reviewed. Then we explain how lower bounds can be obtained using optimal approaches, namely, Lagrangean relaxation and column generation. Next, we provide branching and cutting strategies that can be embedded within these optimal approaches to produce integer solutions. Special cases and extensions to the VRPTW follow as well as our conclusions.

A heuristic column generation method for the heterogeneous fleet VRP

Abstract: This paper presents a heuristic column generation method for solving vehicle routing problems with a heterogeneous fleet of vehicles. The method may also solve the fleet size and composition vehicle routing problem and new best known solutions are reported for a set of classical problems. Numerical results show that the method is robust and efficient, particularly for medium and large size problem instances.

2-Path Cuts for the Vehicle Routing Problem with Time Windows

Abstract: This paper introduces a strong valid inequality, the 2-path cut, to produce better lower bounds for the vehicle routing problem with time windows. It also develops an effective separation algorithm to find such inequalities. We next incorporate them as needed in the master problem of a Dantzig-Wolfe decomposition approach. In this enhanced optimization algorithm, the coupling constraints require that each customer be serviced. The subproblem is a shortest path problem with time window and capacity constraints. We apply branch and bound to obtain integer solutions. We first branch on the number of vehicles if this is fractional, and then on the flow variables. The algorithm has been implemented and tested on problems of up to 100 customers from the Solomon datasets. It has succeeded in solving to optimality several previously unsolved problems and a new 150-customer problem. In addition, the algorithm proved faster than algorithms previously considered in the literature. These computational results indicate the effectiveness of the valid inequalities we have developed.

A Cluster Insertion Heuristic for Single and Multiple Depot Vehicle Routing Problems with Backhauling

Abstract: We investigate an extension to the classical insertion-based heuristic for the vehicle routing problem with backhauling (VRPB). It is based on the idea of inserting more than one backhaul at a time. This method is tested on data sets with single and multiple depots with encouraging results at no additional computational burden. This approach can also be useful in generating good starting solutions for the more computer-intensive meta-heuristics.

Two Evolutionary Metaheuristics For The Vehicle Routing Problem With Time Windows

Abstract: The vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem with a central depot. The objective is to design an optimal set of routes that servic...

Synchronized Development of Production, Inventory, and Distribution Schedules

Abstract: An integrated optimization model for production and distribution planning is proposed, with the aim of optimally coordinating important and interrelated logistic decisions such as capacity management, inventory allocation, and vehicle routing. The integrated model is solved via Lagrangean relaxation and both lower bounds and heuristic feasible solutions are obtained. Computational results on test problems of various sizes are provided to show the effectiveness of the proposed solution scheme. Moreover, the feasible solution obtained is compared to that generated by an alternative decoupled approach in which a production plan is first developed and a distribution schedule is consequently derived. Computational results seem to indicate a substantial advantage of the synchronized approach over the decoupled decision process.

The Logic of Logistics: Theory, Algorithms, and Applications for Logistics and Supply Chain Management

Abstract: Introduction.- Convexity and Supermodularity.- Worst-case analysis.- Average-case analysis.- Mathematical programming based bounds.- Economic Lot Size Models with Constant Demands.- Economic Lot Size Models with Varying Demands.- Stochastic Inventory Models.- Integration of Inventory and Pricing.- Procurement Contracts.- Supply Chain Planning Models.- Facility Location Models.- The Capacitated VRP with Equal Demands.- The Capacitated VRP with Unequal Demands.- The VRP with Time Window Constraints.- Solving the VRP using a Column Generation Approach.- Network Planning.- A Case Study: School Bus Routing.- References.- Index.

Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem

Abstract: In contrast to vehicle routing problems, little work has been done in ship routing and scheduling, although large benefits may be expected from improving this scheduling process. We will present a real ship planning problem, which is a combined inventory management problem anda routing problem with time windows. A fleet of ships transports a single product (ammonia) between production and consumption harbors. The quantities loaded and discharged are determined by the production rates of the harbors, possible stock levels, and the actual ship visiting the harbor. We describe the real problem and the underlying mathematical model. To decompose this model, we discuss some model adjustments. Then, the problem can be solved by a Dantzig Wolfe decomposition approach including both ship routing subproblems and inventory management subproblems. The overall problem is solved by branch-and-bound. Our computational results indicate that the proposed method works for the real planning problem.

A Parallel Hybrid Evolutionary Metaheuristic for the Vehicle Routing Problem with Time Windows

Abstract: The vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem with a central depot. The objective function of the VRPTW considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance (secondary criterion). In this paper, a two-phase procedural approach for solving the VRPTW is parallelized. The aim of the first phase is the minimization of the number of vehicles by means of a (1, λ)-evolution strategy, whereas in the second phase the total distance is minimized using a tabu search algorithm. The parallelization of this sequential hybrid procedure follows the concept of cooperative autonomy, i.e., several autonomous sequential solution procedures cooperate through the exchange of solutions. However, exchanges of solutions lead to the corresponding jumps in the solution space only if certain acceptance conditions are met. The good performance of both the sequential and the parallel approach is demonstrated by means of well-known and new benchmark problems.

