Showing papers on "Vehicle routing problem published in 1991"

A stochastic and dynamic vehicle routing problem in the Euclidean plane

Abstract: We propose and analyze a generic mathematical model for dynamic, stochastic vehicle routing problems, the dynamic traveling repairman problem (DTRP). The model is motivated by applications in which the objective is to minimize the wait for service in a stochastic and dynamically changing environment. This is a departure from classical vehicle routing problems where one seeks to minimize total travel time in a static, deterministic environment. Potential areas of application include repair, inventory, emergency service and scheduling problems. The DTRP is defined as follows: Demands for service arrive in time according to a Poisson process, are independent and uniformly distributed in a Euclidean service region, and require an independent and identically distributed amount of on-site service by a vehicle. The problem is to find a policy for routing the service vehicle that minimizes the average time demands spent in the system. We propose and analyze several policies for the DTRP. We find a provably optima...

GIDEON: a genetic algorithm system for vehicle routing with time windows

Abstract: Addresses the vehicle routing problem with time windows (VRPTW). The VRPTW involves routing a fleet of vehicles, of limited capacity and travel time, from a central depot to a set of geographically dispersed customers with known demands within specified time windows. The authors describe GIDEON, a genetic algorithm system to heuristically solve the VRPTW. GIDEON consists of two distinct modules: a global clustering module that assigns customers to vehicles by a process called genetic sectoring (GENSECT) and a local route optimization module (SWITCH-OPT). On a standard set of 56 VRPTW problems obtained from the literature, GIDEON did better than the alternate methods on 41 of them, with an average reduction of 3.9% in fleet size and 4.4% in distance traveled for the 56 problems. GIDEON took an average of 127 CPU seconds to solve a problem on the Solbourne 5/802 computer. >

Routing Container Ships Using Lagrangean Relaxation and Decomposition

Abstract: International shipping is a multibillon dollar business and shipping companies may expect large benefits from improving the routing and scheduling processes of their ships. In this paper, we describe a container-ship routing scenario in which a shipping company provides services to a network of ports. We formulate a mathematical programming model that maximizes total profit (i.e., revenue minus operating costs) for multiple ships and determines: (a) the optimal sequence of ports of call for each ship, (b) the number of trips each ship makes in a planning horizon, and (c) the amount of cargo transported between any two ports by each ship. The model contains discrete, 0–1 and continuous variables, and nonlinear complicating constraints. The multiple container ship model is quite different from those of vehicle routing and traveling salesman problems. We use a decomposition method for the model as well as for the network in order to solve the problem. Several problems on 10- to 20-port networks are solved an...

Capacitated Vehicle Routing on Trees

Abstract: T = (V, E) is a tree with nonnegative weights associated with each of its vertices. A fleet of vehicles of capacity Q is located at the depot represented by vertex v1. The Capacitated Vehicle Routing Problem on Trees (TCVRP) consists of determining vehicle collection routes starting and ending at the depot such that: the weight associated with any given vertex is collected by exactly one vehicle; the sum of all weights collected by a vehicle does not exceed Q; a linear combination of the number of vehicles and of the total distance traveled by these vehicles is minimized. The TCVRP is shown to be NP-hard. This paper presents lower bounds for the TCVRP based on the solutions of associated bin packing problems. We develop a linear time heuristic (upper bound) procedure and present a bound on its worst case performance. These lower and upper bounds are then embedded in an enumerative algorithm. Numerical results follow.

Designing collection routes through bank branches

Abstract: Most banks must send out vehicle on a regular basis to their branches in order to collect cash and negotiables left by depositors. The problem is modeled as a vehicle routing problem with constraints and objective terms specific to the aprticular banking context, such as penalties for lost interest. Two versions of the problem are studies: the deterministic case, and the stochastic case in which travel times are random. These two versions are modeled as integer mathematical programs, and solved by means of a heuristic procedure. Problems derived from a real situation (a Belgian bank network) are solved under different scenarios. (A)

A Tabu Search Heuristic for the Vehicle Routing Problem

Abstract: The purpose of this paper is to describe TABUROUTE, a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions. The algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route, and reinserting it into another route. This is done by means of a generalized insertion procedure previously developed by the authors. During the course of the algorithm, infeasible solutions are allowed. Numerical tests on a set of benchmark problems indicate that tabu search outperforms the best existing heuristics, and TABUROUTE often produces the bes known solutions. (A)

A 3-OPT based simulated annealing algorithm for vehicle routing problems

Abstract: Simulated Annealing is combined with the 3-opt heuristic to solve the vehicle routing problem. The results are encouraging; two examples out of three large size problems gave results as good as the best known 3-opt solution. Preliminary results with the heuristic algorithm are presented.

