Showing papers on "Vehicle routing problem published in 1981"

A generalized assignment heuristic for vehicle routing

Abstract: : We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used to optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.

Complexity of vehicle routing and scheduling problems

Abstract: The complexity of a class of vehicle routing and scheduling problems is investigated. We review known NP-hardness results and compile the results on the worst-case performance of approximation algorithms. Some directions for future research are suggested. The presentation is based on two discussion sessions during the Workshop to Investigate Future Directions in Routing and Scheduling of Vehicles and Crews, held at the University of Maryland at College Park, June 4–6, 1979.

Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations

Abstract: We consider the problem of routing vehicles stationed at a central facility (depot) to supply customers with known demands, in such a way as to minimize the total distance travelled The problem is referred to as the vehicle routing problem (VRP) and is a generalization of the multiple travelling salesman problem that has many practical applications We present tree search algorithms for the exact solution of the VRP incorporating lower bounds computed from (i) shortest spanning k-degree centre tree (k-DCT), and (ii) q-routes The final algorithms also include problem reduction and dominance tests Computational results are presented for a number of problems derived from the literature The results show that the bounds derived from the q-routes are superior to those from k-DCT and that VRPs of up to about 25 customers can be solved exactly

Capacitated arc routing problems

Abstract: A capacitated node routing problem, known as the vehicle routing or dispatch problem, has been the focus of much research attention On the other hand, capacitated arc routing problems have been comparatively neglected Both classes of problems are extremely rich in theory and applications Our intent in this paper is to define a capacitated arc routing problem, to provide mathematical programming formulations, to perform a computational complexity analysis, and to present an approximate solution strategy for this class of problems In addition, we identify several related routing problems and develop tight lower bounds on the optimal solution

Combinatorial optimization and vehicle fleet planning : perspectives and prospects

Abstract: As a well-structured and costly activity that pervades industries in both the public and private sector, vehicle fleet management would appear to be a splendid candidate for model-based planning and optimization. And yet, until recently the combinatorial intricacies of vehicle routing and of vehicle scheduling have precluded the widespread use of optimization (exact) methods for this problem class. Our discussion in this paper identifies the extent and nature of these problem complexities and draws contrasts with other applications of combinatorial optimization. It also summarizes a number of successful uses of optimization for vehicle fleet planning and highlights potentially fruitful avenues for algorithmic development. In particular, we describe several alternative models and novel algorithms for the vehicle routing problem, show how various modeling approaches for this problem are intimately related, and illustrate the interplay between model formulations and the algorithms that they suggest. This discussion shows that prospects for applying exact methods, possibly in conjunction with heuristics, are far from fully realized and points to vehicle fleet planning as a tempting target of opportunity for further investigation.

Formulation and structure of more complex/realistic routing and scheduling problems

Abstract: We classify the features that seem to be encountered in real vehicle routing problems. Given these features, we try to indicate which features cause the greatest difficulty and which modeling approaches allow us to represent the greatest range of practical considerations or features.

A generalized assignment heuristic for vehicle routing

Abstract: Abstract : We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used to optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.

