Strategies to Optimize the Impact of Supplies Distribution

in Post-disaster Operations

Christophe Duhamel

, Daniel Brasil

2,3

, Andr

ea Cynthia Santos

Eric Ch

atelet

and Babiga Birregah

LIMOS-UBP, Universit

e Blaise Pascal, Aubi

ere, France

ICD-LOSI, Universit

e de Technologie de Troyes, Troyes, France

DCC-UFMG, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

ICD-LM2S, Universi

e de Technologie de Troyes, Troyes, France

Keywords:

Post-disaster Response, Logistics, Distribution, Resilience, Heuristics.

Abstract:

We consider the problem of setting a supplies distribution system in a post-disaster context. The primary

decision variables correspond to the site opening schedule and the secondary variables focus on the supplies

distribution to the population zones. The objective is to optimize the supply delivery to the population, while

satisfying some logistics restrictions, both human and ﬁnancial. We present a non-linear model and we propose

a decomposition approach. The master level problem is addressed by NOMAD solver. The slave subproblem

is treated as a black-box and it is solved by a combination of two heuristics and a VND local search. Numerical

results on both random instances and on one realistic instance, using several scenarios, shows our approach

provides satisfactory results.

1 INTRODUCTION

Recent disasters have shown the critical importance

of setting both a fast, fair and efﬁcient post-disaster

response, especially in terms of supplies distribution.

However, those criteria are often hard to satisfy in

practice due to the limited information, to uncertain

data, to conﬂicting decisions, to limited time among

others (Boin and McConnell, 2007). Moreover, many

areas exposed to natural disasters have structurally

poor infrastructures and high densities of population.

Hence, providing an efﬁcient response and overcom-

ing the logistic challenge is vital to mitigate the risks,

to reduce the impact over the population and to im-

prove the recovery process.

Resilience plays a key role in crisis management,

and especially in the humanitarian context. Several

main approaches have been proposed for modeling

the resilience, among them the PR

(Preparedness,

Response (or Reactiveness) and Recovery) and the R

(Robustness, Resourcefulness, Redundancy and Ra-

pidity) models. The PR

model (Bruneau and Rein-

horn, 2007; Haimes, 2009; Mezzou et al., 2011) aims

at quantifying three criteria: the system preparedness,

its response and its recovery. Preparedness refers to

anticipation strategies, before the perturbation (the

disaster) occurs. The response encompasses the im-

mediate measures applied to overcome the perturba-

tion while the recovery corresponds to the operations

for restoring the system. The R

model (Bruneau

et al., 2003) uses four criteria: the robustness, the re-

sourcefulness, the redundancy and the rapidity. The

robustness quantiﬁes the system’s ability to absorb

the perturbation and the redundancy details the com-

ponents able to partially keep the system operational.

The resourcefulness is the ability to perform supplies

deployment and the rapidity is the system’s ability to

return to its initial state. Those two models are illus-

trated on Figure 1

In the context of humanitarian aid, those models

have to be adapted in order to integrate the human side

of socio-technical systems. The resulting proposed

model is shown in Figure 2.

Our work takes place in this adapted model in

which the monitored performance is the size of the

population in an humanitarian system. We consider

the problem of organizing the best possible way a sup-

plies distribution system in order to reach and help as

much population as possible, while satisfying some

resource limitations. The objective is to optimize the

342

Duhamel C., Brasil D., Cynthia Santos A., Châtelet E. and Birregah B..

Strategies to Optimize the Impact of Supplies Distribution in Post-disaster Operations.

DOI: 10.5220/0004927703420349

In Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems (ICORES-2014), pages 342-349

ISBN: 978-989-758-017-8

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: The R

/PR

resilience model.

Figure 2: Our adapted resilience model.

impact of the aid on the population, considered here

as the population survivability. We propose a mathe-

matical formulation and heuristics which couple a lo-

cal search with a non-linear solver, NOMAD (Le Di-

gabel, 2011).

This work is organized as follows: a bibliograph-

ical review is done in the next section. Section 3

introduces the problem followed by a mathematical

model description. The proposed method is presented

in Section 5. Preliminary numerical results are shown

in Section 6, before concluding remarks.

