Interactive Vehicle Routeing

No single approach to vehicle routeing has either the sophistication or the flexibility needed to tackle many real problems. Interactive routeing which emphasizes the experience of human schedulers may prove helpful. The main requirement would be that computers assist rather than replace humans. Use of one interactive package is described and a comparison with automatically produced results is given for test problems. Application of the approach to a real problem is outlined.     

A Repeated Matching Heuristic for the Vehicle Routeing Problem

A new heuristic for the vehicle routeing problem which makes use of repeated matching is described. The numerical results are comparable to or better than the best published for most of the 14 benchmark problems commonly used to evaluate VRP heuristics.     

Improvements to Vehicle Routeing Heuristics

An interactive method for the vehicle routeing problem has been developed, which attempts to refine routes produced by existing methods. Improvements have been found for some of the standard problems, and the new shortest-distance solutions are reported here.     

Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm

In this paper, we consider the open vehicle routeing problem (OVRP), in which routes are not sequences of locations starting and ending at the depot but open paths. The problem is of particular importance for planning fleets of hired vehicles, a common practice in the distribution and service industry. In such cases, the travelling cost is a function of the vehicle open paths. To solve the problem, we employ a single-parameter metaheuristic method that exploits a list of threshold values to guide intelligently an advanced local search. Computational results on a set of benchmark problems show that the proposed method consistently outperforms previous approaches for the OVRP. A real-world example demonstrates the applicability of the method in practice, demonstrating that the approach can be used to solve actual problems of routing large vehicle fleets.     

Some Applications of the Generalized Travelling Salesman Problem

In the Generalized Travelling Salesman Problem (GTSP), the aim is to determine a least cost Hamiltonian circuit or cycle through several clusters of vertices. It is shown that a wide variety of combinatorial optimization problems can be modelled as GTSPs. These problems include location-routeing problems, material flow system design, post-box collection, stochastic vehicle routeing and arc routeing.     

A Heuristic for Vehicle Routeing and Depot Staffing

This paper discusses the approach taken in solving a specific depot staffing and routeing problem. The problem differs from the normal routeing exercise in that the route passes through a number of outlets where monetary collections are made. Owing to the ever increasing risks of carrying money there is a requirement for the money to be deposited at banks along the route. Consequently, the more traditional routeing and scheduling methodologies and software are not easily applied to the problem. This paper details the approach used and highlights some of the good points and the pitfalls in the proposed solution.     

A Branch and Bound Algorithm for a Class of Asymmetrical Vehicle Routeing Problems

This paper describes a branch and bound algorithm for a general class of asymmetrical vehicle routeing problems. Vehicle routes start and end at a central depot. Visits are made to nodes grouped into clusters: every cluster must receive a minimum number of visits. But not all nodes must be visited: there are specified nodes and non-specified nodes. Vehicle routes are also constrained by capacity and distance restrictions. The problem is formulated as an integer linear program. It is then solved by a branch and bound algorithm which exploits the unimodular structure of the subproblems. Computational results are reported.     

Collision Avoidance in Bi-Directional AGV Systems

The use of a bi-directional, as opposed to a one-way, transportation system, can increase the operational efficiency of automated guided vehicles in both manufacturing and warehousing environments. However, the full potential will only be realized if the routeing algorithms pay particular attention to the problem of collision avoidance. This paper is concerned with the development of such an algorithm. The method is based on the use of delays and deviations to avoid collisions that could arise when using the shortest routes for each vehicle, and is applicable to any transportation system which can be represented as a network with known travel times.     

Further Inprovements to Vehicle Routeing Heuristics

A recent publication reported improved solutions to two of the standard test problems for vehicle routeing. A modification to an interactive heuristic is reported here, leading to further improvements to the best solutions given for two of these test problems.     

An Air Force Crew Allocation and Scheduling Problem

This paper considers an airline crew allocation and scheduling problem faced by certain divisions of the United States Air Force. Two variants of the problem under consideration were posed to us by the U.S. Air Force. This paper reports our experience with two heuristic methods developed, each applicable to either variant of the problem. Although the problem described herein is peculiar to this situation, the heuristic scheduling and dispatching rules developed have been found to be very effective and are generally applicable in other related contexts of routeing and crew and vehicle scheduling problems as well. The two algorithms developed have been applied to a coded set of real world data. The results indicate that each one of the two methods is preferable to the other for one of the two variants of the problem. This suggests an overall effective composite technique.     

Routeing in a Network with Multi-Class Links

Consider a communication network with certain nodes and different types of links. In addition to the normal link cost, a transformation cost is charged if the incoming link and the outgoing link are of different types. An optimal routeing from a given node to its destination node is sought. The major difficulty in handling this problem is that the principle of optimality does not hold. A model with node separation is built to overcome this difficulty. By using the new model, the original routeing problem is no more than a shortest-path problem. Hence, we can implement this model to current electronic switching machines.     

A guided tabu search for the heterogeneous vehicle routeing problem

The aim of this paper is to present a new algorithmic methodology for the heterogeneous fixed fleet vehicle routeing problem (HFFVRP). HFFVRP consists of determining the minimum cost routes for a fleet of vehicles in order to satisfy the demand of the customer population. The fleet composition is fixed and consists of various types of vehicles that differ with respect to their maximum carrying load and variable cost per distance unit. Our proposed algorithm called guided tabu search (GTS) is based on tabu search controlled by a continuous guiding mechanism that modifies the objective function of the problem. The role of this guiding strategy is to diversify the conducted search and help it overcome local optima encountered. The GTS method was applied successfully on HFFVRP benchmark problems producing best-known and new best-known solutions in short computational times.     