Structured partitioning problems

Abstract: In many important combinatorial optimization problems, such as bin packing, allocating customer classes to queueing facilities, vehicle routing, multi-item inventory replenishment and combined routing/inventory control, an optimal partition into groups needs to be determined for a finite collection of objects; each is characterized by a single attribute. The cost is often separable in the groups and the group cost often depends on the cardinality and some aggregate measure of the attributes, such as the sum or the maximum element. An upper bound (capacity) may be specified for the cardinality of each group and the number of groups in the partition may either be fixed or variable. The objects are indexed in nondecreasing order of their attribute values and within a given partition the groups are indexed in nondecreasing order of their cardinalities. We identify easily verifiable analytical properties of the group cost function under which it is shown that an optimal partition exists of one of three increas...

Application of fuzzy sets theory to the saving based vehicle routing algorithm

Abstract: The basic input data for any vehicle routing models are travel time, distances, and cost between nodes in the network. Information on these basic data is not always accurate, since many fa...

A stochastic and dynamic vehicle routing problem in the Euclidean plane

Abstract: We propose and analyze a generic mathematical model for dynamic, stochastic vehicle routing problems, the dynamic traveling repairman problem (DTRP). The model is motivated by applications in which the objective is to minimize the wait for service in a stochastic and dynamically changing environment. This is a departure from classical vehicle routing problems where one seeks to minimize total travel time in a static, deterministic environment. Potential areas of application include repair, inventory, emergency service and scheduling problems. The DTRP is defined as follows: Demands for service arrive in time according to a Poisson process, are independent and uniformly distributed in a Euclidean service region, and require an independent and identically distributed amount of on-site service by a vehicle. The problem is to find a policy for routing the service vehicle that minimizes the average time demands spent in the system. We propose and analyze several policies for the DTRP. We find a provably optima...

Self-organization via competition, cooperation and categorization applied to extended vehicle routing problems

Abstract: Competitive learning in neural networks involving cooperation and categorization is discussed. Extended vehicle routing problems in the Euclidean space are also discussed. A fixed number of vehicles with a shared depot make subtours around precategorized cities and collect demands. The minimal tour length and even loaded demands are conflicting requirements for the optimization. This situation does not appear in a simple traveling salesman problem. The self-organization method gives qualified approximate solutions without computational backtracks. Experiments were made on the USA532 set. All computations can be carried out by a conventional workstation. >

A multiobjective vehicle routing problem with soft time windows: the case of a public library distribution system

Abstract: Over the years, the central focus of vehicle routing problems has been the construction of minimum cost delivery routes, i.e. the creation of spatial utilities without considering temporal aspects. In many public service organizations, however, the minimum cost route without time windows can lead to poor customer service due to its ignorance of delivery deadlines. On the other hand, the most timely route may excessively lengthen vehicle travel distance, thereby increasing the total distribution cost. Consequently, the public distribution system calls for a new vehicle routing model that both considers time windows and analyzes the tradeoff between time and cost. This paper develops such a model and verifies its practical usefulness by applying it to the case of a public library distribution system in the Columbus, Ohio metropolitan area.

Vehicle routing problems via tabu search metaheuristic

Abstract: This paper addresses the application of the Tabu Search technique to the vehicle routing problem with time windows constraints. A simple adaptation of Tabu Search which uses only a short term memory strategy to overcome local optimality is developed. At first, an initial solution is obtained by a sequential route construction algorithm. After that, an arc interchange improving procedure is applied using as move attributes the deleted edges and the added edges. A sensitivity analysis is carried out in order to establish good choices for the number of edges considered tabu in a movement and for the lengths of the tabu lists. The method is tested on a large set of randomly generated routing problems and on a set of classical test problems. (A)

Comments on “One-warehouse multiple retailer systems with vehicle routing costs”

Abstract: In a recent paper, Anily and Federgruen developed a methodology for assigning retailers to vehicle tours, with the objective of minimizing long-run average transportation and inventory costs. This comment demonstrates that coordinating deliveries among tours can reduce cost over their solution.

Integration of adaptive machine learning and knowledge-based systems for routing and scheduling applications

Abstract: The combination of good mathematical models, knowledge-based systems, artificial neural networks, and adaptive genetic searches are shown to be synergistic. Practical applications of this combination produces near-optimal results, which none of the individual methods can produce on its own. We have developed XROUTE, a software system that demonstrates an integrated framework for this synergism, in the domain of computer-aided vehicle routing and scheduling problems. The purpose of this system is to assist researchers and decision makers who are applying the mathematical models to a specific routing problem instance by “tuning” the models to the problem description. The neural network modules store knowledge of previously solved problems and their solutions which facilitates the process of arriving at solutions to new problems. The knowledge-based system stores partial solutions from various knowledge sources, like the neural network and genetic algorithm modules, in the working memory and closely supervises the solution process in heuristic mathematical models. XROUTE provides an experimental, exploratory framework that allows many variations, and compares the alternatives on problems with different characteristics. The resultant system is dynamic, expandable, and adaptive and typically outperforms alternative methods in computer-aided vehicle routing.