The fleet size and mix vehicle routing problem with time windows

Abstract: This paper describes several insertion-based savings heuristics for the fleet size and mix vehicle routing problem with time window constraints. A certain number of candidate fleet compositions are recorded in the construction phase, followed by applying a composite improvement scheme on them to enhance the solution quality. Computational results on 168 sample problems are reported. We found that heuristics with the consideration of a sequential route construction parameter yielded very good results. In addition, results on the 20 benchmarking problems for the fleet and mix vehicle routing problem with no time window constraints also demonstrate the effectiveness of our heuristics.

Theory and Methodology A heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls

Abstract: We consider an extension of the capacitated Vehicle Routing Problem (VRP), known as the Vehicle RoutingProblem with Backhauls (VRPB), in which the set of customers is partitioned into two subsets: Linehaul and Backhaulcustomers. Each Linehaul customer requires the delivery of a given quantity of product from the depot, whereas a givenquantity of product must be picked up from each Backhaul customer and transported to the depot. VRPB is known tobe NP-hard in the strong sense, and many heuristic algorithms were proposed for the approximate solution of theproblem with symmetric or Euclidean cost matrices. We present a cluster-first-route-second heuristic which uses a newclustering method and may also be used to solve problems with asymmetric cost matrix. The approach exploits theinformation of the normally infeasible VRPB solutions associated with a lower bound. The bound used is a Lagrangianrelaxation previously proposed by the authors. The final set of feasible routes is built through a modified TravelingSalesman Problem (TSP) heuristic, and inter-route and intra-route arc exchanges. Extensive computational tests onsymmetric and asymmetric instances from the literature show the e•ectiveness of the proposed approach. O 1999Elsevier Science B.V. All rights reserved.Keywords: Vehicle routing; Lagrangian relaxation; Heuristic algorithms; Local search

An Exact Method for the Vehicle Routing Problem with Backhauls

Abstract: We consider the problem in which a fleet of vehicles located at a central depot is to be optimallyused to serve a set of customers partitioned into two subsets of linehaul and backhaul customers. Each route starts and ends at the depot and the backhaul customers must be visited afterthe linehaul customers. A new (0-1) integer programming formulation of this problem is presented. We describe a procedure that computes a valid lower bound to the optimal solution cost by combining different heuristic methods for solving the dual of the LP-relaxation of the exact formulation. An algorithm for the exact solution of the problem is presented. Computational tests on problems proposed in the literature show the effectiveness of the proposed algorithms in solving problems up to 100 customers.

Applying GIS and Or Techniques to Solve Sears Technician-Dispatching and Home Delivery Problems

Abstract: Sears, Roebuck and Company uses a vehicle-routing-and-scheduling system based on a geographic information system to run its delivery and home service fleets more efficiently. Although the problems to be solved can be modeled as vehicle routing problems with time windows (VRPTW), the size of the problems and thus practical complexity make these problems of both theoretical and practical interest. We constructed a series of algorithms, including the algorithm to build the origin-and-destination matrix, the algorithm to assign resources, and algorithms to perform sequencing and route improvement. The combination of GIS and OR techniques makes the system quite efficient. The system has improved the Sears technician-dispatching and home-delivery business; resulting in over $9 million in one-time savings and over $42 million in annual savings. The success of this application also suggests a promising link between GIS and OR techniques.

Approximating Capacitated Routing and Delivery Problems

Abstract: We provide approximation algorithms for some capacitated vehicle routing and delivery problems. These problems can all be viewed as instances of the following k-delivery TSP: given n source points and n sink points in a metric space, with exactly one item at each source, find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each sink. The only known approximation algorithm for this family of problems is the 2.5-approximation algorithm of Anily and Hassin [ Networks, 22 (1992), pp. 419--433] for the special case k=1. For this case, we use matroid intersection to obtain a 2-approximation algorithm. Based on this algorithm and some additional lower bound arguments, we devise a factor-approximation for k-delivery TSP with arbitrary finite k. We also present a 2-approximation algorithm for the case $k = \infty$. We then initiate the study of dynamic variants of k-delivery TSP that model problems in industrial robotics and other applications. Specifically, we consider the situation where a robot arm (with finite or infinite capacity) must collect n point-objects moving in the Euclidean plane, and deliver them to the origin. The point-objects are moving in the plane with known, identical velocities---they might, for instance, be on a moving conveyor belt. We derive several useful structural properties that lead to constant-factor approximations for problems of this type that are relevant to the robotics application. Along the way, we show that maximum latency TSP is implicit in the dynamic problems, and that the natural "farthest neighbor" heuristic produces a good approximation for several notions of latency.

A parallel algorithm for the vehicle routing problem with time window constraints

Abstract: In this paper, we describe a new parallel tabu search heuristic for the vehicle routingproblem with time window constraints (VRPTW). The neighborhood structure we proposeis based on simple customer shifts and allows us to consider infeasible interim‐solutions.Similarly to the column generation approach used in exact algorithms, all routes generatedby the tabu search heuristic are collected in a pool. To obtain a new initial solution forthe tabu search heuristic, a fast set covering heuristic is periodically applied to the routes inthe pool. The parallel heuristic has been implemented on a Multiple‐Instruction Multiple‐Datacomputer architecture with eight nodes. Computational results for Solomon's benchmarkproblems demonstrate that our parallel heuristic can produce high‐quality solutions.

Improvement Procedures for the Undirected Rural Postman Problem

Abstract: This article describes new construction and postoptimization heuristics for the Undirected Rural Postman Problem. Extensive computational tests indicate that some combinations of these heuristics consistently produce optimal or high-quality solutions.