In this paper we develop monitoring schemes for detecting structural changes
in nonlinear autoregressive models. We approximate the regression function by a
single layer feedforward neural network. We show that CUSUM-type tests based
on cumulative sums of estimated residuals, that have been intensively studied
for linear regression in both an offline as well as online setting, can be extended
to this model. The proposed monitoring schemes reject (asymptotically) the null
hypothesis only with a given probability but will detect a large class of alternatives
with probability one. In order to construct these sequential size tests the limit
distribution under the null hypothesis is obtained.
In this paper the multi terminal q-FlowLoc problem (q-MT-FlowLoc) is introduced. FlowLoc problems combine two well-known modeling tools: (dynamic) network flows and locational analysis. Since the q-MT-FlowLoc problem is NP-hard we give a mixed integer programming formulation and propose a heuristic which obtains a feasible solution by calculating a maximum flow in a special graph H. If this flow is also a minimum cost flow, various versions of the heuristic can be obtained by the use of different cost functions. The quality of this solutions is compared.
In a dynamic network, the quickest path problem asks for a path minimizing the time needed to send a given amount of flow from source to sink along this path. In practical settings, for example in evacuation or transportation planning, the reliability of network arcs depends on the specific scenario of interest. In this circumstance, the question of finding a quickest path among all those having at least a desired path reliability arises. In this article, this reliable quickest path problem is solved by transforming it to the restricted quickest path problem. In the latter, each arc is associated a nonnegative cost value and the goal is to find a quickest path among those not exceeding a predefined budget with respect to the overall (additive) cost value. For both, the restricted and reliable quickest path problem, pseudopolynomial exact algorithms and fully polynomial-time approximation schemes are proposed.