A bi-level stochastic model of emergency supply planning considering transportation network mitigation and traffic congestion

Azeez, Berivan Faris; Rahmani, Arsalan; Hosseini, Meysam

doi:10.22060/ajmc.2025.24205.1390

A bi-level stochastic model of emergency supply planning considering transportation network mitigation and traffic congestion

Articles in Press

Document Type : Original Article

Authors

Berivan Faris Azeez ¹

Arsalan Rahmani ¹

Meysam Hosseini ²

¹ Department of Mathematics, University of Kurdistan, Sanandaj, Iran

² Department of Mathematics, Campus of Bijar, University of Kurdistan, Sanandaj, Iran

10.22060/ajmc.2025.24205.1390

Abstract

Implementing efficient emergency supply planning is one of the most challenging tasks. This article addresses the issue of emergency supply planning, considering both the emergency positioning before a disaster and the dynamic transportation planning after the disaster, taking into account the traffic reduction of the transportation network. The problem is modeled as a bi-level, two-stage stochastic programming model. In the first level, the objective is to minimize the total expected cost related to mitigation, preparation, and various response decisions. In the second level, the objective is to reduce the network traffic. The model is transformed to a single level using the KarushKuhnTucker (KKT) conditions. After utilizing linearization techniques and convexification, a specific rule based on lagrangean relaxation has been employed to minimize the scale of the model. Then a Benders decomposition algorithm is used to solve the reduced-size lagrangean single-level model. This method is significantly effective for solving this type of problem. Lastly, a case study for hurricane threat in the southeastern United States is conducted to demonstrate the benefits of the model and provide insight into optimal network mitigation, pre positioning planning, and transportation planning. It has been shown that the consideration of bi level models to reduce traffic congestion affects dynamic transportation plans and provides spatial and temporal flexibility to achieve better emergency supply plans. The suggested solution approach has been evaluated against two other well-known methods, and a comprehensive sensitivity analysis has been conducted on the model parameters.

Keywords

Emergency supply planning

Pre-positioning

KKT condition

Convexification

Traffic congestion

Benders decomposition algorithm

Subjects