Extensions of the Petal Method for Vehicle Routeing

The petal method for vehicle routeing imposes special structure on the form of a feasible route. In this paper we show that by extending the definition of a petal route, more general forms of vehicle route can be generated without invalidating the important underlying property that optimal petal solutions can be produced very easily. It will also be shown that the optimal generalized petal solution can be produced efficiently by multiple applications of a shortest path algorithm.     

A Tabu Search Approach for Delivering Pet Food and Flour in Switzerland

In this paper, we consider a real-life vehicle routeing problem that occurs in a major Swiss company producing pet food and flour. In contrast with usual hypothetical problems, a large variety of restrictions has to be considered. The main constraints are relative to the accessibility and the time windows at customers, the carrying capacities of vehicles, the total duration of routes and the drivers' breaks. To find good solutions to this problem, we propose two heuristic methods: a fast straightforward insertion procedure and a method based on tabu search techniques. Next, the produced solutions are compared with the routes actually covered by the company. Our outcomes indicate that the total distance travelled can be reduced significantly when such methods are used.     

An Exchange Heuristic for Routeing Problems with Time Windows

In this paper, we compare different exchange heuristics for vehicle routeing problems with time windows. We also introduce a new 2-opt* exchange heuristic, and show that a hybrid approach, based on Or-opt and 2-opt* exchanges, is particularly powerful for problems with time windows. Computational results are reported for randomly generated problems and for a standard test set.     

The Impact of a Decision-Support System for Vehicle Routeing in a Foodservice Supply Situation

Efficient vehicle routeing is critical to the competitive position of firms in many industries. The foodservice industry encounters complex and constantly changing routeing problems in which time is a critical factor. With the cooperation and support of management and staff of Kraft Inc., we implemented an heuristic-based decision-support system, which utilizes computer-graphic pictures of routes in a large foodservice distribution region of Kraft Inc.The system provides the route scheduler with a tool to enable the rapid evaluation of computer-proposed solutions and to easily modify them. In tests conducted by Kraft personnel, system users found potential variable cost savings of 10.7% on 10 actual delivery problems of up to 223 stops. A potential for reductions in fixed costs was also indicated. The system allows the scheduler great flexibility in dealing with unpredictable factors and also aids management in strategic planning for distribution. It is currently in day-to-day use at Kraft.     

An Improved Petal Heuristic for the Vehicle Routeing Problem

Solutions produced by the first generation of heuristics for the vehicle routeing problem are often far from optimal. Recent adaptations of local search improvement heuristics, like tabu search, produce much better solutions but require increased computing time. However there are situations where good solutions must be obtained quickly. The algorithm proposed in this paper yields solutions almost as good as those produced by tabu search adaptations, but at only a small fraction of their computing time. This heuristic can be seen as an improved version of the original petal heuristic. On 14 benchmark test problems, the proposed heuristic yields solutions whose values lie on average within 2.38% of that of the best known solutions.     

Solving the AGV Problem via a Self-Organizing Neural Network

Automated Guided Vehicle (AGV)-based material handling systems (MHS) are used widely in Flexible Manufacturing Systems (FMS). The problem of AGV consists of the decisions and the operational control strategies of dispatching, routeing and scheduling of a set of AGVs under given system environments and operational objectives. One remaining challenge is to develop effective methods of AGV decisions for improved system productivity. This paper describes a prototype neural network approach for the AGV problem in an FMS environment. A group of neural network models are proposed to perform dispatching and routeing tasks for the AGV under conditions of single or multiple vehicles, and with or without time windows. The goal is to satisfy the transport requests in the shortest time and in a non-conflicting manner, subject to the global manufacturing objectives. Based on Kohonen's self-organizing feature maps, we have developed efficient algorithms for the AGVs decisions, and simulation results have been very encouraging.     

The Adult Training Centre Problem: A Case Study

An optimal solution is found to a real-world problem which has the characteristics of a multiple travelling-salesman problem. It deals specifically with methods of obtaining the 'best' routeing for four vehicles which provide a daily service from a depot to 38 locations. The solution technique uses both heuristic and exact algorithms to derive the order for visits to the 38 locations.     

Simple Heuristics for the Vehicle Routeing Problem with Soft Time Windows

We describe three simple heuristics for the vehicle routeing problem with customer time windows that can be violated by paying appropriate penalties. The customer demands are known, and a homogeneous fleet of vehicles stationed at a single depot is considered. The penalty payable to a customer is assumed to be a linear function of the amount of time window violation. Upper limits are imposed on both the penalty payable and the waiting time allowed at any customer. At each customer in a route, the PC-based heuristics simultaneously determine the actual time to begin service, and the next customer to serve. To achieve this, each heuristic uses different measures to compare the cost of waiting and penalty payable, with the benefit obtained by leaving immediately for the next customer. Computational results on a set of benchmark problems show that the procedure is efficient and enables significant reduction in the number of vehicles required and/or the total route distances while controlling both customer penalties and waiting times.