Planejamento do uso de helicópteros no processo de distribuição da última milha em catástrofe

Xavier, Iran Rosa; Bandeira, Renata Albergaria de Mello; Silva, Leandro de Oliveira; Bandeira, Adriano de Paula Fontainhas; Campos, Vânia Barcellos Gouvêa; Leobons, Camila Maestrelli

Iran Rosa Xavier

Instituto Militar de Engenharia –IME, Seção de Fortificação e Construção – SE/2, Programa de Pós-graduação em Engenharia de Transportes, Rio de Janeiro, RJ, Brasil. E-mail: leandro.oliveira.sil@gmail.com

https://orcid.org/0000-0002-0027-5675

Renata Albergaria de Mello Bandeira

Instituto Militar de Engenharia –IME, Seção de Fortificação e Construção – SE/2, Programa de Pós-graduação em Engenharia de Transportes, Rio de Janeiro, RJ, Brasil. E-mail: leandro.oliveira.sil@gmail.com

https://orcid.org/0000-0002-2776-2473

Leandro de Oliveira Silva

Instituto Militar de Engenharia –IME, Seção de Fortificação e Construção – SE/2, Programa de Pós-graduação em Engenharia de Transportes, Rio de Janeiro, RJ, Brasil. E-mail: leandro.oliveira.sil@gmail.com

https://orcid.org/0000-0002-9280-6946

Adriano de Paula Fontainhas Bandeira

Instituto Militar de Engenharia –IME, Seção de Fortificação e Construção – SE/2, Programa de Pós-graduação em Engenharia de Transportes, Rio de Janeiro, RJ, Brasil. E-mail: leandro.oliveira.sil@gmail.com

Escola de Comando e Estado Maior de Exército – ECEME, Programa de Pós-graduação em Ciências Militares, Rio de Janeiro, RJ, Brasil

https://orcid.org/0000-0002-9701-6839

Vânia Barcellos Gouvêa Campos

Instituto Militar de Engenharia –IME, Seção de Fortificação e Construção – SE/2, Programa de Pós-graduação em Engenharia de Transportes, Rio de Janeiro, RJ, Brasil. E-mail: leandro.oliveira.sil@gmail.com

https://orcid.org/0000-0001-5244-8200

Camila Maestrelli Leobons

Instituto Militar de Engenharia –IME, Seção de Fortificação e Construção – SE/2, Programa de Pós-graduação em Engenharia de Transportes, Rio de Janeiro, RJ, Brasil. E-mail: leandro.oliveira.sil@gmail.com