The vehicle routing problem: an overview of exact and approxiamte algorithms

Abstract: The Vehicle Routing Problem (VRP) can be described as the problem of designing optimal delivery or collection routes from one or several depts to a number of geographically scattered cities or customers, subject to side constraints. the VRP plays a central role in the fields of physical distribution and logistics. There exists a wide variety of VRPs and a broad literature on this class of problems (see, for example, the surveys of Bodin et al. (1983), christofides (1985a), Laporte and Norbert (1987), Laporte (1990), aw well as the recent classification scheme proposed by Desrochers, Lenstra and Savelsbergh (1990)). The purpose of this paper is to survey the main and approximate algorithms developed for the VRP, at a level appropriate for a first graduate course in combinatorial optimization. The paper is organized as follows: 1) definition; 2) exact algorithsm; 3) heuristic algorithms; 4) conclusions. (A)

The Simultaneous Origin-Destination Assignment and Vehicle Routing Problem

Abstract: The problem we consider is that of preparing a minimum cost transportation plan by simultaneously solving the following two subproblems: first the assignment of units available at a series of origins to satisfy demand at a series of destinations and second, the design of vehicle tours to transport these units, when the vehicles have to be brought back to their departure point. We present a solution method for this problem using a minimum cost flow model followed by heuristic tour construction and improvement procedures. This approach allows large problems to be solved quickly, and solutions to large test problems have been shown to be 1% or 2% from the optimum. Results are presented for a problem involving the transport of 24,000 students working on an environmental cleanup project.

Algorithm management using genetic search for computer-aided vehicle routing

Abstract: Research into alternative ways of employing artificial intelligence techniques to direct mathematical algorithms is described. The authors have developed a software system called XVRP-GA that demonstrates an integrated framework for this synergism, in the domain of computer-aided vehicle routing and scheduling problems. The system assists researchers and decision makers in applying mathematical algorithms to a specific routing problem instance by intelligently adapting the algorithm to the problem description. The genetic search adaptively refines the parameters that control the work of the underlying algorithm. The resultant solutions are uniformly superior to the best known algorithms working alone. To reduce the computational overhead of genetic search, a mechanism for improving the performance of the search is employed. Several evaluation functions that permit the parallel investigation of multiple peaks in the search space are utilized, resulting in significantly increased efficiency in the genetic search. >

A pc based implementation of the control zone model for agvs design

Abstract: A computerized decision support system is introduced for implementation of the zone control model for AGVS design. A hypothetical design problem is introduced and defined in terms compatible with the system database. The application of the computer model is illustrated through a series of six adjustments in the original design profile corresponding to variation in AGVS design variables including guidepath layout, vehicle routing, vehicle dispatching, and load transfer point location. For each variation, the package is used to study the performance of the proposed system including gridlocking risk factors and the minimum vehicle fleet size needed to meet a fixed throughput requirement.

Computational approaches to stochastic vehicle routing problems

Abstract: We report computational test results for several graph-based a priori heuristics for the Euclidean plane versions of two well-known stochastic optimization problems, the probabilistic traveling salesman problem (PTSP) and the probabilistic (or stochastic) vehicle routing problem (PVRP). These heuristics are termed a priori because they design vehicle routes prior to realization of demands. Our tests compare the quality of such solutions to sample averages of a posteriori solutions of the deterministic realizations—the underlying TSPs and VRPs. Our results indicate that the simplest implementations give average cost performance within 5% of the latter, while the best implementations show a gap of only about 1%. Since running times are modest, we conclude that the a priori approaches offer a large potential benefit to the practitioner seeking to obtain good performance in a situation where solving repeated deterministic instances of the TSP or VRP is impractical or otherwise undesirable.

A routing and scheduling method in considering trade-off between the user's and the operator's objectives

Abstract: A routing and scheduling model is proposed for the one depot, multi‐vehicle, many‐to‐one, and vehicle capacity constraint problem. The model takes both the operator's and the user's objectives into account. The operator's objective is assumed to be the minimization of transportation cost or distance travelled; while the user's objective is represented by the minimum time difference between the desired and the actual times of vehicle arrival. The routing model is based on the classical Clarke‐Wright algorithm; however, node pairs in the model are ranked by an index generated by the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Thus, unlike the traditional Clarke‐Wright model, this model incorporates not only transportation cost but also the desired time of vehicle visit in the route development. Furthermore, different sets of routes can be produced depending upon the degree of preference attached to each objective. A step‐by‐step computation procedure and a set of examples are al...