2 RELATED WORKS

Quantitative models for designing the humanitarian

logistics have been proposed recently in (Rottkem-

per et al., 2012; Berkoune et al., 2012; Nolz et al.,

2010). They focus on two key components: the lo-

cation of warehouses and the routing system. Aside

from the theoretical hardness of those core problems,

additional features are also considered. Both the un-

certainty on the data (Rottkemper et al., 2012) and

various evaluation criteria (Nolz et al., 2010) increase

the overall complexity of the problem. (Berkoune

et al., 2012) propose a decision support system to be

used in crisis situations. They consider three major

decisions to be made. The ﬁrst decision stands for the

number of sites to be opened. The second relies on

the aid that will be provided in each site. And third,

how the aid will be distributed. The objective is to

minimize the deployment time. They solve the mod-

els with a branch-and-bound algorithm using CPLEX,

and compare the solutions in terms of quality of solu-

tion and computational time. This approach has re-

cently been extended in (Abounacer et al., 2014) in

which an exact method is proposed to solve the prob-

lem of locating facilities and providing a distribution

network under several criteria.

The multi-criteria humanitarian aid distribution

problem where the transportation network is subject

to reliability issues is considered by (Vitoriano et al.,

2011). Several criteria are modeled: cost, dura-

tion, equity, priority, reliability and security. They

are aggregated in a goal-programming approach us-

ing GAMS and Cplex solver. This method is then

evaluated on data about the Port-au-Prince earthquake

catastrophe. The work has been extended in (Lib-

eratore et al., 2014) by taking into account both the

transportation network restoration (roads and bridges)

and the supplies distribution. Six criteria are used:

maximal arrival time, total served demand, maximal

ransack probability, global security, minimal arc re-

liability and global network reliability. The resulting

proposed RecHADS model aims at ﬁnding the best

infrastructure recovery plan while providing supplies

to the population. The coordination of the network

restoration and the aid distribution subproblems on

the same instance as before is shown to provide bet-

ter global solution than a sequential approach where a

better ﬁnal network is preferred over a better distribu-

tion.

The problem of multi-criteria warehouse location-

routing problem has been addressed by (Rath and

Gutjahr, 2014) for disaster relief. It consists in lo-

cating warehouses and designing vehicles routes to

deliver supplies to the population. Three criteria are

considered: the opening costs, the distribution costs

and the demand covered. A matheuristic combining a

Mixed-Integer Linear Program with a Variable Neigh-

borhood Search is proposed and compared with the

Non-dominated Sorting Genetic Algorithm II.

Some works have been focused on routing and dis-

tributing supplies to clusters areas as in (Prins et al.,

2012; Afsar et al., 2012; Afsar et al., 2014). The

authors deal with a medium-long terms macro distri-

bution. Some hypothesis have been considered such

as the center sites distribution are known in advance

and thus demands are leaved in a central facility for

each clusters. Moreover, a ﬂeet of vehicles is used,

but the number of available vehicles is unknown a

priori. Even if the authors do not focus on the ben-

eﬁts of such distribution in a resilience system, it may

contribute in a medium-to-long term recovery phase.

Very sophisticated heuristics and exact methods are

StrategiestoOptimizetheImpactofSuppliesDistributioninPost-disasterOperations

343

proposed to solve the mentioned problem.

3 PROBLEM DEFINITION

In this work, we consider the problem of setting a

distribution system in order to deliver supplies to the

population. Two sets of decisions have to be taken:

ﬁrst, where and when to open distribution centers and

second, how much, when and where to send supplies.

The distribution centers play a critical role as they

deﬁne an intermediate layer between the supplies ar-

rival point (a port or an airport for instance) and the

population. Their location must be carefully chosen

in order to be as close as possible to the population,

thus limiting the logistic distance. The set of poten-

tial distribution centers typically includes safe build-

ings able to store the supplies and to ensure vehicles

arrival/departure, for instance warehouses, stadium,

schools.

Choosing the right set of distribution centers is a

difﬁcult task as it involves several criteria. Besides,

some centers could be ﬁrst open at some locations and

later transferred to other locations. Here, we consider

only the ﬁrst part of the humanitarian delivery of sup-

plies. Thus site relocation is not allowed and one must

select the best set of locations on which to open sites.

Moreover, adapting a site in order to make it worth

safely storing supplies takes time. This is also con-

sidered in our model.

The population is located in several non-

overlapping zones and the amount of supplies dis-

tributed for each zone impacts the survival rate. Our

problem is to select the distribution centers and the

daily distributions in order to maximize the survival

rate of the population. The survival rate is a non-linear

function and thus our resulting model is non-linear.

