CHAPTER II

LITERATURE REVIEW

2.1 Broader Views on Disaster Management

2.1.1 Definition of Disaster

Disaster has been defined in some different ways. Indeed, there is no precise definition for a disaster (Eshghi & Larson, 2008).

In complete form, Emergency Events Database (EM-DAT) defines disasters as “A situation or event which overwhelms local capacity, necessitating a request to the national or international level for external assistance, or is recognized as such by a multilateral agency or by at least two sources, such as national, regional or international assistance groups and the media” (Centre for Research on the Epidemiology of Disasters (CRED), 2004). Below et al. (2007) propose “an accumulation of widespread losses over multiple economic sectors, associated with a natural hazard event, that overwhelms the ability of the affected population to cope” as a definition of a disaster. International Federation on Red Cross and Red Crescent (IFRC) defines a disaster as “a sudden, calamitous event that seriously disrupts the functioning of a community or society and causes human, material, and economic or environmental losses that exceed the community's or society's ability to cope using its own resources…” (IFRC, 2008). van Wassenhove (2006) proposes “a disruption that physically affects a system as a whole and threatens its priorities and goals” as a definition of disaster, while Asian Disaster Reduction Center (ADRC, 2008) defines disaster as “a serious disruption of the functioning of society, causing widespread human, material or environmental losses which exceed the ability of affected society to cope using only its own resources”, which is similar with Reliefweb's (2008) definition. Emergency Management Australia (EMA, 2008) defines disaster as “a serious disruption to community life which threatens or causes death or injury in that community and/or damage to property which is beyond the day-today capacity of the prescribed statutory authorities and which requires special mobilization and organization of resources other than those normally available to those authorities”, while emergency is defined as ‘An event, actual or imminent, which endangers or threatens to endanger life, property or the environment, and which requires a significant and coordinated response.' (EMA, 2008).

2.1.2 Disaster Types

With a wide variability of disaster definition, it is understandable to have different initial classifications for disasters (Eshghi & Larson, 2008; Shaluf 2007a, b). Canadian Disaster Database (2008) categorises disasters into five different types as summarized in Table 1.

Table 1. Disaster types

(Source: Canadian Disaster Database, 2008)

Disaster types

Encompasses

Biological

Epidemic, infestation

Geological

Earthquake, landslide, tsunami

Meteorological and hydrological

Cold wave, drought, flood, hail/ thunderstorm, heat wave, hurricane/ typhoon, snow avalanche, storm surges, storm-freezing rain, storm-unspecified/ other, storm-winter, tornado, wildfire

Conflict

Terrorism, civil unrest

Technological

Accident-industrial, accident-other, accident-transport, fire, hazardous chemicals

van Wassenhove (2006) proposes a metrics (see Table 2) to understand disasters.

Table 2. Categorization of disasters based on van Wassenhove (2006)

Natural

Man-made

Sudden-onset

Earthquake, hurricane, tornado

Terrorist attack, coup d'etat, chemical leak

Slow-onset

Famine, drought, poverty

Political crisis, refugee crisis

In general, Shaluf (2007a, b) categorises disasters into three types:

1. Natural disasters, which are catastrophic events resulting from natural causes such as volcanic eruptions, tornadoes, earthquakes, etc.

2. Man made disasters, which are those catastrophic events that result from human decisions.

3. Hybrid disasters are those disasters that result from both human error and natural forces.

In further detail, Shaluf (2007b) breaks down each type of disasters and gives examples and characteristics, as can be seen in Table 3.

Table 3. Disaster types, taken from Shaluf (2007b)

Disaster type

Characteristics

Sub-disaster

Name of disasters

Natural

A natural disaster is a natural phenomenon;

A natural disaster is an unplanned and socially disruptive event with a sudden and severe disruptive effect;

A natural disaster is single event over which no human has control;

The impact of natural disaster is localized to a geographical region and specific time period;

The consequences of a natural disaster are felt at the place and time of its occurrence;

The disaster can be a high-impact disaster (e.g. a flood) that has a greater direct effect on the community over a longer period;

Rapid onset disasters include earthquakes, flash floods, hurricanes, volcanic eruptions, landslides, tsunamis, slow onset disasters, droughts, floods, and epidemics

Natural phenomena beneath the earth's surface

Earthquakes

Tsunamis

Volcanic eruptions

Topographical phenomena

Landslides

Avalanches

Meteorological/ hydrological phenomena

Windstorms (Cyclones, typhoons, hurricanes)

Tornadoes

Hailstorms and snowstorms

Sea surges

Floods

Droughts

Heat waves/ could waves

Biological phenomena

Infestations (locust swarms, mealy bug)

Epidemics (cholera, dengue, ebola, malaria, measles, meningitis, yellow fever, HIV/ AIDS, tuberculosis)

Man-made

Characteristics of socio-technical disasters:

A socio-technical disaster is a man-made event;

A socio-technical disaster occurs in an organisation due to the interaction between internal factors and external factors;

It arises suddenly: when the disaster occurs it does so as a shock;

A socio-technical disaster is a complex system of interdependence;

The impact of a socio-technical disaster sometimes transcends geographical boundaries and can even have trans-generational effects (e.g. Three Mile Island, Bhopal, Chernobyl);

Socio-technical disasters do not always have their worst consequences at the point of occurrence; the worst effects can occur long after the event;

Socio-technical disasters are characterized by a low probability/ high consequences event;

Sudden-impact disasters (e.g. air/road/rail accident) are usually of short duration and have a limited direct effect on the local community;

Socio-technical disasters arise not because of a single factor but of accumulated unnoticed events;

Disaster involves management procedures which must be maintained, and management problems must be coped with under the conditions of a major technical emergency involving threats of injury and loss of life;

Rapid onset disasters include fires, technological disasters, industrial accidents, and transportation accidents;

An inquiry report is required

Socio-technical

Technological disasters

Fire

Explotions (munitions explosions, chemical explosions, nuclear explosions, mine explosions)

Leakage

Toxic release

Pollutions (pollution, acid rain, chemical pollution, atmospheric pollution)

Structural collapse of physical assets

Transportation disasters

Air disasters

Land disasters

Sea disasters

Stadia or other public places failures

Fire

Structural collapse

Crowd stampede

Production failure

Computer system breakdown

Distribution of defective products

Warfare

National

Civil war between armed groups in the same country

Civil strikes

Civil disorder

Bomb threats/ terrorist attack

Inter-national

Conventional war

War between two armies from different countries

Sieges

Blockades

Non-conventional war

Nuclear

Chemical

Biological

Hybrid

The characteristics of a hybrid disaster can be the characteristics of both man-made and natural disasters

Natural and man-made events

Floods ravage community built on known floodplain

Location of residential premises, factories, etc., at the foot of an active volcano, or in an avalanche area

Landslides

Slightly different from those, EM-DAT (2008a) classifies disasters into three groups:

1. Natural disasters

2. Technological disasters

3. Complex emergencies

Regarding its scope in terms of sufferer number and/ or geographic areas affected, Gad-el-Hak (2008) distinguishes disasters into five categories as can be seen in Table 4.

