bilevel programming

In this paper, a two-player Stackelberg game between the defender (leader) and attacker (follower) is considered , when the attacker tries to attack a strategic site and damage to communication paths , the defender aims to reduce the damage caused by the goal of locating the optimal number and the best type of military equipment due to resource constraints. This research attempts to present a bi-level mathematical model to optimize the location of military equipment, which aims to increase the distance between the attacker and the strategic site. Considering the bi-level model and because the military equipment location problem is in a class of NP-hard problems, a metaheuristic hybrid approach based on teaching-learning based optimization and dijkstra method is used. At the end of the research, with the help of large-scale numerical examples of the problem, the full description of the model and the proposed solution algorithm has been discussed.

In today's competitive world, maintaining competitive power of industries is the requirement of remaining in the competition. In the case of small industries, it also needs to think about strategies of making the industries more competitive in order to survive and have successful activity in competition. In many countries, one of the methods that have gained successful experience in increasing competitive power of SMEs is clustering these firms in a frame of “industrial clusters”. Considering the importance of industrial clusters’ role in regional economic development programs, providing the solutions of improving the performance of the clusters was always a concern for researchers and specialists of this field.
In this study, the process of product pricing as one of the most important factors which affects the profitability of industrial clusters is discussed by game theory approach. The proposed model focuses on the structural differences between supply chains and industrial clusters where the concept of Stackelberg game and bilevel programming model is used to determine the price of cluster’s products. In order to test the validity of the proposed model, the stone cluster data of Tehran are collected and using MATLAB software they are implemented in propose pricing game. Then, the results of the Stackelberg game between leader and cluster’s Stakeholders is been analysed.