3.1 Mathematical Formulation

The mathematical model we propose couples the hu-

manitarian aid distribution with an approximation of

the survivability rate. People which receive aid are

more likely to survive a post-disaster situation, hence

we are looking for the distribution with the highest

impact. Each supply unit is meant for covering the

need for an individual over one period of time. The

model is built on the assumption of a fair distribution

over a group of persons, that is the number of units

is fairly spread over the group. Thus the group acts

as a homogeneous entity. Consequently, the surviv-

ability rate is considered for the population and it is

improved with a better distribution of supplies. Be-

sides, the survivability rate is parameterized on the

daily needs covering. As a consequence, given a pop-

ulation size p and a delivery d over the time period,

the survivability rate τ is deﬁned as a non-linear func-

tion f () of the daily covered needs:

τ = f (d/p) (1)

The model relies on two components: (i) facility

location to chose the location and opening time and

(ii) distribution planning to deliver aid to the popula-

tion. An initial inventory is supposed to be available

after the disaster, at the beginning of the humanitar-

ian operations, and the model is indexed over the time

periods. Only immediate help is considered, which

does not taken into account waste cleaning, buildings

consolidation or reconstruction or durable population

relocation into safer areas.

Let T be the number of time periods for the im-

mediate humanitarian operations. It corresponds to

the interval time, considered here in days, needed to

provide the immediate humanitarian aid. Let Q be the

total amount of available supplies (e.g. food, water,

bandages and drugs), H be the available logistics hu-

man resources (e.g. personals and materials to operate

the network distribution system) and C be the avail-

able budget. Furthermore, I and J are respectively the

set of zones to be attended and the potential sites to

set a distribution center (store and distribute supplies).

For each potential site j ∈ J, let H

and Q

be respec-

tively the number of human resources needed to open

and operate it, and its distribution capacity. The cost

for operating a distribution site j and the unit distribu-

tion cost from site j to zone i are respectively denoted

and C

i j

. The initial population size for the zone i

is deﬁned as P

Variables p

determine the population for zone i

at time t. The distribution is given by variables x

i j

which tells the amount of supplies provided by site i

to zone i, at the time t. Variables y

specify the date

the site i is opened.

A mathematical formulation is provided from (2)

to (16), where the objective is to maximizing the ﬁnal

population, considering all zones and times.

z = max

∑

i∈I

(2)

∑

j∈J

∑

t=1...T

(T − y

) ≤ H (3)

∑

i∈I

i j

≤ Q

∀ j ∈ J, ∀t = 1 . . . T (4)

∑

t=1...T

∑

j∈J

∑

i∈I

i j

≤ Q (5)

∑

j∈J

∑

t=1...T

∑

i∈I

i j

≤ C (6)

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T · u

≥ y

∀ j ∈ J (7)

· w

i j

≥ x

i j

∀i ∈ I, ∀ j ∈ J,∀t = 1 . . . T (8)

= P

∀i ∈ I (9)

t+1

= p

· f

∑

i∈I

i j

∀i ∈ I, ∀t = 1 ...T − 1

(10)

≤ T ∀ j ∈ J (11)

≥ 0 ∀i ∈ I, ∀t = 1 ...T (12)

i j

≥ 0 ∀i ∈ I, ∀ j ∈ J,∀t = 1 . . . T (13)

∈ N ∀ j ∈ J (14)

∈ {0,1} ∀ j ∈ J (15)

i j

∈ {0,1} ∀i ∈ I, ∀ j ∈ J,∀t = 1 . . . T (16)

The objective function (2) aims at maximizing the

population size at the end of the time period. Inequali-

ties (3) guarantee the human resources to be deployed

to all open distribution centers at each time period do

not exceed H. Restrictions (4) and (5) state the lim-

its of supplies that can be distributed. Constraints (4)

determine the distribution capacity for each center j

at each period of time. Inequality (5) limits the total

amount of supplies available for distribution. Con-

straint (6) sets the global ﬁnancial limit. Since y

are

integer and x

i j

are continuous, auxiliary binary vari-

ables u

and w

i j

, deﬁned in (7) and (8), have been

introduced to properly add the corresponding cost in

(6). Variable u

tells if center j is open, and w

i j

tells

if there is distribution from center j to zone i on time

The initial population size in each area is set in

Equations (9). Equations (10) set the population evo-

lution in each area at each period of time. The vari-

ables deﬁnition are provided in (12) to (16).