Table 4. Disaster scope in terms of number of victims and/ or geographic area affected

(Source: Gad-el-Hak, 2008)

Scope

Category

No. of sufferers

Geographic areas affected

Scope I

Small disaster

< 10 persons

Or

< 1 km2

Scope II

Medium disaster

10-100 persons

or

1-10 km2

Scope III

Large disaster

100-1,000 persons

Or

10-100 km2

Scope IV

Enormous disaster

1,000-104 persons

Or

100-1,000 km2

Scope V

Gargantuan disaster

> 104 persons

Or

> 1,000 km2

While the definition of natural disasters and technological disasters are principally the same as those proposed by Shaluf (2007a, b), complex emergencies need a further exploration. Alballa-Bertrand (see Alballa-Bertrand, 2000) proposes the following definition for a complex humanitarian emergency or, in short, complex emergency:

‘A purposeful and unlikely neutral response, intended mostly to counteract the worse effects of the massive human destitution that derive from an overt political phenomenon, which takes the form of a violent, entrenched and long-lasting factionalist conflict or imposition with ultimate institutional aims'.

On the other hand, ReliefWeb (2008) defines a complex emergency as “A multifaceted humanitarian crisis in a country, region or society where there is a total or considerable breakdown of authority resulting from internal or external conflict and which requires a multi-sectoral, international response that goes beyond the mandate or capacity of any single agency and/or the ongoing UN country program. Such emergencies have, in particular, a devastating effect on children and women, and call for a complex range of responses.” While Complex Emergency Database (CE-DAT) (2008) defines complex emergency as all crises characterized by extreme vulnerability that display the following features:

1. There exist the unwillingness or incapability of the government to give effective response, leading call for external assistance;

2. Political oppression or armed conflict;

3. Displacement;

4. Increased mortality.

2.1.3 The Increasing Trend of Disaster Occurrences

Lichterman (1999) predicts that the frequency of disasters and their effects seem to be increasing. By reviewing various related published sources from 1900-2005, Eshghi and Larson (2008) confirm Lichterman's prediction. A disaster leads to a severe trouble of society, including extensive human misery and physical loss or damage (Davis & Lambert, 2002). Both natural and man-made disasters are likely to raise another five-fold over the next fifty years (from the year 2005) due to environmental degradation, rapid urbanization and the spread of HIV/AIDS in less developed world (Thomas & Kopczak, 2005). More than 250 million people in the world are affected by disasters every year (IFRC, 2008). In the sense of natural disasters - which are then divided into biological, geophysical, climatological, hydrological, and meteorological disasters -, CRED (see Scheuren et al., 2008) reports that there were 414 natural disaster occurrences (excluding biological disasters) in year 2007 which killed 16847 persons, affected more than 211 million others and caused over 74.9 US$ billion in economic damages. Until year 2004, over 90 percent of natural disasters occurred in developing countries (United Nations ISDR, 2004).

By including biological disasters and regrouping natural disasters into three different categories, as follows:

1. Hydro-meteorological disasters: comprising floods and wave surges, storms, droughts and related disasters (extreme temperatures and forest/scrub fires), and landslides & avalanches;

2. Geophysical disasters: earthquakes & tsunamis and volcanic eruptions fall into this category;

3. Biological disasters: consisting of epidemics and insect infestations;

International Strategy for Disaster Reduction (ISDR) (2008) provides data which shows that there is an increasing trend on the occurrences of natural disasters from 1900 to 2005, as can be seen in Table 5.

Table 5. Distribution of natural disasters: by origin

(1900-2005, by decades*)

*) 2000-2005, six year period

The increasing trends of the occurrences of natural disasters between 1900-June 2008 is also documented in EM-DAT (2008b).

Regarding the victims, there were 3,470,162,961 people affected by natural disasters for the period of 1991-2005 with a total of 960,502 deaths. Most of the victims (98.1% of people affected and 92.1% of people killed) were located in developing countries and least-developed countries (IFRC, 2008).

2.1.4 Disaster Management

Disaster management - also known as emergency management (Reliefweb, 2008) - is defined as comprehensive approach and activities to reduce the adverse impacts of disasters (Reliefweb, 2008), while disaster operations could be considered as the set of activities that are performed before, during, and after a disaster which are aimed at preventing loss of human life, reducing its impact on the economy, and returning to a normal situation (Altay & Green III, 2006). Using the terminology of disaster relief operations (DRO) as substitute to disaster operations, Pujawan et al. (2009) state that DRO consists of a variety of activities such as assessing demands, acquiring commodities, finding out priorities as well as receiving, classifying, storing, tracing and tracking deliveries. Regarding its phases, disaster management could be divided into four phases (Altay & Green III, 2006): disaster mitigation, disaster preparedness, disaster response, and disaster recovery.

2.1.5 The Importance of Logistics in Disaster Management

Logistics could be defined as follows (see Sheu, 2007a: 655):

“Logistics is the process of planning, implementing, and controlling the efficient, effective flow and storage of goods, services and related information from the point of origin to the point of consumption for the purpose of conforming to customers['] requirements at the lowest total cost.”

Its system operation consists of network design, information, transportation, inventory, warehousing, material handling, and packaging (see Wu & Huang, 2007: 429). There are several Operational Research (OR) techniques utilised in logistics context, including the use of transportation model to determine the location of warehouses and the use of assignment/ allocation model to locate production facilities (Slats et al., 1995: 12), to name a few.

In particular, humanitarian logistics could be defined as “the process of planning, implementing and control­ling the efficient, cost-effective flow and storage of goods and materials, as well as related information, from point of origin to point of consump­tion for the purpose of meeting the end beneficiary's requirements” (Thomas & Mizushima, January 2005). Similarly, Thomas and Kopczak (2005) define it as “the process of planning, implementing and controlling the efficient, cost-effective flow and storage of goods and materials, as well as related information, from the point of origin to the point of consumption for the purpose of alleviating the suffering of vulnerable people”. Whereas Sheu (2007a) proposes ‘‘a process of planning, managing and controlling the efficient flows of relief, information, and services from the points of origin to the points of destination to meet the urgent needs of the affected people under emergency conditions'' as a definition of emergency logistics.

Moreover, disaster relief is usually put aside for sudden upheavals such as natural disasters (earthquakes, avalanches, hurricanes, floods, fires, volcano eruptions, etc.) and very few man-made disasters such as terrorist acts or nuclear disasters (Kovács & Spens, 2007). Relief itself could be understood as “assistance and/or intervention during or after disaster to meet the life preservation and basic subsistence needs. It can be of emergency or protracted duration” (Reliefweb, 2008).

