Designing a Bi-objective Post-Disaster Relief Logistics Model Considering Cost and Time of Utilizing Helicopters and Chance-Constraint Programming

Document Type : Original Article

Authors

1 Ph.D. Student, Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.

2 Professor, Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.

Abstract

Introduction: Disaster management in the post-disaster phase is crucial for minimizing damages. Relief logistics enable the rapid deployment of relief personnel and necessary materials to affected areas and the rescue of victims. During natural disasters like earthquakes, physical infrastructures such as roads and bridges are often destroyed, making access to affected areas extremely difficult or even impossible. For this reason, helicopters are the most suitable means of transport to assist the injured. In this context, another critical issue is the difference in service times between helicopters. Naturally, shorter service times result in higher costs. Therefore, it is essential to strike a balance between the dual objectives of time and cost.
Methods: This paper proposes a mathematical model for post-disaster relief logistics following a catastrophic earthquake in a mountainous region. The model aims to plan the deployment of helicopters to affected areas and manage the rescue and transportation of injured individuals to temporary facilities. The issue of uncertainty regarding the affected population and the demand for rescue personnel is also addressed. Initially, a deterministic mathematical model is proposed. Subsequently, the model is adapted using the chance-constraint programming method to incorporate the stochastic nature of the aforementioned parameters, converting them into deterministic constraints. Additionally, two approaches, the LP-metric method and the epsilon constraint method, are employed to solve the bi-objective model concerning time and cost.
Results and discussions: A key finding of this research is the formulation of decision variables in the mathematical model. One critical decision variable is the capacity allocated for preparing and dispatching relief personnel at each temporary facility. This designed capacity must not exceed a maximum allowable value due to technical constraints and, operationally, must also accommodate the total number of personnel deployed by all helicopters from the facility across multiple trips. Similar constraints apply to the capacity for treating injured individuals at each temporary facility. Specifically, this capacity must not exceed a predefined maximum and must also meet or exceed the population of injured individuals transported to the facility by various helicopters over multiple trips. Two additional important constraints addressed in this research include adherence to the maximum flight hours of each helicopter and ensuring a minimum level of service to cover the affected population. These constraints are made feasible through the defined decision variables. Another significant finding pertains to the modeling of the trade-off between helicopter service costs and times, represented as a bi-objective model. Moreover, given the uncertainty of the two exogenous parameters—relief force demand and the population of affected areas—these parameters are assumed to follow a normal distribution with specific means and standard deviations, and their associated constraints are ultimately converted into deterministic forms.
Conclusions: The proposed model is solved using the epsilon constraint method and the LP-metric method for a case study involving the Tabriz fault. In a pilot scenario, 13 affected areas were considered, with 3 potential locations for establishing temporary facilities and 5 types of helicopters. The results indicate that increased demand for relief personnel and affected areas leads to higher costs and longer service times, demonstrating the logical functionality of the developed model.

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Journal of Industrial Management Perspective
Volume 14, Issue 4 - Serial Number 56
Issue in Progress
2024
Pages 142-164

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