New algorithms for deterministic and stochastic vehicle routing problems

Abstract: In this dissertation, a comprehensive approach to stochastic vehicle routing is developed. Effective solution procedures for various forms of this complex problem are proposed and computationally tested. These solution procedures are adapted from solution procedures that are effective for related problems such as the Traveling Salesman Problem and the Vehicle Routing Problem. In general, given a set of points on a graph (locations on a map) the problem is to route one or more vehicles in such a way that each point and the total distance traveled is minimized. When there is one vehicle which must visit every location and return to its start location, the problem is called the Traveling Salesman Problem. This problem has been widely studied and has many applications in the transportation and scheduling fields. When there are multiple vehicles, each with a specific capacity, and a portion of this capacity is demanded at each point visited (e.g., delivery trucks), the problem is called the Vehicle Routing Problem. Such diverse operations as garbage collection, school busing, small package air mail service, along with a host of commercial distribution systems (e.g., milk, petroleum, etc.) fit this description and have benefited from algorithms designed to efficiently route the vehicles involved. When the demands at the various points are random variables whose values only become known when the vehicle serving that point arrives, the problem is a Stochastic Vehicle Routing Problem and must be treated differently than a deterministic problem above. In stochastic vehicle routing, the problem is to design a route system which has a short overall distance, but at the same time meets the demands on each route with regularity. If too many demand points are placed on one route, the vehicle assigned to that route will often be too small to meet all the demands. When this occurs, either some of the customers will not be served, or a special expense will be incurred in finishing the failed route. Both of these alternatives involve a cost which must be considered when designing the route system. Before specifically addressing the Stochastic Vehicle Routing Problem, this dissertation presents two efficient algorithms for the Traveling Salesman Problem. These algorithms are described in detail and then tested on a set of problems from the literature. The new algorithms produce better solutions to these test problems than several similar heuristic algorithms that have been proposed by other authors. After discussing these algorithms for the Traveling Salesman Problem, a new heuristic algorithm for deterministic vehicle routing is presented. It is based on an effective algorithm for the Traveling Salesman Problem, and has generated the best known solutions to several test problems in the literature. Having presented these new algorithms, the Stochastic Vehicle Routing Problem is formulated in two different forms, a chance constrained model and a penalty function model. These models are developed and tested computationally. The new vehicle routing algorithm presented previously is adapted to handle stochastic demands and is used to generate solutions to some test problems. The final phase of this dissertation involves adapting the stochastic vehicle routing models to the Subscriber Bus Routing Problem. This problem arises when a subscriber bus system in which customers sign up in advance for bus service to and from some large employment center is used as an alternative to the personal car. Such systems have arisen as a result of the recent escalation of automobile and gasoline costs.

Optimization on Refuse Collection Systems

Abstract: A solution to the vehicle routing problem for refuse collection in large cities is presented. The algorithm accommodates real world constraints and employs a combined heuristic and computer approach. The results of a case study in the Municipal Corporation of Greater Bombay brings out the efficacy of the algorithm in identifying the optimal refuse collection routes.

Algorithms for the set covering problem

Abstract: Solution methods for the set covering problem are presented. An extensive literature survey shows that the set covering problem has been applied to crew scheduling, circuit theory, database design, production planning, vehicle routing and location problems. All the new algorithms presented here compute lower bounds to the set covering problem that are then embedded in a tree search. Comparisons are made between the new algorithms and previously known methods of Korman, Balas and Ho, and linear programming. Two lower bounds are computed from network flow problems and two from graph theory. These bounds are then improved using subgradient optimization. State space relaxation, an incomplete dynamic programming or tree search technique, is used to compute lower bounds. A new decomposition method can be applied to a wide range of integer programs can also be used to obtain excellent lower bounds, albeit not too quickly. These methods use integer programming duality. A branching strategy using rows is described. The algorithms are described procedurally and by using an example. Data structures required to implement the algorithms are also given.

Mathematical Programming Methods for Logistics Planning.

Abstract: : This project was concerned with the application of mathematical programming models and techniques to logistics planning problems. Basic research was performed on a new approach, called inverse optimization, to the parametric analysis of mixed integer programming models. The approach was implemented and tested for the capacitated plant location problem. Basic research was also performed on three other logistics planning models with cyclic structures; namely, lot-size problems when demand and costs are cyclic, vehicle routing and cyclic staffing. A final research effort, partially suggested by the contract, was the construction and optimization, using decomposition methods, of a model of the U.S. coal supply and demand markets.

Vehicle Routing Algorithms for Local Delivery at Naval Supply Centers.

Abstract: : This thesis examines the local delivery operations at the Naval Supply Centers in Oakland and San Diego. The local delivery problem is formulated as a model applicable to these supply centers. Specifically, the model involves routing a fleet of vehicles from a central depot to each of a set of customers so as to satisfy their demands. Twelve heuristic solution methods applicable to this model are reviewed and illustrated with examples. They are also compared with respect to quality of resulting solutions and computational efficiency. Finally, recommendations on improving the routing of vehicles at the two Naval Supply Centers are made. (Author)

Use of Interactive Computer Graphics to Solve Routing Problems

Abstract: An interactive computer graphics package to solve vehicle routing problems is presented in this paper It uses computer graphics interactively to direct the use of a hybrid algorithm to solve individual routing problems This ability permits the user judiciously to tailor improved versions of existing algorithms to individual routing problems to alleviate the shortcomings of individual algorithms while capitalizing on their favorable characteristics The interactive computer graphics package is designed to permit an individual with little or no training in vehicle routing to find near optimal routes for a real problem in a short period of time