It has been already generally well-known that logistics play a vital role in emergency management. Sheu (2007a) declares that, due to the possibility of disasters' occurrences anytime around the world with huge effects, emergency logistics management had appeared as a worldwide-noticeable subject matter. People which are affected by disasters and are uprooted from their rights for food, housing, livelihood and other means of supporting themselves need the delivery of food, medicine, tents, sanitation equipment, tools and other necessities (Whybark, 2007). The science of logistics and supply chain management is becoming more vital for humanitarians (van Wassenhove, 2006), and “the subject of disaster management is an absolutely fascinating one that is growing in importance” (van Wassenhove, 2003: 19). Oloruntoba (2005) states that, regarding the Indian Ocean tsunami context, the scale of damage and subsequent response lead to problems of coordination, transportation and distribution among responding groups. In other affected areas of the Indian Ocean tsunami, Thomas (summer/fall 2006) reports that, at the 60-day point, regardless of the enormous relief efforts, only 60% of the families reported receiving well-timed and sufficient aid. It is therefore acceptable to conclude that good logistics planning plays an important role to the success of an emergency program (Davis & Lambert, 2002: 109).

Humanitarian logistics is essential to disaster relief for some reasons (Thomas & Kopczak, 2005):

1. It is crucial to the effectiveness and speed of response for main humanitarian programs, such as health, food, shelter, water, and sanitation;

2. It can be one of the most expensive elements of a relief effort as it includes procurement and transportation;

3. Since the logistics department handles tracking of commodities through the supply chain, it is often the repository of data that can be analyzed to offer post-event knowledge.

In his paper, McEntire (1999) states that the disaster studies must discover ways to improve the provision of relief after certain catastrophe hits. This statement is in line with Perry's (2007) finding which accentuates the availability of logistician cadres as a key element of disaster response, as part of needs assessment and for procuring, transporting, and distributing the relief provisions. Regarding the relief of the Indian Ocean tsunami, the humanitarian organizations providing those relieves acknowledged that relief can and needs to be faster and more efficient (Thomas, 2005). Together with hurricane “Katrina” disaster, the Indian Ocean tsunami lead to the gap of “the inability to connect the aid provided with the aid received” (Thomas, 2005) in spite of the unprecedented giving during those two misfortunes. It is also pointed out by Tolentino Jr. (2007) that the Indian Ocean tsunami has provided the will to radically improve disaster management and planning, an issue Trim's (2004: 224) research agrees with, in a broader disaster relief context. Furthermore, the development of new technology for track/trace and disaster relief supply chains is proposed as one of ways to improve the delivery of humanitarian relief (Baluch, 2007). In the context of the participation of non-governmental organizations (NGOs) in worldwide emergencies (e.g. volcanic eruptions, earthquakes, floods, war), Beamon and Kotleba (2006) point out that the capability of an NGO's supply chain and logistics operations directly influences the success of a relief effort. Whereas Pujawan et al. (2009) propose information visibility, coordination, accountability, and professionalism as successful requirements of logistics for DRO.

2.2 Some Previous Works in Logistics Management

The following paragraphs will give a short overview on several aspects in logistics management, especially those which are perceived as having relevance with the current research. They include distribution network design problem, location-allocation problem (LAP), vehicle routing problem (VRP), and location-routing problem (LRP), respectively.

2.2.1 Distribution Network Design Problem

Citing Chopra (2003), distribution can be seen as “the steps taken to move and store a product from the supplier stage to a customer stage in the supply chain”. While distribution networks can be defined as “networks that carry the flow of some commodity or entity, using a routing rule that is intended to be effective and even optimal” (Whittle, 2007), and distribution network itself could be viewed as similar with the terminology producer network (Ambrosino & Scutellà, 2005: 611).

Distribution network design problem tackles the issues of optimizing the flows of commodities through an existing distribution network as well as improving the performance of the existing network by selecting the most appropriate setting of the facilities in the network aimed at satisfying the company's goal at one hand and minimising the overall costs at the other hand (Ambrosino & Scutellà, 2005: 611). It involves facility location, transportation and inventory decisions (Ambrosino & Scutellà, 2005: 611). In other words, the aim of distribution network design problem is on deciding the best way of moving goods or products from resource/ supply points to destination/ demand points which is performed by determining the structure of the network, in a such a way that the customer demands are satisfied and the total distribution costs are minimized (Ambrosino et al., 2009: 442). In Amiri's (2006: 567-568) paper, distribution network design is stated as involving the simultaneous decisions on the best settings of both plants and warehouses and on the best strategy in the sense of product distribution from the plants to the warehouses and from the warehouses to the customers, respectively.

Meanwhile, the term “distribution system design” refers to “the strategic design of the logistics infrastructure and logistics strategy to deliver products from one or more sources to the customers” (Goetschalckx, 2008: 13-1) and - similar to Ambrosino et al.'s (2009) statement on distribution network design problem - focuses on five phases of interconnected decisions, as follows (Goetschalckx, 2008: 13-2):

1. Establishing the appropriate quantity of distribution centers (DCs);

2. Setting up the location of each DC;

3. Allocating customers to each DC;

4. Allocating appropriate commodities to each DC; and

5. Determining the throughput and storage capacity of each DC.

Various models and approaches that have been built for designing distribution system or distribution network, to name a few, are (Goetschalckx, 2008: 13-8-13-15; Lapierre et al., 2004): K-median model, location-allocation model, warehouse location model, Geoffrion and Graves distribution system design model, models that focus on mathematical description of cost functions on each route in order to incorporate returns to scale, models of which concentration are in shipments on hub-to-hub routes regarding discounts, and models that aim at solving the freight transportation problem precisely.

2.2.2 Location-Allocation Problem (LAP)

As previously stated in Goetschalckx (2008), LAP could be seen as part of distribution network design problems. Given the place of a set of customers with different demands, LAP is concerned with the selection of supply centres' positions dedicated for serving the customers as well as the decision of the allocation of the customers to supply centres, with both of them are aimed at optimizing a given criterion (Hsieh & Tien, 2004: 1017). It is also assumed that there is no interaction among supply centres. The criterion could be single such as transportation costs (see, for example, Goetschalckx, 2008; Zhou & Liu, 2003; Manzini & Gebennini, 2008) or it may comprises several aspects (see, for example, Mitropoulos et al., 2006).

The following paragraphs provide some previous researches on LAP.

The un-capacitated-type LAP with rectilinear distances could be found in Hsieh and Tien (2004). In this paper, the authors propose a heuristic method which is based on Kohonen self-organising feature maps (SOFMs).

Sometimes distribution networks are built in hierarchies, where high-level distribution channels are constructed in straight lines from which low-level channels stem. Furthermore, destinations are allocated to branching facilities in high-level channels through low-level channels. Due to cost considerations, the number and locations of branching facilities as well as the allocation of the destinations to the aforementioned branching facilities need to be determined correctly. Eben-Chaime et al.'s (2002) paper addresses this type of problem by formulating appropriate mathematical optimisation models and subsequently proposing heuristic solution methods.

Capacitated LAP with stochastic demands is addressed by Zhou and Liu (2003). More specifically, they propose three types of stochastic programming models: (1) expected value model (EVM), (2) chance-constrained programming (CCP), and (3) dependent-chance programming (DCP). To solve these models efficiently, the authors develop a hybrid intelligent algorithm within which three type stochastic simulations are used. The proposed algorithm integrates the network simplex algorithm, stochastic simulation and genetic algorithm.