https://orcid.org/0000-0001-8303-2793

Paper	Data	Objective Function	Restrictions	Period	Depot	Fleet	Resolution Method
Haghani & Oh (1996)Haghani, A., & Oh, S. C. (1996). Formulation and solution of a multi-commodity, multi-modal network-ow model for disaster relief operations. Transportation Research Part A, Policy and Practice, 30(3), 231-250. http://dx.doi.org/10.1016/0965-8564(95)00020-8. http://dx.doi.org/10.1016/0965-8564(95)0...	Deterministics	Min OC	U / LF	Multi	Multi	Het.	Heur.
Barbarosoğlu et al. (2002)Barbarosoğlu, G., Özdamar, L., & Çevik, A. (2002). An interactive approach for hierarquical analysis of helicopter logistics in disaster relief operations. European Journal of Operational Research, 140(1), 118-133. http://dx.doi.org/10.1016/S0377-2217(01)00222-3. http://dx.doi.org/10.1016/S0377-2217(01)...	Stochastics	Min OC / Min TT	Un.	Mono	Multi	Het.	Heur.
Barbarosoğlu & Arda (2004)Barbarosoğlu, G., & Arda, Y. (2004). A two-stage stochastic programming framework for transportation planning in disaster response. The Journal of the Operational Research Society, 55(1), 43-53. http://dx.doi.org/10.1057/palgrave.jors.2601652. http://dx.doi.org/10.1057/palgrave.jors....	Deterministics	Min OC	Un.	Multi	Multi	Het.	Exact
Özdamar et al. (2004)Özdamar, L., Ekinci, E., & Küçükyazici, B. (2004). Emergency logistics planning in natural disasters. Annals of Operations Research, 129(1-4), 217-245. http://dx.doi.org/10.1023/B:ANOR.0000030690.27939.39. http://dx.doi.org/10.1023/B:ANOR.0000030...	Stochastics	Min CUD	W / LF / WTW	Multi	Multi	Het.	Heur.
Yi & Özdamar (2007)Yi, W. E., & Özdamar, L. (2007). A dynamic logistics coordination model for evacuation and support in disaster response activities. European Journal of Operational Research, 179(3), 1177-1193. http://dx.doi.org/10.1016/j.ejor.2005.03.077. http://dx.doi.org/10.1016/j.ejor.2005.03...	Stochastics	Min TT / Min OC	W / LF	Multi	Mono	Hom.	Heur.
De Angelis et al. (2007)De Angelis, V., Mecoli, M., Nikoi, C., & Storchi, G. (2007). Multiperiod integrated routing and scheduling of World Food Programme cargo planes in Angola. Computers & Operations Research, 34(6), 1601-1615. http://dx.doi.org/10.1016/j.cor.2005.07.012. http://dx.doi.org/10.1016/j.cor.2005.07....	Deterministics	Max MCD	U / TW / LF / CP / MD	Multi	Multi	Het.	Exact
OTAN (2008)North Atlantic Treaty Organization – OTAN. (2008). Computer based decision support toll for helicopter mission planning in disaster relief and military operations (pp. 1-298). Brussels: Research and Technology Organization. - M. C1	Stochastics	Min TT	W / Un / LF / RF	Mono	Multi	Het.	Meta Heur.
OTAN (2008)North Atlantic Treaty Organization – OTAN. (2008). Computer based decision support toll for helicopter mission planning in disaster relief and military operations (pp. 1-298). Brussels: Research and Technology Organization. - M. NC2	Stochastics	Min OC	W / Un / RF	Mono	Multi	Het.	Meta Heur.
OTAN (2008)North Atlantic Treaty Organization – OTAN. (2008). Computer based decision support toll for helicopter mission planning in disaster relief and military operations (pp. 1-298). Brussels: Research and Technology Organization. - M. AN3	Stochastics	Min CUD / Min TT / Max MCD	Un.	Mono	Multi	Meta Het.	Heur.
OTAN (2008)North Atlantic Treaty Organization – OTAN. (2008). Computer based decision support toll for helicopter mission planning in disaster relief and military operations (pp. 1-298). Brussels: Research and Technology Organization. - M. AN4	Stochastics	Min TT / OT	Un.	Mono	Multi	Het.	Meta Heur.
Balcik et al. (2008)Balcik, B., Beamon, B., & Smilowitz, K. (2008). Last mile distribution in humanitarian relief. Journal of Intelligent Transport Systems, 12(2), 51-63. http://dx.doi.org/10.1080/15472450802023329. http://dx.doi.org/10.1080/15472450802023...	Dynamics	Min OC / Min CUD	V / WTW / LF	Multi	Mono	Het.	Heur.
Özdamar (2011)Özdamar, L. (2011). Planning helicopter logistics in disaster relief. OR-Spektrum, 33(3), 655-672. http://dx.doi.org/10.1007/s00291-011-0259-y. http://dx.doi.org/10.1007/s00291-011-025...	Deterministics	Min TT	W / Un / LF / RF	Mono	Multi	Hom.	Exact
Berkoune et al. (2012)Berkoune, D., Renaud, J., Rekik, M., & Ruiz, A. (2012). Transportation in disaster response operations. Socio-Economic Planning Sciences, 46(1), 23-32. http://dx.doi.org/10.1016/j.seps.2011.05.002. http://dx.doi.org/10.1016/j.seps.2011.05...	Deterministics	Min TT	W / V / WTW	Mono	Multi	Het.	Heur.
Najafi et al. (2013)Najafi, M., Eshghi, K., & Dullaert, W. (2013). A multi-objective robust optimization model for logistics planning in the earthquake response phase. Transportation Research Part E, Logistics and Transportation Review, 49(1), 217-249. http://dx.doi.org/10.1016/j.tre.2012.09.001. http://dx.doi.org/10.1016/j.tre.2012.09....	Stochastics	Min OC / Min CUD	W / V	Multi	Multi	Het.	Otim. Rob.
Battini et al. (2014)Battini, D., Peretti, U., Persona, A., & Sgarbossa, F. (2014). Application of humanitarian last mile distribution model. Journal of Humanitarian Logistics and Supply Chain Management, 4(1), 131-148. http://dx.doi.org/10.1108/JHLSCM-01-2013-0001. http://dx.doi.org/10.1108/JHLSCM-01-2013...	Deterministics	Min OC	Un.	Multi	Multi	Het.	Exact
Rivera et al. (2015)Rivera, J. C., Afsar, H. M., & Prins, C. (2015). A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem. Computational Optimization and Applications, 61(1), 159-187. http://dx.doi.org/10.1007/s10589-014-9713-5. http://dx.doi.org/10.1007/s10589-014-971...	Deterministics	Min TT	W/V/LF/TW	Multi	Multi	Het.	Heur.
Liu et al. (2018)Liu, Y., Lei, H., Zhang, D., & Wu, Z. (2018). Robust optimization for relief logistics planning under uncertainties in demand and transportation time. Applied Mathematical Modelling, 55, 262-280. http://dx.doi.org/10.1016/j.apm.2017.10.041. http://dx.doi.org/10.1016/j.apm.2017.10....	Stochastics	MinOC	U/V/LF/WTW	Multi			Otim. Rob.

