Emergency logistics for disaster management under spatio-temporal demand correlation: The earthquakes case

Rodrigo A. Garrido; Ivan Aguirre

doi:10.3934/jimo.2019058

Article Contents

2020, Volume 16, Issue 5: 2369-2387. Doi: 10.3934/jimo.2019058

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Emergency logistics for disaster management under spatio-temporal demand correlation: The earthquakes case

Rodrigo A. Garrido^1, , and
Ivan Aguirre^2,

1.
Faculty of Engineering and Sciences, Universidad Diego Portales, Av. Ejercito 441, Santiago Centro, Santiago, Chile
2.
Diagonal Las Torres 2300, Santiago, Chile

^* Corresponding author: rodrigo.garrido@udp.cl
^* Corresponding author: rodrigo.garrido@udp.cl

Received: September 2018

Revised: February 2019

Early access: May 2019

Published: August 2020

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Abstract

Emergency logistics is crucial to ameliorate the impact of large earthquakes on society. We present a modeling framework to assist decision makers in strategic and tactical planning for effective relief operations after an earthquake's occurrence. The objective is to perform these operations quickly while keeping its total expenses under a budget. The modeling framework locates/allocates resources in potentially affected zones, and transportation capacity is dynamically deployed in those zones. Demand uncertainty is directly incorporated through an impulse stochastic process. The novelty of this approach is threefold. It incorporates temporo-spatial dependence and demands heterogeneity. It incorporates the availability of transportation capacity at different zones. It incorporates tight budget constraints that precludes the total satisfaction of demands. The resulting model is a large size stochastic mixed-integer programming model, which can be approximately solved through Sample Average Approximation. An example is provided and a thorough sensitivity analysis is performed. The numerical results suggest that that the response times are highly sensitive to the availability of inventory at each period. In addition, all logistics parameters (except for inventory capacity) have approximately the same impact on the total response time. The elasticity for all these parameters indicate constant returns to scale.

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Mathematics Subject Classification: Primary: 90C15, 90C11; Secondary: 90B15.

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Figure 1. Level of Service vs. Budget

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Table 1. Sensitivity scenarios and parameters' variations

Parameters	Base	Scen. 1	Scen. 2	Scen. 3	Scen. 4
Number of Periods	4	2	3	5	6
Number of Products	2	1	3	4	5
Number of Zones	6	2	4	8	10
Inventory capacity per period (units)	100	90	95	105	110

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Table 2. Sensitivity of the average objective function with respect to each parameter's variation

Parameters	Scen. 1	Scen. 2	Scen. 3	Scen. 4
Number of Periods	-52%	-27%	26%	52%
Number of Products	-52%	52%	105%	158%
Number of Zones	-69%	-35%	34%	69%
Inventory Capacity per Period	9%	6%	-8%	-19%

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Table 3. Objective function's Coefficient of Variation for each sensitivity scenario

Parameters	Scen. 1	Scen. 2	Scen. 3	Scen. 4
Number of Periods	0.08	0.06	0.05	0.04
Number of Products	0.08	0.04	0.04	0.06
Number of Zones	0.11	0.08	0.04	0.04
Inventory Capacity per Period	0.03	0.04	0.07	0.10

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Table 4. Elasticity of the average objective function with respect to each parameter's variation

Parameters	Scen. 1	Scen. 2	Scen. 3	Scen. 4
Number of Periods	1.04	1.08	1.04	1.04
Number of Products	1.04	1.04	1.05	1.05
Number of Zones	1.03	1.06	1.03	1.03
Inventory Capacity per Period	-0.87	-1.20	-1.60	-1.85

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Table 5. Variation of the solution under different probabilities of earthquake's occurrence

Total Access Time	Earthquake Pr. = 20%	Earthquake Pr. = 10%	PEarthquake Pr. = 2%	Earthquake Pr. = 1%
Lower Bound	500	700	2,900	4,000
Upper Bound	1,000	1,200	3,900	4,800
Relative Gap	100%	71%	34%	20%
Absolute Gap	500	700	1000	800

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