In more recent paper, Zhou and Liu (2007) address the LAP with fuzzy demands by developing three types of fuzzy programming models - fuzzy expected cost minimisation model, fuzzy -cost minimisation model, and credibility maximisation model with respect to different decision criterion. To solve these models, the authors apply a hybrid intelligent algorithm developed previously (see Zhou and Liu, 2003). Nonetheless, instead of using stochastic simulations, they are developing and employing fuzzy simulations.

Similar with the abovementioned paper, Wen and Imamura (2008) also address LAP with fuzzy demands. For this type of problem, they build a fuzzy -cost model under the Hurwicz criterion. The problem is subsequently solved using the same algorithm as in Zhou and Liu (2007).

The establishment of mixed integer programming optimisation models for multi-period, multi-stage LAPs could be found in Manzini and Gebennini (2008). In their paper, the authors develop optimisation models each for the following classes of multi-period, multi-stage LAPs: (1) single-commodity, multi-period, two-stage LAPs, (2) multi-commodity, multi-period, two-stage LAPs, (3) single-commodity, multi-period, two-stage open/ closed LAPs, and single-commodity, multi-period, three-stage LAPs.

The application of various search methods to a generalised class of LAPs known as multi-facility location problem with generalised objects (MFLPO) is presented by Bischoff and Dächert (2009). The end of the paper gives comparison of the involved search methods for various sizes of test problem.

Research on LAP in health service context could be found in Harper et al. (2005) and Mitropoulos et al. (2006). The former addresses the need to plan health services which takes geographical aspects into consideration. The problem is formulated as a stochastic LAP. The latter paper, on the other hand, develops a bi-objective model to solve the LAP arise in determining the location of hospitals and health centres and the allocation of the patients to those facilities.

2.2.3 Vehicle Routing Problem (VRP)

In its most basic form (e.g. Bulbul et al., 2008; Laporte, 2007), VRP is concerned with the optimal delivery or collection routes for a limited number of identical vehicles with limited capacities from a central depot/ warehouse to a set of geographically scattered customers. It assumes that the vehicles are at the central depot/ warehouse initially. It also requires the existence of the routes that connect the central depot/ warehouse to customers and customers to customers as well. In this type of VRP, a route must start and finish at the depot and a customer is visited by exactly one vehicle. The total demand of customers served by one vehicle could not exceed the vehicle's capacity, and the ultimate goal is to minimise the total routing costs.

Since its introduction by Dantzig and Ramser in 1959 (Bulbul et al., 2008), it has given rise to a rich body of works (Laporte, 2007). In 2008, searching the words vehicle routing problem by using Google scholar search results more than 21,700 entries (Golden et al. (eds), 2008).

Laporte's (1992) paper provides various exact methods and heuristics developed to solve the VRP. Several meta-heuristics intended to solve the classical VRP could be traced from his more recent paper (2007), while Toth and Vigo's (2002) paper presents various existing exact algorithms for the solution of classical VRP. The comparison of descent heuristics, simulated annealing, and tabu search in solving VRP is addressed by Van Breedam (2001). Jozefowiez et al. (2008), on the other hand, give a survey on works that have been carried out on multi-objective VRP.

A range of VRP variants can be seen in Crainic and Laporte (eds., 1998), Bulbul et al. (2008), and Golden et al. (eds., 2008). Other variants also exist: VRP with stochastic demands and VRP with backhaul. Different classification of VRP could be found in Pisinger and Ropke's (2007) paper. The following sub-sections mention examples of works on some of them, while new directions in modelling and algorithms for various types of LRP could be found in Part II of Golden et al.'s (eds., 2008) edited book.

2.2.3.1 VRP with Time Windows

In this type of VRP, customer i may only be visited within a time window [ai, bi] (see, e.g., Kontoravdis & Bard, 1995; Badeau et al., 1997; Bouthillier & Crainic, 2005; Fügenschuh, 2006; Hsu et al., 2007; Kim, et al., 2006; Dondo & Cerdá, 2007; Kallehauge et al., 2007).

2.2.3.2 VRP with Pickup and Delivery

When the vehicles need to deliver commodities to customers and collect items - for example, defective products - from them as well, then this is called a VRP with pickup and deliveries. Research papers by Nagy & Salhi (2005), Wassan et al. (2008), Wassan et al. (2008), Gribkovskaia et al. (2008), Hoff et al. (2009), and Ai & Kachitvichyanukul (2009) are several examples on it.

2.2.3.3 VRP with Backhaul

In this type of VRP, the customers are separated into two mutually exclusive subsets so that the first subset of customers receives commodities whereas the second one sends back the products. Additionally, the second subset of customers are only served after the first one. The first subset is called line-haul customers and the second one is named backhaul customers. The followings are some previous research works on this category of VRP: Goetschalckx and Jacobs-Blecha (1989), Toth and Vigo (1997), Mingozzi et al. (1999), Wade and Salhi (2002), Süral and Bookbinder (2003), Tavakkoli-Moghaddam et al. (2006), Brandão (2006), Ghaziri and Osman (2006), Ropke and Pisinger (2006), Wassan (2007), and Gajpal and Abad (2009).

2.2.3.4 Dynamic VRP

As implied in its name, this class of VRP is concerned with time-varying VRP, within which the problem parameters could change over time (Bulbul et al., 2008). Previous works by Tighe et al. (2004), Branke et al. (2005), Montemanni et al. (2005), Du et al. (2005), Fabri and Recht (2006), Chen and Xu (2006), Hanshar and Ombuki-Berman (2007), and Hvattum et al. (2007), to name a few, could be categorised as dynamic VRP-type papers.

2.2.3.5 Inventory Routing Problem (IRP)

In IRP (Bulbul et al., 2008; Yu et al., 2008), single warehouse/ central depot continuously transport one product to many customers using a given set of vehicles over a planning horizon. The quantity of product that has to be sent to certain customers is led by the inventory level of those customers. Previous works by Yu et al. (2008), Zhao et al. (2008), Savelsbergh and Song (2007, 2008), Chen and Lin (2008), Abdelmaguid et al. (2008), and Raa and Aghezzaf (2009) are some examples of this type of VRP.

2.2.3.6 VRP with Stochastic Demands

In many cases, demands for certain products are characterised by their stochastic nature. The process of determining the optimal delivery or collection routes for this type of demand is called VRP with stochastic demands. The followings are some example of works that have been done on this type of VRP: Dror et al. (1989), Laporte et al. (2002), Teng et al. (2003), Bianchi et al. (2006), Christiansen and Lysgaard (2007), and Haughland et al. (2007).

2.2.4 Location-Routing Problem (LRP)

Considering the general acceptability of the interrelationship between facility location problem and VRP (Nagy & Salhi, 2007: 650) and given a set of candidate depot sites and customer requirements, LRP in its least complex form can be seen as comprising the determination of the depots' location and the routes of the vehicles devoted to serve the customers, in such a way that some constraints, which generally relate to the capacity of depots and vehicles, length and duration of routes, and all the requirements stem from the customers, are met and, at the same time, an objective function which usually incorporates routing costs, vehicle fixed costs, depot fixed costs and depot operating costs, is minimized (Ambrosino & Scutellà, 2005). Regarding this definition, it is reasonable to conclude that LRP addresses some aspects of distribution network design problem ((Ambrosino & Scutellà, 2005; Ambrosino et al., 2009).