Index set	Description
d	set of hub 2 (distribution centers), d = {1,2, …, i}
c	set of POD, c = {1,2, …, j}
p	Set of supply types for humanitarian aid, p = {1,2, …, a}
h	set of vehicle types, h = {1, 2, …, m_d}
k	set of vehicles type h available, k = {1, 2, … n_dh}
v	set of trips made on the assessed day, v = {1,2, …, r}
Variables sets
$X_{d c k h c}$	decision variable; defined as 1 if the delivery of hub 2 (d) to PODc occurs using the k-th vehicle type h in trip number v; 0 if it occurs otherwise
QT_dcpkhv	quantity of supplies p transported from hub 2 (d) to the PODc by the k-th vehicle type h in trip number v
QEVAC_dckhv	number of victims transported from POD c to hub2 d using k-th vehicle type h in trip number v
Parameters sets
DEM_cp	quantity of supplies p required at the POD c, in units
NVR_c	number of victims to be transported from PODc, in units
ZPH_c	conditions of the landing zone at the PODc, where {1,2,3,4}
DISP_dp	availability of supplies type p in hub 2 d, in units
COORD_d	co-ordinates of hub 2 d
COORD_c	co-ordinates of POD c
DIST_dc	distance between hub 2 d and PODc, in km
T_dch	travel time between hub 2 d the POD c using vehicle type h, in hours
PU_p	volume of a unit of supply p, in kg
VU_p	volume of a unit of supply p, in m³
CAT_h	category of vehicle type h, in {1,2,3}
VEL_h	cruising speed of vehicle type h, in km/h
CAPW_h	transport capacity for vehicle type h, in tonnes
CAPV_h	transport capacity for vehicle type h, in m³
CAPPAX_h	transport capacity of people of vehicle type h, in units
CTHV_h	cost of one hour of flight of vehicle type h, in monetary unit
α_ph	time for loading/unloading a unit of supply o in a vehicle type h, in hours/unit
τ_hc	approach time of vehicle type h at PODc, in hours/unit
λ_h	time for embark/disembark of victims in a vehicle type h, in hours/unit
MJ_h	maximum daily journey for each k-th vehicle type h, in hours
CCOMB_h	fuel consumption for each vehicle type h, in liters/hour
DCMB_d	availability of fuel in the hub 2d, in liters
MHVD_h	maximum availability of flight hours for vehicles type h
ORC	maximum budget availability for air operation, in monetary units

Product	Demand - POD (uniform distribution)		Wieght (kg)	Volume (m³)	Loading time per product (seconds/unit)
Product	µ	σ	Wieght (kg)	Volume (m³)	Aircraft 1	Aircraft 2	Aircraft 3	Aircraft 4
P1	80	30	20	0,027	15	15	16	20
P2	100	20	9	0,009	10	12	12	15

Aircraft (helicopters)	Weight (kg)	Volume (m³)	MJT (min)	τ_hc (min)	CAPPAX (und)	λ_h (min/und)	Speed (km/h)	CComb (kg/h)
Aircraft 1	400	3	720	2	3	1	235	157
Aircraft 2	1800	6	720	2	10	0.8	205	275
Aircraft 3	2000	8	720	2	12	0.667	280	440
Aircraft 4	2200	9	720	2	22	0.545	260	490

Aircraft (helicopters)	hub 2-A	hub 2-B
Aircraft 1	6	6
Aircraft 2	2	2
Aircraft 3	2	2
Aircraft 4	4	4

Number of POD		20	40	60
Number of variables		29210	58410	87610
Number of restrictions		29577	58837	88097
Average processing time (seconds)		62.70	223.61	> 3599
Average load carried (kg)		34458	70499	103910
Average number of people transported (pax)		242	487	778
60 seconds	Gap %	0.36	0.84	1.79
60 seconds	Optimal solution	9	3	0
120 seconds	Gap %	0.36	0.53	0.92
120 seconds	Optimal solution	9	9	0
600 seconds	Gap %	0	0.41	0.75
600 seconds	Optimal solution	10	9	0

[1] Notes: Objective Function: - Min OC: Minimize Operational Cost; Min TT: Minimize Total Time of Operation; Min CUD: Minimize Unmet Demand; OT: Other Type; Max MCD: Maximize beneficiaries. Restrictions: - U: Transported Units; V: Transported Volume: W: Transported Weight; LF: Fleet Limitation; TW: Time Window; WTW: Allowable Working Time; DCF: Fractional Delivery and Collect; CP: Parking Availability Restriction; MD: Minimal Demand; NV: Number of Travel; RF: Refueling.

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Planejamento do uso de helicópteros no processo de distribuição da última milha em catástrofe

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