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Shortest Path problems are among the most studied network flow optimization problems. Since the end of the 1950's, more than two thousand scientific works have been published in the literature, most of them in journals and conference proceedings concerning general combinatorial optimization on graphs, but also in numerous specialized journals. One of the most interesting application fields is transportation.In many transportation problems, shortest path problems of different kinds need to be solved. These include both classical problems, for example to determine shortest paths (under various measures, such as length, cost and so on) between some given origin/destination pairs in a certain area, and also non standard versions, for example to compute shortest paths either under additional constraints or on particular structured graphs. Due to the nature of the applications, transportation scientists need very flexible and efficient shortest path procedures, both from the running time point of view and in terms of memory requirements. Since no "best" algorithm exists for every kind of transportation problem, Le. no algorithm exists which shows the same practical behavior independently of the structure of the graph, of its size and of the cost measure used for evaluating the paths, research in this field has recently moved to the design and the implementation of "ad hoc" shortest path procedures, which are able to capture the peculiarities of the problems under consideration. Much of the focus has been on the choice and implementation of efficient data structures (see, for instance, Tarjan, 1983). P. Marcotte et al. (eds.), Equilibrium and Advanced Transportation Modelling

The authors settle the complexity status of the robust network design problem in undirected graphs. The fact that the flow-cut gap in general graphs can be large, poses some difficulty in establishing a hardness result. Instead, the authors introduce a single-source version of the problem where the flow-cut gap is known to be one. They then show that this restricted problem is coNP-Hard. This version also captures, as special cases, the fractional relaxations of several problems including the spanning tree problem, the Steiner tree problem, and the shortest path problem.

We present a very large-scale neighborhood (VLSN) search algorithm for the capacitated facility location problem with single-source constraints. The neighborhood structures are induced by customer multi-exchanges and by facility moves. We consider both traditional single-customer multi-exchanges, detected on a suitably defined customer improvement graph, and more innovative multicustomer multi-exchanges, detected on a facility improvement graph dynamically built through the use of a greedy scheme. Computational results for some benchmark instances are reported that demonstrate the effectiveness of the approach for solving large-scale problems. A further test on real data involving an Italian factory is also presented.location problems, large-scale optimization, neighborhood search, negative cycles

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We study the Home Care Problem under uncertainty. Home Care refers to medical, paramedical and social services that may be delivered to patient homes. The term includes several aspects involved in the planning of home care services, such as caregiver-to-patient assignment, scheduling of patient requests, and caregiver routing. In Home Care, cancellation of requests and additional demand for known or new patients are very frequent. Thus, managing demand uncertainty is of paramount importance in limiting service disruptions that might occur when such events realize. We address uncertainty of patient demand over a multiple-day time horizon, when assignment, scheduling and routing decisions are taken jointly, both from a methodological and a computational perspective. In fact, we propose a non-standard cardinality-constrained robust approach, analyse its properties, and report the results of a wide experimentation on real-life instances. The obtained results show that, for instances of moderate size, the approach is able to efficiently determine robust solutions of good quality in terms of balancing among caregivers and number of uncertain requests that can be managed. Also, the robustness of the solutions with respect to possible realizations of uncertain requests, evaluated on a small subset of instances, appears to be significant. Furthermore, preliminary experiments on a decomposition method, obtained from the robust one by fixing the scheduling decisions, show a drastic gain in computational efficiency, with the determination of robust solutions of still good quality. Therefore, the approach appears to be very promising to cope with robustness even on Home Care instances of larger size

Routing real-time traffic with maximum packet delay in contemporary telecommunication networks requires not only choosing a path, but also reserving transmission capacity along its arcs, as the delay is a nonlinear function of both components. The problem is known to be solvable in polynomial time under quite restrictive assumptions, i.e., Equal Rate Allocations (all arcs are reserved the same capacity) and identical reservation costs, whereas the general problem is N P-hard. We first extend the approaches to the ERA version to a pseudopolynomial Dynamic Programming one for integer arc costs, and a FPTAS for the case of general arc costs. We then show that the general problem can be formulated as a mixed-integer Second-Order Cone (SOCP) program, and therefore solved with off-the-shelf technology. We compare two formulations: one based on standard big-M constraints, and one where Perspective Reformulation techniques are used to tighten the continuous relaxation. Extensive computational experi-

In this paper, we study dynamic shortest path problems that determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem and the minimum cost walk problem. The minimum time walk problem is to find a walk with the minimum travel time. The minimum cost walk problem is to find a walk with the minimum weighted sum of the travel time and the excess travel time (over the minimum possible travel time). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. In this paper: (i) we show that the minimum cost walk problem is an NP-hard problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic lights.