Location routing problem can also be seen as a certain type of location analysis (Nagy & Salhi, 2007) which addresses facility location and vehicle routing aspects simultaneously. Different from location-allocation problem which assumes the straight-line or radial journey from the supply centres to the customer locations (Min et al., 1998), LRP necessitates the tours in the journey process from the depot's locations to the customers' sites (Min et al., 1998).

A combined location-routing model has the following general formulae (see Chan, 2005: 210):

Maximize [ (demand coverage) - (depot costs + routing costs)]

Subject to the following constraints:

1. Certain demand sites must be served

2. Intermediate-stop requirements for vehicle routes

3. Route restrictions

4. Depot restrictions

5. Forcing/ linking constraints between location and routing decisions

The decision variables involved are depot-location, routing and demand-allocation variables. All variables are integers with the first two have binary values.

To the best knowledge of the researcher, there are three previous works on classifying LRP. The following sentences will explore those works briefly.

Min et al. (1998) state that the LRP could be viewed from two different edges: (1) by regarding its problem perspective, and (2) by considering its solution method. Table 4 gives detail classification of LRP as proposed by Min et al. (1998).

The second classification of LRP could be found in Chan's (2005) book. According to him, types of LRP are as follows:

1. Single-facility/ single-route/ multi-criteria problem

2. Single-facility/ multi-tour/ allocation problem

3. Single-facility/ multi-tour/probabilistic-demand model

4. Multi-facility/ multi-tour/ allocation model

5. Multi-facility/ multi-tour/ hierarchical model

6. Multi-facility/ multi-route/ multi-criteria/ nested model

Table 4. Classification of LRP as proposed by Min et al. (1998)

Classification of LRP with regard to its problem perspective

Hierarchical level

Single stage

Two stage

Nature of demand/ supply

Deterministic

Stochastic

Number of facilities

Single facility

Multiple facilities

Size of vehicle fleets

Single vehicle

Multiple vehicles

Vehicle capacity

Un-capacitated

Capacitated

Facility capacity

Un-capacitated

Capacitated

Facility layer

Primary

Secondary/ intermediate

Planning horizon

Single period (static)

Multiple period (dynamic)

Time windows

Unspecified time with no deadline

Soft time windows with loose deadlines

Hard time windows with strict deadlines

Objective function

Single objective

Multiple objectives

Type of model data

Hypothetical

Real-world

Classification of LRP in respect with its solution method

Exact algorithm

Direct tree search/ branch and bound

Dynamic programming

Integer programming

Nonlinear programming

Heuristic

Location-allocation-first, routing-second

Routing-first, location-allocation-second

Savings/ insertion

Improvement/ exchange

For more recent classification of various works on LRP, see Nagy and Salhi (2007). The classification is carried out based on the view that facility location problem is the master problem in LRP whereas a vehicle routing problem is viewed as sub-problem. In order to solve the location problem, however, both the location problem and the routing problem need to be worked out simultaneously.

The paper classifies LRP based on the following aspects:

1. Hierarchical structure:

a. Main structure: several facilities servicing a number of customers and being connected to their depot by means of vehicle tours. Routes connecting facilities to each other are not allowed.

b. Other structures: many-to-many LRP, vehicle routing-allocation, multi-level LRP, and road-train routing

2. Type of input data: deterministic or stochastic

3. Planning period: single-period or multi-period

4. Solution method: exact method or heuristic

5. Objective function: overall cost minimisation, multiple objectives

6. Solution space: discrete, network, or continuous

7. Number of depots: single depot, multiple depots

8. Number and types of vehicles: not fixed in advance and homogenous; not fixed in advance and heterogeneous

9. Route structure:

a. Usual: starting out from a depot, passing through a number of customer nodes, sending commodities at each customer nodes, and finally going back to the same depot.

b. Variation 1: instead of traversing through nodes, the vehicles are passing through edges (known as arc routing)

c. Variation 2: Multiple trips are allowed for vehicles

d. Variation 3: Vehicle routes may contain both deliveries and pickups

e. Variation 4 (round-trip location problem): Vehicles start out from a depot, visit a customer to take up some load, deliver it to other customer, and finally go back to the depot.

f. Variation 5 (which is called many-to-many LRP: several customers wish to send commodities to others; assuming inter-hub routes are direct whereas hub-to-customer routes are multi-stop, the problem is to locate a network of hubs - and each of their routes -, taking routing costs into consideration.

The following provides several research papers on LRP after Nagy and Salhi's (2007) work.

Alumur and Kara (2007) propose a multi-objective LRP model for managing hazardous waste materials. The model incorporates two objectives: (1) minimising total costs incurred, and (2) minimising transportation risks. It seeks to respond to the following questions: (1) where to locate treatment facilities and with which technologies, (2) where is the appropriate location of disposal centres need to open, (3) how to send different sorts of hazardous waste to which of the appropriate technologies, and (4) how to ship waste residues to disposal centres.

The development of a decision-support tool for a capacitated LRP can be found in Lopes et al. (2008). The tool seeks to determine which depots with certain capacities must be built and to find out the distribution routes from these depots to the customers with certain demands. Its objective is total cost minimisation, whereas distance between locations is in Eucledian form.

Ambrosino et al.'s (2009) paper deals with a distribution network design problem that involves decisions on location, fleet assignment, and routing. Characterised by one central depot, a set of customers clustered into regions, and a heterogeneous fleet vehicles, the problem is solved in order to find out the following: (1) the location of one regional depot in each region, (2) the vehicles' assignment to each region, and (3) the vehicle routes, each starting and ending at the central depot. This is carried out with regard to the following requirements: (1) the regional depot in each region is visited once by the vehicles allocated to that region, (2) the vehicle capacities are not exceeded, and (3) the customer demands are met. The objective is to minimise the overall distribution costs. In order to achieve the aforementioned objective, the authors develop a two-phase heuristics. An initial feasible solution is determined at phase I, whereas phase II is intended to improve the solution.

2.3 Some Previous Works Related with Disaster Management

This part will give focus on some previous works on several areas related to disaster management. They include research on performance measurement and several works on disaster modelling and optimisation. Logistical aspects of disaster management - the most relevant area of research to that of the author's - are explored and put in sub-section 2.4. Disaster response - within which the current research takes the position - is explained in sub-section 2.5.

It should be noted that other disaster-related areas of works - such as research on how the casualties perceive the disasters they suffer from - also exist. Regarding their less relevance with the proposed research undertaken by the author, these types of research are excluded from further review.

