Multi-level facility location-allocation problem for post-disaster humanitarian relief distribution: A case study

Nomenclature

SetsV

the set of nodes (v, v′∈V)

J

the set of candidate locations (j, j^'∈J, J⊆V)

Scalars and parametersM

A large positive number

d_jj′

Euclidean distance between facility j and facility j′

d_jv

Euclidean distance between facility j and node v

λ_υ

the demand located on edge (v, v′)

E

the endurance of each drone

M_t

the maximum allowed length of the route from demand point to its assigned launching station

k

the maximum number of relief centers to be established

N

the maximum number of recharge stations to be established

VariablesL_j=1

if a launching station is established in location j; 0, otherwise

R_j=1

if a refueling station is established in location j; 0, otherwise

y_j=1

if a facility is established in location j; 0, otherwise

x_jv=1

if node v is assigned to facility j; 0, otherwise

t_jv

the length of the shortest path from facility j to demand node v

Highlights

• A multi-level FLP is used to simultaneously account for both relief centers and recharge stations.

• The model aims to optimize waiting times, total travel distance, survival rate and topology of the humanitarian relief system.

• The number of required resources including centers and drones is minimized without risking the efficiency of the system.

• A hybrid genetic algorithm is proposed for solving the model.

• A case study is investigated to evaluate the performance of the proposed method.

1. Introduction

Millions of disasters occur each year on the planet Earth. Only during 15 years between 2000 and 2015, there have been 800,000 lost lives just because of earthquakes (Lamb and Jones, 2012). In years 1999–2008, 1.2m lives were lost due to 7,000 disasters worldwide (Overstreet et al., 2011). Each year disasters disturb the lives of 250m individuals (United Nations, 2007). Recent incidents such as the tsunami in the Indian Ocean in 2004 and the 2003 storm in the Philippines have further highlighted the significance of humanitarian relief (Garner and Harrison, 2006; Carlson et al., 2016). The trend of disaster and rate of their occurrences...