This problem is NP-hard as it generalizes the lo-

cation problem. Moreover, it is non-linear due to the

functions f . Thus, solving it exactly might require a

too large time, even on small instances, in a context

of crisis logistics.

4 HEURISTIC STRATEGIES

We propose a decomposition-based heuristic to com-

pute solutions of good quality. The master level con-

sists in choosing which site to open and at which pe-

riod of time. The slave level computes a supplies

distribution in order to maximize the ﬁnal popula-

tion, given opening dates for the sites (see Figure 3).

Thus, the master level retains most of the combinato-

rial complexity of the problem while the slave prob-

lem deals with the complexity of the population dy-

namics. The later should ideally be tackled by simu-

lation.

population size

violations

opening dates

slave (local)

Master (global search)

Figure 3: The master-slave organization.

In this decomposition, the master problem is in

charge of ﬁnding the best combination of opening

dates for the potential sites by setting the y vector.

The slave subproblem receives the y vector from the

master and computes the best distribution schedule (x

variables) in order to optimize the population size z

at the end of the considered period of intervention.

Then, it returns the best value z found, given y.

This mathematical decomposition is considered as

a black-box optimization system. NOMAD solver

(Le Digabel, 2011) is used to compute the y vec-

tor. The slave subproblem is treated as a black-box

which provides evaluation and violations measures

given input values set by NOMAD. The evaluation

corresponds to the value z and the violations refer to

structural constraints (3) and (6). Indeed, the solver

cannot handle explicitly constraints on the y vector

and unfeasible vectors may be submitted to the slave.

The subproblem is solved by a local search. Its

ﬁrst step consists in checking the violations of the hu-

man and ﬁnancial resources constraints. If y is unfea-

sible, an inﬁnite value and the violations are returned.

Otherwise, an initial distribution is computed by a

constructive heuristic and the solution is improved by

a local search procedure (see Figure 4).

The constructive heuristic H

works by ﬁrst set-

ting each site availability according to y. The ﬁnan-

cial resources are updated accordingly. Then, for

StrategiestoOptimizetheImpactofSuppliesDistributioninPost-disasterOperations

345

read input feasible? greedy heuristic

local search

return

value & violations

yes

Figure 4: The algorithmic scheme of the black-box.

each time period, the supplies are assigned to the

open sites, respecting their capacities and the avail-

able stock of supplies. The distribution is performed

for each site. The zones are sorted on their distance

to the site and the distribution starts with the closest

one. Once the need for a zone is fulﬁlled, the next

next zone is considered, until the supplies are all dis-

tributed or all the zones are covered. Since H

relies

on a greedy approach for distributing the supplies, it

can run short of supplies at the last periods of time.

Thus another heuristic, H

, is proposed. It tries to de-

ﬁne a more balanced distribution by ﬁrst computing

the total distribution capacity for the sites open. Then

the supplies are assigned to each site and each period

of time, using the ratio of the capacity over the total

capacity. The way the supplies are distributed to the

zones is similar to H

Three neighborhood structures, N

, N

and N

are

proposed to improve the distribution, while respecting

the site availability and the ﬁnancial constraint. Each

kind of move addresses the distribution balance with

respect to one dimension of the problem (the set of

zones, the set of sites and the time periods), see Fig-

ure 5. A move from the structure N

considers one

site and one zone. It looks for supplies transfer from

one time period to another one in such a way the ﬁ-

nal population of the zone is improved. A move from

the second neighborhood structure N

considers one

site and one period of time. It tries to balance the

supplies distribution by transferring supplies from a

zone to another one in order to improve the total ﬁnal

population size of the two zones. A move from the

third neighborhood structure N

considers one zone

and one period of time. It aims at reducing the distri-

bution cost by transferring supplies from one site to

another one. Such a move does not have any impact

on the population since the amount of delivered sup-

plies does not change. However, by reducing the cost,

the objective is to allow moves from N

and N

that

were previously forbidden due to the ﬁnancial limita-

tion.

