Bi-level programming model and KKT penalty function solution approach for reliable hub location problem

Tactical and operational decisions must nowadays be made in production and distribution systems to allocate the best possible locations for the establishment of service centers. These systems seek to provide their services the fastest and the most reliably. In the meantime, hub location problems are classified as the most important categories of such decisions. These problems include locating hub facilities and establishing communication networks between facilities and demand centers. This paper aims to design a bi-level programming model to minimize the costs of establishing a hub network at the first decision-making level and reduce service loss due to disruption and failure in service processes at the second decision-making level. Therefore, the reliable bi-level hub location problem was analyzed, and an integer programming model was developed. The KKT method was then employed to solve the model, whereas a two-step heuristic method with a penalty function was proposed to first offer a feasible solution through an innovative algorithm. After that, a process was formulated to improve the feasible solution through the penalty function logic. Data of 37 major cities were collected from the Civil Aviation Organization of Islamic Republic of Iran to validate the proposed model. In brief, the developed hub location problem model managed to efficiently solve some real-world distribution problems through a bi-level programming approach. Moreover, the traffic reliability and total location routing cost of the network were incorporated into a mathematical model.