One of the key issues raised in NETWORKs ow is its INTERDICTION. Keshavarzi et al. scrutinized the issue with the multi-sources and multi-sinks conditions in mind while considering the speci c conditions of ow being sent from sources to sinks [R. Keshavarzi et al., Multi-source-sinks NETWORK ow INTERDICTION problem, International Journal of Academic Research, 2015]. Moreover, the matter was also examined in the state of multi-interdictors and a practical solution was presented [Keshavarzi and, Salehi, Multi commodity multi source-sinks NETWORK ow INTERDICTION problem with several interdictors, Journal of Engineering and Applied Sciences, 2015]. In this paper, the NETWORKs ow INTERDICTION in multi-source and multi-sink conditions was addressed; meanwhile, bearing in mind the uncertain data (from a speci ed beginning to an ending interval), an optimal interval was presented. Finally, a numerical example for this issue was provided and then solved by the program "Lingo".

In this paper, we state the problem of the NETWORK flow INTERDICTION in a set of initial and destination nodes so that each initial is capable of only delivering products to certain pre-determined destinations. The NETWORK user’s purpose is to deliver the highest value of flow from the sources to the sinks and the NETWORK interdictor’s purpose is to reduce the highest value of flow being used. In this paper, the NETWORKs flow INTERDICTION in multi-source and multi-sink conditions are addressed in a way that the parameters of arc capacity are trapezoidal fuzzy sets.

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.

The importance of locating critical facilities in hierarchical service delivery systems and fortification them against intentional attacks is the main subject of many researches, which helps the stability of the service system during intentional attacks by making appropriate decisions on location and fortification.‎ In this paper , for the first time , the problem of locating hierarchical facilities with regard to the fortification and INTERDICTION operations in a tri-level programming model between system designer , defender and attacker has been proposed.‎‎ The aim of the system designer at the first level is to minimize the location cost and service distance between the demand points and two categories of facilities.‎ The defender's objective is to adopt appropriate fortification operations at the second level in order to minimize the distance between customers and the nearest facility to receive primary services and referrals for secondary services according to available location resources.‎ Meanwhile, the attacker in the third level of the model, as a follower, seeks to make decisions to assign customers to two categories of facilities and INTERDICTION operations in order to maximize the service system distances.‎ To solve the new problem, a hybrid metaheuristic method based on genetic algorithm, simulated annealing algorithm and CPLEX has been proposed, and by solving several numerical examples, the the analysis of the results and the relation between the model parameters and the goals of the hierarchical service system is investigated.

The purpose of the matching INTERDICTION problem in the weighted graph G is to find a subset of vertices R*Í V such that the weight of the maximum matching in the graph G [V\R*] is minimized. According to the maximum matching in G, an approximate solution, denoted by R, for this problem is presented. Suppose that v (G) is the weight of the maximum matching in G. In this paper, we consider dendrimers as graphs such that the weights of edges are the bond lengths. We obtain the maximum matching in some types of dendrimers. Then, we compute the value of (v (G)-v (G [V\R*])) (v (G) - v (G [V\R])) for them. It is shown that this ratio in these classes of dendrimers is equal to the maximum value.

In the maximum flow NETWORK INTERDICTION problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of NETWORK. In this paper, our focus is on the nodal INTERDICTION for NETWORK instead of the arc INTERDICTION. Two path inequalities for the node-only INTERDICTION problem are represented. It has been proved that the integrality gap of relaxation of the maximum flow NETWORK INTERDICTION problem is not bounded below by a constant, even when strengthened by the path inequalities. We show that this result is also established for the nodal INTERDICTION problem.