Those moves are used in a Variable Neighborhood

Descend (VND) local search. This method has been

proposed by (Mladenovic and Hansen, 1997) and it is

sites

zones

time

Figure 5: The impact of each neighborhood.

well-suited to the use of several neighborhood struc-

tures. The structures are ﬁrst sorted according to their

complexity, i.e. N

. Only one structure is ac-

tive each iteration. The method starts with the initial

solution s

and the ﬁrst neighborhood structure, that

is N

. Given an iteration, let k be the index of the ac-

tive structure and s the current solution. If an improv-

ing solution s

is found, it becomes the new current

solution (s ← s

) and k ← 1. Otherwise the current

solution does not change and k ← k + 1. The VND

stops when k > 3, i.e. when both three structures

have failed identifying an improving solution. Thus

the current solution is a local optima with respect to

the three neighborhood structures.

5 COMPUTATION RESULTS

The experiments were carried out on an Intel Xeon

CPU at 2.27GHz, with 8 cores, 8MB of cache, 16GB

of RAM, and using the operating system Ubuntu ver-

sion 10.04. The algorithms were implemented in C++

using the GCC version 4.6.3. The solver NOMAD

has been set to perform up to 500 evaluations and the

initial solution given to NOMAD is set with all sites

closed.

Several experiments have been performed over a

set of simulated scenarios and one real scenario from

the city of Belo Horizonte in Brazil. These instances

are described in the sequence (Section 5.1). The ﬁrst

set of experiments aims at evaluating the impact of the

heuristics and the local searches under the considered

scenarios (Section 5.2). The second set is dedicated

to measuring the quality of the overall framework, in-

cluding the NOMAD solver (Section 5.3).

5.1 Test Scenarios

Let a scenario be a set of parameters which corre-

sponds to a post-disaster situation. Some simpliﬁca-

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346

tions have been used in order to better evaluate the

impact of the proposed methods. Two majors set of

scenarios are considered in the computational experi-

ments.

The ﬁrst and the second set of scenarios contains

the ﬁxed parameters given in Table 1.

Table 1: Parameters statements for the ﬁrst and the second

sets of scenarios.

First scenario

Parameters Values

Number of time periods 8 days

Number of zones 10 zones

Number of sites varies from 2 to 12 sites

Size of the population 100,000 people

Supplies for distribution 6 days

Budget Unlimited

Human resources Unlimited

Second scenario

Parameters Values

Number of time periods 8 days

Number of zones 10 zones

Number of sites 10 sites

Size of the population 100,000 people

Supplies for distribution varies from 1 to 8 days

Budget Unlimited

Human resources Unlimited

For the sake of clarity, the parameter supply for

distribution means that the variable resources cover a

number of days. Using those characteristics for the

ﬁrst scenario, experiments have been designed vary-

ing the number of sites from 2 to 12. Considering the

second set of scenarios, the variability is set on the

amount of available supplies to be distributed which

ranges from 1 to 8 days.

The real scenario uses data from Belo Horizonte.

The main 9 urban zones are considered, with their

population, as shown in Table 2

Table 2: Population size for Belo Horizonte (2012).

zone population

Barreiro 282,552

Centro-sul 283,776

Leste 238,539

Nordeste 290,353

Noroeste 268,038

Norte 212,055

Oeste 308,549

Pampulha 226,110

Venda nova 265,179

Total 2,375,151



UTM SAD69 23S

Organização: SMAPL/SMPL

Base Cartográfica: PRODABEL; IBGE

Lagoa da Pampulha

Pampulha

Centro Sul

Leste

Noroeste

Oeste

Nordeste

Barreiro

Venda Nova

Norte

Mariano

de Abreu

Boa Vista

Abílio

Machado

Floresta/

Santa Tereza

Caiçara

Padre Eustáquio

Santa

Efigênia

Jardim

América

Serra

Cafezal

Morro

das Pedras

Santo

Antônio

Anchieta/

Sion

Mangabeiras

Cabana

Prudente

de Morais

São Bento

/Sta. Lúcia

Bairro

das Indústrias

Belvedere

Cristiano

Machado

Jardim

Montanhês

Instituto

Agronômico

Antônio

Carlos

Concórdia

Santa

Inês

Cachoeirinha

São

Francisco

UFMG

Estoril/Buritis/

Pilar Oeste

Barreiro

de Baixo

Barreiro

de Cima

Pampulha

Primeiro

de Maio

São

Bernardo

Olhos

D'Água

Tupi/Floramar

Ribeiro

de Abreu

Capitão Eduardo

Furquim

Werneck

Jardim

Felicidade

São João

Batista

Piratininga

Barreiro-Sul

Lindéia

Jatobá

Cardoso

Barro Preto

Centro

Francisco Sales

Savassi

Barragem

Pompéia

Taquaril

Baleia

Gorduras

São Paulo/Goiânia

Glória

Camargos

PUC

Santa Maria

Prado Lopes

Jaqueline

Isidoro Norte

Planalto

Barroca

Betânia

Garças/Braúnas

Santa Amélia

Jaraguá

Sarandi

Castelo

Ouro Preto

Confisco

Mantiqueira/Sesc Serra Verde

Jardim Europa

Venda Nova

Céu Azul

Copacabana

Vespasiano

Santa

Luzia

Nova

Lima

Sabará

Brumadinho

Ibirité

Contagem

Ribeirão

das Neves

Unidades de Planejamento

Belo Horizonte - 2009

Figure 6: The 9 zones of Belo Horizonte.

5.2 First Set of Experiments

Figures 7 and 8 illustrate the impact of the proposed

greedy heuristics (H

and H

) and the three neighbor-

hoods (N

, N

and N

) on the ﬁnal population.

Results in Figure 7 show that when the number of

sites increases, the greedy heuristic H

has a worst

performance than the heuristic H

. But the local

search is able to achieve the same level of solution

quality. In addition, when there are more sites avail-

able as for 10 and 12, the heuristic H

consumes the

total amount of supplies in the ﬁrst time periods. As

consequence, the neighborhood N

has a higher im-

pact since it works on the time period.

Figure 7 shows that, as the number of sites in-

crease, the number of people assisted gets higher, un-

til it reaches a maximum, on instances with 8, 10 or

12 sites. This happens because on the ﬁrst 3 instances,

the capacity of the sites are bottlenecks to the distri-

bution. Furthermore, the greedy heuristic H

has a

worse performance on the last instances. With more

sites, H

tends to spend all material resources on the

beginning, and lack supplies to use on the ﬁnal time

periods. Nevertheless, after the local search, the solu-

tions obtained are similar, meaning that the search is

robust enough to cope with different initial solutions.

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The same behavior is seen on Figure 8. It presents

a clear increase on the quality of the solution, as the

amount of food available increases. On the last in-

stance, when there is food enough for all days, the

greedy heuristics are capable of distributing the food

efﬁciently. Figure 11 and Figure 12 corroborate with

the analysis made for Figure 7 and Figure 8.

In terms on execution times, both Figures 9 and

Figure 10 show that neighborhoods N

and N

are re-

sponsible for most of the time consumption. This can

be explained by the computational complexity of the

operations. The greedy heuristics is O(n

logn), while

the local search is O(n

). The neighborhood N

does

not take as long as N

and N

because, since it does

not affect the population directly, there is no need to

recompute the population after a move, meaning that

it can be evaluated in O(n

), opposed to N

and N

that take O(n

) operations.

Figure 7: The impact on the population considering the ﬁrst

scenario.

Figure 8: The impact on the population considering the sec-

ond scenario.

Figure 9: The impact of the proposed heuristics on the run-

ning time for the ﬁrst scenario.

Figure 10: The impact of the proposed heuristics on the

running time for the second scenario.

5.3 Second Set of Experiments

For the realistic instance (Tables 11 and 12), H

still

produces worse results than H

. Neighborhood struc-

ture N

helps reaching the same quality as H

. Af-

ter the VND, solutions from both heuristics have the

same level of performance.

Figure 11: The impact on BH instance considering the ﬁrst

scenario.

Figure 12: The impact on BH instance considering the sec-

ond scenario.

6 CONCLUSIONS

We have considered the problem of setting a supplies

distribution system in a post-disaster context. The pri-

mary decision variables correspond to the site open-

ing schedule and the secondary variables focus on the

supplies distribution to the population zones. The ob-

jective is to optimize the supply delivery to the pop-

ulation, while satisfying some logistics restrictions.

We have proposed a decomposition in which the mas-

ter level is addressed by NOMAD solver. The slave

is considered as a black-box and it consists of two

ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems

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heuristics and a VND local search. Numerical re-

sults on both random instances and one realistic in-

stance, using several scenarios, shows our approach

provides satisfactory results. Besides, the overall re-

sponse time is kept limited since NOMAD is able to

work with very few calls to the black-box. We are cur-

rently investigating several extensions in order to deal

with more realistic population evolution dynamics.

