A districting-based heuristic for the coordinated capacitated arc routing problem

The purpose of this paper is to solve a multi-period garbage collection problem involving several garbage types called fractions, such as general and organic waste, paper and carboard, glass and metal, and plastic. The study is motivated by a real-life problem arising in Denmark. Because of the nature of the fractions, not all of them have the same collection frequency. Currently the collection days for the various fractions are uncoordinated. An interesting question is to determine the added cost in terms of traveled distance and vehicle fleet size of coordinating these collections in order to reduce the inconvenience borne by the citizens. To this end we develop a multi-phase heuristic: (1) small collection districts, each corresponding to a day of the week, are first created; (2) the districts are assigned to specific weekdays based on a closeness criterion; (3) they are balanced in order to make a more efficient use of the vehicles; (4) collection routes are then created for each district and each waste fraction by means of the FastCARP heuristic. Extensive tests over a variety of scenarios indicate that coordinating the collections yields a routing cost increase of 12.4%, while the number of vehicles increases in less than half of the instances.</p

A Mixed Integer Linear Program for the Rapid Transit Network Design Problem with Static Modal Competition (Short Paper)

We present a mixed integer linear program for the rapid transit network design problem with static modal competition. Previous discrete formulations cannot handle modal competition for realistic size instances because of the complexity of modeling alternatives for each flow in the network. We overcome this difficulty by exploiting a pre-assigned topological configuration. Results of a case study will be presented at the conference

Exact solution of the evasive flow capturing problem

The Evasive Flow Capturing Problem is defined as the problem of locating a set of law enforcement facilities on the arcs of a road network to intercept unlawful vehicle flows traveling between origin-destination pairs, who in turn deviate from their route to avoid any encounter with such facilities. Such deviations are bounded by a given tolerance. We first propose a bilevel program that, in contrast to previous studies, does not require a priori route generation. We then transform this bilevel model into a single-stage equivalent model using duality theory to yield a compact formulation. We finally reformulate the problem by describing the extreme rays of the polyhedral cone of the compact formulation and by projecting out the auxiliary variables, which leads to facet-defining inequalities and a cut formulation with an exponential number of constraints. We develop a branch-and-cut algorithm for the resulting model, as well as two separation algorithms to solve the cut formulation. Through extensive experiments on real and randomly generated networks, we demonstrate that our best model and algorithm accelerate the solution process by at least two orders of magnitude compared with the best published algorithm. Furthermore, our best model significantly increases the size of the instances that can be solved optimally

Exact solution of the evasive flow capturing problem

The Evasive Flow Capturing Problem is defined as the problem of locating a set of law enforcement facilities on the arcs of a road network to intercept unlawful vehicle flows traveling between origin-destination pairs, who in turn deviate from their route to avoid any encounter with such facilities. Such deviations are bounded by a given tolerance. We first propose a bilevel program that, in contrast to previous studies, does not require a priori route generation. We then transform this bilevel model into a single-stage equivalent model using duality theory to yield a compact formulation. We finally reformulate the problem by describing the extreme rays of the polyhedral cone of the compact formulation and by projecting out the auxiliary variables, which leads to facet-defining inequalities and a cut formulation with an exponential number of constraints. We develop a branch-and-cut algorithm for the resulting model, as well as two separation algorithms to solve the cut formulation. Through extensive experiments on real and randomly generated networks, we demonstrate that our best model and algorithm accelerate the solution process by at least two orders of magnitude compared with the best published algorithm. Furthermore, our best model significantly increases the size of the instances that can be solved optimally.</p

A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges