We described the two-stage Maximum flow network interdiction problem under endogenous stochastic interdiction. Our model consists of two adversary agent playing a Stackelberg game. A smuggler who wishes to maximize the expected flow of some illicit commodities (same as drugs), can be transmitted between a source node and a sink node without being detected. On the other hand, an attacker tries to minimize the objective of the smugglers by installing some detectors or adding some security controls on critical arcs to increase the probability of detection. Most previous stochastic network interdiction problems in the literature deal with exogenous uncertainty, while we consider stochastic programs under endogenous uncertainty in which the interdictor’ s decisions can alter the probability measures. The problem can be formulated as a bi-level program, at the top level the attacker by a limited budget, choosing critical arcs to install detectors and enhance the interdiction probability of those arcs endogenously. The bottom level problem is a two-stage problem which is solved to find the Maximum flow in the network by smugglers. In the first stage, he chooses some links to transmit the flow. In the second stage an indicator variable is used to show if he would be detected under each scenario. The bi-level decomposition algorithm has been applied to solve the problem by adding some Benders’ cuts iteratively. We applied a successive method, to deal with non-linearity rise in the probability measure of each path. A case study of drug trafficking network is applied to recognize which countries have the most significant effect in interdicting the drug trafficking network. The police can concentrate on those areas to decline the amount of drug flow. Our results demonstrate that if the critical arcs are chosen wisely and the probability of drug seizers decreases slightly, a significant decrease in the expected total flow of drugs can be achieved.

We consider the Maximum flow network interdiction problem. We provide a new interpretation of the problem and define a concept called ”optimalcut”. We propose a heuristic algorithm to obtain an approximated cut, and we also obtain its error bound. Finally, we show that our heuristic is an α-approximation algorithm for a class of networks. By implementing it on three network types, we show the advantage of it over solving the model by CPLEX.

Some relations for flood design estimating in sub-catchments in east and west part of north basin (Khazer basin).are established using multiple regression and index flood method.There are 31 sub-catchments in east part and 22 in west part of this area as gauged catchments.Factor analysis approach has realized that amongst several factors affecting on instantneous peak discharge, area of watershed, length of main channel, mean slope of watershed, mean annual precipitation, drainage density and compactness coefficient harv the largest effects, thus they are used in regional flood estimation analysis. Four homogenous groups of catchments are classified for each part of whole area and also entire area as one group using cluster analysis, Anderw curves and discrimination test. Some relations have been established for each of these groups and also for entire area of both part of Khazer basin using flood index method as well as multiple regression analysis. The results are successful in comparison with previous works have been done by others in this area.

The ultimate pit limit optimization (UPLO) serves as an important step in the mine planning process. Various approaches of Maximum flow algorithms such as pseudoflow and push-relabel have been used for pit optimization, and have given good results. The Boykov-Kolmogorov (BK) Maximum flow algorithm has been used in solving the computer vision problems and has given great practical results but it has never been applied in UPLO. In this work, we formulate and use the BK Maximum flow algorithm and the push-relabel Maximum flow algorithm in MATLAB Boost Graph Library within the MATLAB software in order to perform UPLO in two case studies. Comparing both case studies for the BK Maximum flow algorithm and pushrelabel Maximum flow algorithm gives the same Maximum pit values but the BK Maximum flow algorithm reduces the time consumed by 12% in the first case and 16% in the second case. This successful application of the BK Maximum flow algorithm shows that it can also be used in UPLO.

One of the most important factors in pipeline hydraulics and its protection against probable damages is keeping the pressure in a specific limit and also knowing how the pressure functions in the pipe through the pipeline route. Pressure function and pressure amount differ from each other regarding the phase of the fluid (single phase or multiple phase), and when gas phase (air) enters the pipeline, it affects the flow regime (simultaneously when gas-liquid flows there are such regimes as stratified, slug, etc. ) and the applied pressure. The present study aims to investigate the effects of flow patterns and phases on Maximum pressures along pipelines and to compare it with those of single-phase flows. Results show that the geometry and the percentage of entrained air are the main factors affecting flow patterns and pressure experienced by pipeline systems. For single phase mode, pressure is increased up to 26% in vertical upward flows compared to air-water flows with a different air percentage. Moreover, among various geometries considered in this research for two-phase flows, pressure at most has a 23-percent increase compared to that of single-phase flows.

To obtain the Maximum output power of a fast-axial-flow CW-CO2 laser, gas flow velocity can be optimized by using genetic algorithms. Our theoretical approach shows that the gas flow velocity after optimization increases the laser output power substantially from 500W, obtained in our present system, to 2203W.