We consider a vehicle routing problemwith a heterogeneous fleet of vehicles having various capacities, fixed costs and variable costs. An approach based on column generation (CG) is applied for its solution, hitherto successful only in the vehicle routing problem with time windows. A tight integer programming model is presented, the linear programming relaxation of which is solved by the CG tec...

Based on the characteristics of perishable goods, we extend the location-routing problem with distance constraints by adopting chance constrained goal programming approach to solve the uncertainty and to express the different priority levels of decisions. The random of depot construction costs and vehicle routing travel time is taken into account. Meanwhile, a two-stage genetic algorithm incorp...

This paper presents a column generation algorithm for the Vehicle Routing Problem with Time Windows (VRPTW). Traditionally, column generation models of the VRPTW have consisted of a Set Partitioning master problem with each column representing a route, i.e., a resource feasible path starting and ending at the depot. Elementary routes (no customer visited more than once) have shown superior resu...

Vehicle routing is a complex optimization problem with numerous variants related to various forms of transport planning. Particularly in an operational planning situation, the dynamic and stochastic aspects of the problems are important. The research project Dynamic Optimization in Transportation (DOiT) addresses vehicle routing in such a dynamic setting. In this survey, we give an overview of ...

The Split Delivery Vehicle Routing Problem (SDVRP) allows customers to be assigned to multiple routes. Two hybrid genetic algorithms are developed for the SDVRP and computational results are given for thirty-two data sets from previous literature. With respect to the total travel distance and computer time, the genetic algorithm compares favorably versus a column generation method and a two-pha...

This paper presents an algorithm to obtain lower bounds for the Split Delivery Vehicle Routing Problem. An extended formulation over a large set of variables is provided and valid inequalities are identified. The algorithm combines column and cut generation and was able to improve the lower bound for almost all instances tested.

This paper presents the development of a novel framework that optimizes the evacuation of large cities using multiple modes including vehicular traffic, rapid transit, and mass transit shuttle buses. A large-scale evacuation model is developed for the evacuation of the City of Toronto in cases of emergency. A demand estimation model is first designed to accurately quantify the evacuation demand...

Distribution planning in urban areas faces a lack of available parking space at customer sites. One approach to mitigate the issue is to cluster nearby customers around known parking locations. Deliveries from each parking location to its assigned customers occur by a second mode of transport (for example by foot). These lead to long service times at each of the clusters. However, long service ...