A bilevel model formulation for solving a post-hurricane damaged timber management problem. (December 2021) - Aghalari, Amin; Marufuzzaman, Mohammad; Aladwan, Badr Saleh; Tanger, Shaun; Da Silva, Bruno Kanieski
Highlights: Developed a mathematical model to manage the wood market interactions in the post-hurricane timber market. Maximizing the total profit of the landowners and the mills in the post-hurricane timber market. Developed two decomposition methods to speed up the solution process. A case study is developed to visualize and validate the modeling results. Abstract: Among other factors, the softwood industry is disrupted by a large number of hurricanes that landfall in the southern U.S. Lack of efficient tools to manage the wood market interactions in the post-hurricane situation increases timber salvage loss drastically. In this study, we propose a bi-level mixed-integer linear programming model that captures important features such as the hurricane's degree, quality of damaged timbers, price-related issues, optimizes different critical decisions (e.g., purchasing, storage, and transportation decisions) of a post-hurricane damaged timber management problem. The overall goal is to provide an efficient decision-making tool for planning and recovering damaged timber to maximize its monetary value and mitigate its negative ecological impacts. Due to the complexity associated with solving the proposed model, we developed two exact solution methods, namely, the enhanced Benders decomposition and the Benders-based branch-and-cut algorithms, to efficiently solve the model in a reasonable timeframe. We use 15 coastal counties in southeast Mississippi to visualize and validate the algorithms' performance. Key managerial insights are drawn on the sensitivity of a number of critical parameters, such as selling/purchasing prices offered by the landowners/mills, quality-level, and deterioration rate of the damaged timbers on their economic recovery following a natural catastrophe.