| Summary: It is possible to encounter the shortest path problems in every field of life. Real life problems such as transportation, routing and telecommunication can be given as examples of the shortest path problems. However, in real life problems, weather conditions, traffic, demand and cost of resources, etc. parameters may be uncertain. Due to these uncertainties, determining the cost of the path will be difficult for the shortest path problem based on deterministic approach. There are many ways to handle these uncertainties. Robust optimization is one of the methods used by decision makers in order to obtain the most appropriate solution in the shortest path problems where uncertainties are taken into consideration. Within the scope of this thesis, it is assumed that the arc lengths between nodes are continuous among limit values to express uncertainty in robust optimization. Minimum regret criteria are used to deal with the uncertainty of interval arc lengths. In the study, mathematical models have been developed for the minimum regret shortest path problems such as traditional (single source-single sink), single source-multi sink, multi source-single sink and multi source multi-sink node. The mathematical models are applied in different network structures and the paths were determined for the decision maker to reach the sink node(s) with minimum regret. As a result, it has been shown that the shortest path problem based on mininum regret criteria is applicable in different networks structures. |
