Mathematical model recommendations for the shortest path network interdiction problems in different structures

Companies have to reach the fastest solutions in their every basic process in order to be able to continue their lives in a competitive environment. Likewise, in the event of an emergency, the fastest way to get help from the shortest path has a vital importance. In this concept, there are many applications of shortest path problems in the field such as economy, business, engineering, military, emergency logistics in today's world. Some sides aim to prolong the their opponents processes' times. These processes can be commercial activities or terrorist acts that involve emergency situations that need to be helped as quickly as possible. In this context, it is very important to identify the important links on the network. In this study, the shortest path network interdiction problems are dealt with which include the number of different start and end nodes in which the two sides, namely the network operator who is trying to use the shortest path and the interdictor side who tries to maximize by making interdiction to the shortest path of operator. The problems are thought of as a two-player game with two opponents, called leaders and followers, and then mathematical models have been prepared to provide the optimum solution quickly. In this study, numerical results were obtained by applying the mathematical models to the sample networks.