2.3.1 Some Works on Performance Measurement in Disaster Management

In the sense of measuring the logistical performance of disaster management, Davidson (2006) develops four criteria which measure logistic performance of disaster management:

1. Appeal coverage which consists of percent of appeal coverage (refers to the number of items that have been committed by donors out of the total quantity of items requested for the operation) and percent of items delivered (which is further defined as the percentage of items that have been delivered on-site actually out of the total quantity of items requested for the operation);

2. Donation-to-delivery time which constitutes time length for an item to be delivered to the destination country after a donor has committed to donate that item;

3. Financial efficiency which comprises three metrics: (1) a comparison between the budgeted prices and the actual prices for items delivered in the operation using a relative method, (2) an absolute method to compare the budgeted prices to the actual prices for items delivered in the operation, and (3) the transportation cost of transferring the relief to the recipients;

4. Assessment accuracy which shows how much the operation's final budget changed over time from the original budget.

Still in the scope of performance measurement of humanitarian logistics, Beamon and Balcik (2008) propose a relief chain metrics which comprises three main metrics: (1) resource metrics with the goal of high level of efficiency, (2) output metrics with the goal of high level of effectiveness, and (3) flexibility metrics with ability to respond to a changing environment as its goal. Performance measurement in community participation and empowerment, performance measurement in community development, performance measurement in the combined relief and development mission, and understanding the role and effects of cooperation and coordination in the relief chain are said as future work in the context of relief chain performance measurement.

2.3.2 Some Previous Works related with Disaster Modelling and/ or Optimisation

Esogbue (1996) gives various roles of fuzzy approach in addressing disaster-related problems. He feels that fuzzy set theory could systematically and substantially assist proper evaluation of such descriptors as ‘high stimulation', ‘little or none', and ‘doubtful', etc. This is also the case with the evaluation of damages or costs of disasters, especially when this evaluation need to be achieved rather quickly as is usually the case in the chaotic and painful moments immediately following the disasters. To address this problem, the author proposes fuzzy mathematical models of the disaster control problem, which consist of two versions. In version 1, the problem is posed as a multistage decision making problem in a fuzzy environment with the system under control represented as a conditioned fuzzy set which is represented via its membership function. Similarly, the controls, constraints and systems dynamics are all expressed in terms of their membership functions. The model has three fuzzy goals, different for each measure, and three fuzzy constraints, as well as a fuzzy initial system state. Each of these is expressed in terms of their membership functions. Version 2, on the other hand, has two components: (1) the core, and (2) the expanded models. While the algorithm built in the later version has three levels: the regional, national and a model for coordination.

The evaluation of military, non-military and composite models in responding a particular disaster or emergency is found in Pettit and Beresford's (2005) paper. Started by providing phases of disaster management, the middle part of the paper presents key issues appear in each phase, the strengths and weaknesses of available transportation and distribution modes in disaster relief, and the roles of military in relief logistics. This part is followed by an exploration on some existing disaster relief models and a composite model proposed by the authors. Information and data needed are obtained primarily by applying a stratified Delphi study with 45 participants. Other resources are based on previous related research carried out by the authors.

Considering the deficiencies of current US emergency management systems, Tovia (2007) develops an Emergency Response Model (ERM) which is intended as an aid in the following: (1) Evaluating response capabilities of particular emergency management agencies, (2) Assessing logistics challenges in the presence of natural disaster, and (3) Conducting what-if analysis on the threat of a weather disturbance system. To build the ERM, she firstly defines the mechanisms and coordination that must exist among different emergency agencies in the presence of a natural disaster. Secondly, the author describes the logistics - in terms of activities and time frame - that have to be implemented. Finally, a simulation model is developed in order to enable the evaluation on the effectiveness of existing emergency management systems relative to the proposed systems. Having a conclusion of insufficiency of the existing operating policies and available resources, the author encourages the use of school bus systems and residential shelters as well as alternative solutions to evacuate and cover the population promptly.

Research on modelling and optimising the evacuation process could be found in Chien and Korikanthimath (2007). By regarding the importance of evacuating people and/ or goods in densely populated areas immediately after a disaster occurs, the authors develop a model of simultaneous and staged emergency evacuations. With the objectives of minimising evacuation time and delay as well, the developed model is intended to determine the optimum values of decision variables - including the number and sizes of staged zones - which minimise the stated objectives.

It is generally accepted that, following the occurrence of a natural disaster, the damage of infrastructures - including roadways - is most likely to happen. It needs restoration actions to be performed. Regarding the need to repair the damaged roadway networks in rural fields resulted from a major disaster, Yan and Shih (2008) formulate a multi-objective, mixed-integer, multi-commodity network flow problem model. This effort is preceded by developing an emergency repair time-space network as well as a relief distribution time-space network. To obtain the solution for the problem formulation, the authors develop a heuristic algorithm which is then computed using CPLEX.

2.4 Previous Works on Logistics in Disaster Management

Research dealing with the logistical aspects of disaster management are challenging (Sheu, 2007a) and showing a growing . Generally, they could be classified into the following: (1) research on inventory problems in disaster context; (2) research on relief distribution problems; (3) research on evacuation process routing problems; (4) research on facility location problems; (5) research on location-allocation problems; (6) research on relief distribution and evacuation process routing problems; and (7) research on location-routing problems.

2.4.1 Research on Inventory Problems in Disaster Context

Beamon and Kotleba's (2006) research paper builds a stochastic inventory mathematical model in the presence of complex emergencies in South Sudan relief effort context. The proposed inventory model is intended to optimize the reorder quantity and reorder level by using reordering, holding and back-order costs as bases.

Issues in managing disaster relief inventories are discussed in Whybark's (2007) paper. Based on terms of acquisition, storage, and distribution, the author explores the characteristics of disaster relief inventories relative to enterprise inventories. In the end of the paper, he proposes several disaster relief inventories-related research agenda for the future.

The inventory control problem that comes up as a hurricane takes place with the availability of wind speed information updates is addressed by Lodree Jr. and Taskin (2009). With the possibility of predicting hurricane characteristics more accurately during the later stages of planning horizon relative to that at the earlier phases, the authors formulate the inventory control problem following the presence of a hurricane as an optimal stopping problem with Bayesian wind speed information updates. A dynamic programming algorithm is then proposed to solve the problem. Demonstration of the proposed algorithm on real hurricane historical data from the HURDAT database is provided afterward.

2.4.2 Research on Relief Distribution Problems

Preceded by the statement that “The basic underlying logistical problem for disaster relief management is to move a number of different commodities using a number of different modes of transportation, from a number of origins to one or more destinations over a transportation network in a timely manner effectively and efficiently” (Haghani & Oh, 1996: 231-232) which is a multi-commodity, multi-modal network flow problem with time windows (pp. 232), Haghani and Oh's (1996) paper aims at developing a decision making tool which can potentially be used by emergency response managers in planning for disaster relief operations. Specially, the paper is concerned with “the problem of determining the detailed routing and scheduling of the available transportation modes, delivery schedules of the various commodities at their destinations, and the load plans for each of the transportation modes” (pp. 232). Its ultimate goal is to create a decision support system which can be employed by the Federal and State authorities of USA in emergency response management. Indeed, such planning tools did not exist at the time of the paper writing. They formulate a single objective mixed integer programming with two different solution procedures: (1) Algorithm I, which decomposes the model into sub-problems based on the relaxation of linkage constraints to exploit the special structure of the model, and (2) Algorithm II, which fixes integer variables gradually at every iteration until all integer variables are fixed to integer values. The model development is made based on certain assumptions, as follows: (1) Transfer is only allowed at the origin nodes that also have a role of transhipment nodes and at the trans-shipment nodes, (2) All the cost functions are linearly assumed, (3) All the product quantities at supply and demand nodes are known, (4) Vehicles can be recycled, (5) A number of different modes are available, (6) An average size vehicle is assumed for each mode, and (7) Mode shift is allowed. The paper is ended by giving future research directions, as follows: (1) Non-linear cost functions in the model formulation which are dependent on flows can be explored to represent the model more realistically. Hence, they suggested to develop innovative solution procedures for such a model, (2) The need for introducing uncertainties into the model, (3) A need to accelerate the current solution procedures to be used in the real-world operation, for instance, by using faster computer and other powerful LP software such as CPLEX, and (4) A need to improve the solution Algorithm I using the solution from Algorithm II as a bound.