REFERENCES

Abounacer, R., Rekik, M., and Renaud, J. (2014). An

exact solution approach for multi-objective location-

transportation problem for disaster response. Com-

puters & Operations Research, 41:83–93.

Afsar, H. M., Prins, C., and Santos, A. C. (2012). Exact and

heuristics strategies for solving the generalized vehi-

cle routing problem. In Proceedings of the 5th Inter-

national Workshop on Freight Transportation and Lo-

gistics, ODYSSEUS, pages 91–94, Mykonos, Greece.

Afsar, H. M., Prins, C., and Santos, A. C. (2014). Ex-

act and heuristic algorithms for solving the general-

ized vehicle routing problem with ﬂexible ﬂeet size.

International Transactions in Operational Research,

21(1):153–175.

Berkoune, D., Renaud, J., Rekik, M., and Ruiz, A. (2012).

Transportation in disaster response operations. Socio-

Economic Planning Sciences, 46:23–32.

Boin, A. and McConnell, A. (2007). Preparing for critical

infrastructure breakdowns: the limits of crisis man-

agement and the need for resilience. Journal of Con-

tingencies and Crisis Management, 15(1):50–59.

Bruneau, M., Eeri, A. M., Chang, S. E., Eeri, B. M., T, R.,

Eeri, C. M., Lee, G. C., Eeri, A. M., Orourke, T. D.,

Eeri, D. M., Reinhorn, A. M., Eeri, E. M., Shinozuka,

M., Kathleen, F., Eeri, G. M., Wallace, W. A., and I,

D. V. W. (2003). A framework to quantitatively as-

sess and enhance the seismic resilience of communi-

ties. Earthquake Spectra, 19:733–752.

Bruneau, M. and Reinhorn, A. (2007). Exploring the con-

cept of seismic resilience for acute care facilities.

Earthquake Spectra, 23(1):41–62.

Haimes, Y. Y. (2009). On the deﬁnition of resilience in sys-

tems. Risk Analysis, 29(4):498–501.

Le Digabel, S. (2011). Algorithm 909: NOMAD:nonlinear

optimization with the MADS algorithm. ACM Trans-

actions on Mathematical Software, 37(4):1–15.

Liberatore, F., Ortuo, M., Tirado, G., Vitoriano, B., and

Scaparra, M. (2014). A hierarchical compromise

model for the joint optimization of recovery opera-

tions and distribution of emergency goods in human-

itarian logistics. Computers & Operations Research,

42(0):3 – 13.

Mezzou, O., Birregah, B., and Ch

atelet, E. (2011). A the-

oretical study of the interactions between the compo-

nents of resilience in critical urban infrastructures. In

Smart and Sustainable City (ICSSC 2011), IET Inter-

national Conference on, pages 1–6.

Mladenovic, N. and Hansen, P. (1997). Variable neigh-

borhood search. Computers & Operations Research,

24(11):1097–1100.

Nolz, P. C., Doerner, K. F., Gutjahr, W. J., and Hartl, R. F.

(2010). A bi-objective metaheuristic for disaster relief

operation planning. In Coello, C. A. C., Dhaenens, C.,

and Jourdan, L., editors, Advances in Multi-Objective

Nature Inspired Computing, volume 272 of Studies in

Computational Intelligence, pages 167–187. Springer.

Prins, C., Santos, A. C., and Afsar, H. M. (2012). Splitting

procedure and a relaxed iterated local search for the

generalized vehicle routing problem. In Procedings

of the Latino-Iberoamericano de Investigaci

on Oper-

ativa, Simp

osio Brasileiro de Pesquisa Operacional,

CLAIO-SBPO, Rio de Janeiro, Brazil.

Rath, S. and Gutjahr, W. J. (2014). A math-heuristic for the

warehouse locationrouting problem in disaster relief.

Computers & Operations Research, 42:25–39.

Rottkemper, B., Fischer, K., and Blecken, A. (2012). A

transshipment model for distribution and inventory re-

location under uncertainty in humanitarian operations.

Socio-Economic Planning Sciences, 46:98–109.

Vitoriano, B. n., Ortu

no, M., Tirado, G., and Montero, J.

(2011). A multi-criteria optimization model for hu-

manitarian aid distribution. Journal of Global Opti-

mization, 51(2):189–208.

StrategiestoOptimizetheImpactofSuppliesDistributioninPost-disasterOperations

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