A dynamic leader-follower model based on lack of central authority in emergency situations

Abstract

Most of the time, the government of the affected country cannot handle the entire relief operations. Under such conditions, international organizations act independently but are obliged to obey the law of the country. In this paper, we propose a dynamic multi-level programming where the affected country and international organizations dynamically change their roles, being leader or follower, according to a game. The application of the proposed model is investigated for a case problem where real data are utilized to design a network for humanitarian logistics during potential earthquakes. The advantages of using multi-level modeling against considering just one player's point of view are provided to guide decision-makers under a variety of conditions. The results show for the first three periods, the government of the affected area cannot handle the demand for the rescue operation. Thus, the international suppliers act as the leader for the first three periods. However, by decreasing the demand for the rescue operation in the last three periods, the government can manage the evacuation operation properly.

Providing homeland security strategies against interdictions in the city transportation network: A case study in Turkey

“…Wood developed a 'min-max' formulation to reformulate the maximum flow NIP and reduced it to a one-level integer programming model (IP) [17]. With the study of Wood, the number of NIP studies has increased and NIP becomes a well-studied research topic from many different scopes, such as minimizing the maximum flow or maximizing the shortest path on a given network, national defense [18,19], humanitarian logistics [20], facility or sensor locations [21,22], nuclear smuggling interdiction [23,24].…”

“…The objective function (20) determines the total distance of the shortest path used by the network user after the interdictions of the attacker. Constraint sets (21)(22)(23)(24) are dual constraints.…”

“…Besides the network 𝐺 (9,20) discussed in Section 3, the performance of I-Model(F) is tested on the networks 𝐺 (21,79), 𝐺 (43,234), 𝐺(86, 476), and 𝐺 (190,1542) in terms of runtime (in seconds). The experimental results are summarized in terms of attained runtimes achieved and objective function values for each level of the interdiction budget and given in Table 4 for all generated instances.…”

“…13) 0.46 2 (4-25) 0.58 3(10)(11) 0.74 3(15)(16)(17)(18)(19)(20)(21)(22)(23) 0.74 3 (22-23) 0.35 2 (27-34) 0.49 2 (2-15) 0.27 2 (4-29) 0.52 3 (11-12) 0.58 3 (16-17) 0.85 4 (22-25) 0.42 2 (28-31) 00.92 4 (12-16) 0.55 3 (17-30) 0.92 4 (25-28) 0.49 2 (31-32) 0.72 3 (3-25) 0.55 3 (7-8) 0.49 2 (13-16) 0.61 3 (18-19) 0.45 2 (25-29) 0.63 3 (32-33) 0.56 3 (3-26) 0.60 3 (7-12) 0.77 4 (13-19) 0.72 3 (18-24) 0.53 3 (25-31) 0.55 3 (33-34) 0.38 2 A, D, and I.C. represent arcs, distances (km), and interdiction cost (number of required equipments), respectively.…”