Similar with Haghani and Oh's paper is the paper of Oh and Haghani (1997). The difference is on its emphasis, which the latter gives emphasis on testing and evaluation of the proposed model.

Regarding the occurrence of famine, Hwang (1999) proposes a distribution model to deal with complex vehicle routing problems incorporating inventory assignment and optimal distribution of foods. The objective incorporated is of minimising the amount of pains and starving. In order to achieve the objective, the author develops three sub-models: optimal inventory allocation (incorporating the determination of optimal distribution patterns, the minimisation of total number of pains and starving, and the minimisation of the total travel distance and time); distribution sector-clustering (consisting of sector-clustering of each supply point by taking the capacities of supply centres and vehicles into consideration); and vehicle routing-scheduling.

The use of helicopter logistics in disaster relief operations is proposed by Barbarosoğlu et al. (2002). Situation tackled in this paper is as follows:

1. Once an emergency signal is received, the response mobilization is started by calling for different helicopters from air force bases to a single operation base where all logistical actions are coordinated and controlled;

2. The mobilization of logistical resources in a mission covers both tactical and operational decisions:

a. D1: the determination of the helicopter fleet composition by assigning helicopters from the air force bases to the operation base;

b. D2: the allocation of pilots with given aviation capabilities to the helicopters;

c. D3: the determination of the number of trips to be undertaken by each helicopter;

d. D4: the vehicle routing of helicopters from the operation base to disaster points in the emergency region;

e. D5: the load/unload, delivery, transhipment and rescue plans of each helicopter in every trip;

f. D6: the re-fuelling schedule of each helicopter at the operation base

The problem includes the covering problem, trans-shipment problem, and the multi-commodity, multi-modal network flow problem with multiple trips and partial services. To overcome the problem, the authors develop the following mathematical models for scheduling helicopter activities in a disaster relief operation: (1) a mixed integer mathematical program model at top level (phase I), which basically deals with tactical decisions and covers D1, D2, and D3. It aims at minimizing a qualitative measure of preferences; and (2) a base level model in the form of vehicle routing of helicopters from the operation base to disaster nodes in the emergency region, the load/unload, delivery, transhipment and rescue plans of each helicopter in each tour, and the re-fuelling schedule of each helicopter given them solution of the top level. The aim of this model is minimizing the make-span.

To enable the information exchange between phase I and phase II, an iterative coordination heuristics is used. The paper ends up with several suggestions regarding the future enhancements, as follows: (1) The development of efficient solution procedures for both sub-problems, (2) The development to link both sub-problems to a database system, and (3) The implementation of a desirable user-interface. This will subsequently lead to an intelligent decision support system which includes human assessment and knowledge accompanied by a strong backbone of optimization algorithms.

Özdamar et al. (2004) develop a planning model that is to be integrated into a natural disaster logistics decision support system. The problem addressed in their paper is a hybridisation of the multi-commodity network flow problem and the vehicle routing problem. It is subsequently converted into a mixed integer multi-period multi-commodity network flow problem wherein the integer part represents the vehicles. The mathematical model developed for this problem is then decomposed into two multi-commodity network flow problems, the first one being linear and for conventional commodities and the last one being integer and for vehicle flows. In the solution approach, these two sub-models are then coupled with relaxed arc capacity constraints using Lagrangean relaxation.

The transportation planning of crucial first-aid supplies as well as emergency team to disaster-affected regions is performed by Barbarasoğlu and Arda (2004). Considering the stochastic nature of demand, supply, and route capacity as well, they treat the problem as a probabilistic, multi-commodity, multi-modal network flow problem using a two-stage stochastic programming.

In order to design 3-layer relief delivery systems in a real case, Tzeng et al. (2007) construct a relief-distribution model using a fuzzy multi-objective programming method. The model consists of three objectives: minimizing the total cost, minimizing the total travel time, and maximizing the satisfaction during the planning period. Mathematical model developed is then applied to a real case and further analyzed using LINGO software.

Sheu (2007b) proposes a hybrid fuzzy clustering-optimization approach to the operation of 3-layer emergency logistics co-distribution (relief suppliers, urgent relief distribution centre, and relief-demanding area). It is aimed to respond to the urgent relief demands during the crucial rescue period (initial 3 days) right after the happening of a serious natural disaster. The model comprises two recursive mechanisms: (1) the grouping of disaster-affected area, and (2) relief co-distribution. The model formulated is based on the following assumptions: (1) The quantity of affected regions (denoted by I) and the corresponding geographic relationships are known, (2) The relief supply channels including the corresponding supply points and URDC (urgent relief distribution centre) are given, (3) The updated information regarding disaster-induced damage conditions and sufferers associated with each affected region can be acquired during the crucial rescue period, (4) The time-varying relief demand needed in a given affected region is greatly correlated with the quantity of corresponding local survivals, and (5) Different types of relief are allowed to be loaded in a vehicle to serve the affected areas. Correspondingly, each vehicle is permitted to load with multiple types of relief in any given relief distribution mission. The paper is summed up by providing the potentials for getting better the operations performance in emergency logistics distribution, by suggesting the following to do: (1) Putting together more detailed emergency logistics resource allocation methodologies and vehicle dispatching strategies, (2) The provision of real-time and accurate information in the sense of survivals and disaster-induced damage conditions in traffic networks is needed so as to update the time-varying relief demands and adjust the relief distribution priority in the operations of quick-responsive emergency logistics distribution, and (3) Expanding the current study scope and methodology to the international emergency logistics domain

Three different goals in the sense of obtaining effectiveness, pursuing economic values, and maximising the satisfaction of affected areas in three-layer emergency relief distribution are proposed by Liu and Zhao (2007). These three different goals are presented as a composite weighted multi-objective approach for emergency logistics distribution under consideration. A numerical example related to an earthquake happened in Nanjing, China, is subsequently presented.

Research on last mile distribution in humanitarian relief could be found in Balcik et al. (2008). In order to handle the problems of assigning the relief supplies from local distribution centres (LDCs) to a variety of demand points as well as resolving delivery schedules/ routes for vehicles through the planning horizon, the authors propose a mixed integer programming model of which objectives are the minimization of transportation costs and the maximization of benefits to aid recipients. Regarding the higher complexity in more complex problems, they also develop heuristic algorithms that - as they expect - will give good solutions to their current last mile distribution problem.

