On the tour partitioning heuristic for the unit demand capacitated vehicle routing problem

The tour partitioning heuristic for the vehicle routing problem assumes an unlimited supply of vehicles. If the number of vehicles is fixed, this heuristic may produce infeasible solutions. We modify the heuristic to guarantee feasibility in this situation and we analyze the worst-case performance of the modified heuristic.     

Beam element modelling of vehicle body-in-white applying artificial neural network

In this study a large knowledge base is first established through numerous designs of experiments on beam elements, based on a validated finite element model of a reference vehicle body-in-white. Then a recurrent artificial neural network is applied to extract the input/output relationship between the crash dynamic characteristics and beam element features. With such established relationship, beam element features are predicted according to expected crash dynamic characteristics. Our analyses show that the predicted beam element model enables generating essential crash dynamic characteristics for concept BIW design evaluation at a reasonable level of accuracy. Last, a data assurance criterion is developed to quantitatively validate the beam element modelling.     

Solving a school bus scheduling problem with integer programming

In many rural areas in Germany pupils on the way to school are a large if not the largest group of customers in public transport. If all schools start more or less at the same time then the bus companies need a high number of vehicles to serve the customer peak in the morning rush hours. In this article, we present an integer programming model for the integrated coordination of the school starting times and the public bus services. We discuss preprocessing techniques, model reformulations, and cutting planes that can be incorporated into a branch-and-cut algorithm. Computational results show that in our test counties a much lower number of buses would be sufficient if the schools start at different times.     

Heuristic methods for the sectoring arc routing problem

The sectoring arc routing problem (SARP) is introduced to model activities associated with the streets of large urban areas, like municipal waste collection. The aim is to partition the street network into a given number of sectors and to build a set of vehicle trips in each sector, to minimize the total duration of the trips. Two two-phase heuristics and one best insertion method are proposed. In the two-phase methods, phase 1 constructs the sectors using two possible heuristics, while phase 2 solves a mixed capacitated arc routing problem (MCARP) to compute the trips in each sector. The best insertion method determines sectors and trips simultaneously. In addition to solution cost, some evaluation criteria such as imbalance, diameter and dispersion measures are used to compare algorithms. Numerical results on large instances with up to 401 nodes and 1056 links (arcs or edges) are reported and analysed.     

Agent scheduling in a multiskill call center

This is a summary of the author’s PhD thesis, supervised by Pierre L’Ecuyer and Roberto Musmanno and defended on 21 February 2008 at the Università della Calabria. The thesis is written in English and is available from the author upon request. This work deals with the comparison of simulation-based algorithms for solving the agents scheduling problem in a multiskill call center minimizing their costs under service levels constraints. A solution approach, combining simulation, with integer or linear programming, and cut generation, is proposed. Considering realistic problems, it performs better than the two-step approach proposed in the literature. It is also shown that a randomized search, extending the one defined for the single-period staffing problem in Avramidis et al. [IIE Trans (in press), 2008], yields highly suboptimal solutions. Finally, an extension of the cutting plane method to directly control the probability on the customers abandonments is designed.      

On an optimal control problem involving first order hyperbolic systems with boundary controls

In this paper, we consider an optimal control problem involving a class of first order hyperbolic systems with boundary controls. A computational algorithm which generates minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated. Moreover, a necessary and sufficient condition for optimality is derived and a result on the existence of optimal controls is obtained.     

Generalized impedance boundary conditions for the maxwell equations as singular perturbations problems

In this paper the Maxwell equations in an exterior domain with generalaized impedance boundary conditions of Engquist-Nédélec are considered. The particular form of the assumed boundary conditions can be considered to be a singular perturbation of the Dirichlet boundary conditions. The convergence of the solution of the Maxwell equations with these generalized impedance boundary conditions to that of the corresponding Dirichlet problem is proven. The proof uses a new integral equations method combined with results dealing with singular perturbation problems of a class of pseudo-differential operators.     

Aggregate-level demand management in evacuation planning

Without successful large-scale regional evacuations, threats such as hurricanes and wild-fires can cause a large loss of life. In this context, automobiles are oftentimes an essential transportation mode for evacuations, but the ensuing traffic typically overwhelms the roadway capacity and causes congestion on a massive scale. Congestion leads to many problems including longer, costlier, and more stressful evacuations, lower compliance rates, and increased risk to the population. Supply-based strategies have traditionally been used in evacuation planning, but they have been proven to be insufficient to reduce congestion to acceptable levels. In this paper, we study the demand-based strategies of aggregate-level staging and routing to structure the evacuation demand, both with and without congestion. We provide a novel modeling framework that offers strategic flexibility and utilizes a lexicographic objective function that represents a hierarchy of relevant evacuation-based goals. We also provide insights into the nature and effect of network bottlenecks. We compare our model with and without congestion in relation to tractability, normative optimality, and robustness under demand uncertainty. We also show the effectiveness of using demand-based strategies as opposed to using the status quo that involves a non-staged or simultaneous evacuation process. Effective solution procedures are developed and tested using hypothetical problem instances as well as using a larger study based on a portion of coastal Virginia, USA.