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September  2020, 16(5): 2369-2387. doi: 10.3934/jimo.2019058

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

 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

Received  September 2018 Revised  February 2019 Published  May 2019

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.

Citation: Rodrigo A. Garrido, Ivan Aguirre. Emergency logistics for disaster management under spatio-temporal demand correlation: The earthquakes case. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2369-2387. doi: 10.3934/jimo.2019058
##### References:

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##### References:
Level of Service vs. Budget
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
 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
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%
 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%
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
 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
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
 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
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
 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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