Hsueh et al. (2008) propose a model formulation for dynamic vehicle routing problem for relief logistics in natural disasters (DVRP-RL). The formulation of the DVRP-RL is in the form of a mixed integer programming model sequential taking place in the continuing time horizon.

An effort to optimize resource allocation for emergency response (particularly during the search and rescue (SAR) period)) is performed by Friedrich et al. (2000). They try to find out the best allocation of available resources to operational areas at the initial SAR period after strong earthquakes by developing a dynamic combinatorial optimization model with minimising the total number of fatalities during this period as the goal function, which is then resolved by using simulated annealing and tabu search as solution methods in C++.

Gong and Batta (2007) develop models on ambulance allocation and reallocation for a post-disaster relief operation. Initially focuses on allocating the correct number of needed ambulances to each casualty groups at the early stage of the evacuation process, they further investigate the reallocation of ambulances between casualty groups as the disaster progressed.

The use of data fusion in developing a robust methodology for the dispatching and routing of emergency transportation in disaster mitigation context is performed by Jotshi et al. (2008). Regarding a large amount of information in terms of casualties, road, traffic conditions, etc., the data fusion aimed at providing estimates of the entities under consideration is needed. The fusion resulted is then used to transmit and direct emergency vehicles (EVs) to the location of the victims. It is also used to transfer the victims to the hospitals.

A decision support, namely ARES, is introduced by Brown and Vassiliou (1993). It has the following features: (1) Decision support simulator acts as a coordinating program between user and various system and data components; (2) Operational assignment model (IP) is an integer program. It finds good aggregate assignments of tasks to units without explicit consideration of unit relocation, (3) Operational assignment model (IPL) is an integer program. Different from IP model, it finds good movements of units to locations from which they will be assigned good aggregate groups of tasks to perform, and (4) Tactical allocation model (GNk) is a linear program which functions to allocate resources to the tasks assigned to unit k.

2.4.3 Research on Facility Location Problems

This category of research could be further broken down into four types of research papers: (1) research on the location of casualty collection points; (2) research on location and/ or allocation of shelters/ temporary housing/ other public facilities; (3) research on distribution centre location; (4) research on transfer point location.

The determination of casualty collection points (CCPs) locations in cases of disaster occurrences situated by the infrastructure damages (freeway, roads, emergency medical services, etc) is performed by Drezner (2004) and Drezner et al. (2006), respectively. In these CCPs, emergency medical attention is given to the victims. Both papers assume that the victims have to go to these CCPs by their own. It is also assumed that hospitals might themselves become the casualties or be overwhelmed by patients otherwise. At the same time, the transportation service of medical facilities to the hospitals is assumed to probably be inhibited, unavailable, or not operational due to the damage to some main roadways.

Researchers also pay attention to location and/ or allocation of either shelters or temporary housing or other public facilities. The following few paragraphs provide previous research on this aspect.

Sherali et al. (1991) formulate a non-linear mixed-integer programming model to represent the selection of a set of candidate shelters from a given set of alternatives and the allocation of disaster's victims to those selected shelters. The proposed model also incorporates an extraneous flow of evacuees not using the selected shelters as destinations. To solve the proposed mathematical model, the authors develop a heuristic and an exact implicit enumeration algorithm which is based on Benders decomposition method. To test the proposed model as well as the developed problem solving tools, they employ a set of realistic test problems consisting of 74 total nodes with 9 source nodes, 15 nodes acting as shelter location alternatives, and 118 arcs.

The allocation of disaster shelters by employing geographic information system (GIS) in combination with fuzzy models is conducted by Tsai et al. (2008). In their paper, Takagi-Sugeno (T-S) fuzzy model is used to cope with GIS fuzzy data. An example of the applicability of the proposed model is given in the last part of the paper.

Chowdhury et al.'s (1998) paper, on the other hand, is concerned with a cyclone shelter planning for the vulnerable-from-floods coastal areas in Bangladesh. To deal with the problem of giving shelter protection to the residents, the authors develop various multi-objective mathematical programming models which search for the optimum allocation of shelters to various planning units under a specified budget.

Like Chowdhury et al.'s paper, research conducted by EL-Anwar et al. (2008) also applies a multi-objective optimisation technique. It seeks to find out the optimum allocation of temporary housing for the victims of Northridge earthquake. The objectives incorporated are the minimisation of socioeconomic disruption, the maximisation of temporary housing safety, the minimisation of environmental impact, and the minimisation of public expenditures, respectively.

By taking risks of inundation imposed by tsunami into account, Doerner et al. (2009) propose a multi-objective mathematical programming approach to determine the optimum location of public facilities in tsunami-vulnerable coastal areas. As solution approaches, they develop a heuristic and a decomposition technique as well. Both approaches are subsequently tested on two different cases located in the district of Galle, southern Sri Lanka.

Distribution centre location is another aspect of disaster logistics. The subsequent paragraphs provide a review on some previous works on it.

Effort to find out the quantity and locations of distribution centres and the total quantity of relief supplies to be kept at each distribution centre in a humanitarian relief network is conducted by Balcik and Beamon (2008). For these purposes, they develop a maximal-covering-location-variant model. Their model is characterized by the following features: (1) putting together facility location and inventory decisions, (2) incorporating multiple types of commodities, and (3) considering budgetary constraints and capacity limitations as well. At the end of the paper, they suggest to extend their proposed model by focusing on the development of more sophisticated inventory policies for relief aids responding to sudden-onset disasters. As they suggest, it could be conducted by using real data instead of estimates for some parameters and by developing heuristics approaches for similar problems with larger sizes.

Different from the aforesaid paper, Jia et al. (2007) propose three different models of emergency medical service (EMS) facility location-allocation in the context of large-scale emergencies. Each model is claimed as suitable for maximal covering problems, P-median problems, and P-centre problems, respectively. By using three different cases of large-scale emergencies for each of the aforementioned type of problems, the authors come to conclusion that the proposed models perform better than those of traditional ones.

Flood emergency of which main characteristics is uncertainties in term of its rescue demand is studied by Chang et al. (2007). More specifically, they put attention to a scenario planning for the problem of flood emergency logistics preparation. Preceded by building the structure of rescue organization and distribution, they subsequently develop two types of models: (1) the grouping and classifying model and (2) the two-stage stochastic programming location-distribution model. The former aims to group the disaster rescue regions and classify their level of importance, whereas the latter is intended to threefold: (a) to decide which selected rescue regions need to be set up after the happening of floods, (b) to determine the total amount of available rescue equipments in the warehouses of all levels, and (c) to find out the plans for distributing those equipments. The inputs for the latter model come from the outputs of the first one. The locations of demand points and the total rescue equipments needed under different rainfall scenarios are estimated by applying geographic information system (GIS) method. The result of this step is then used to determine the quantities of rescue equipment for each demand point under various flooding scenarios. To overcome both mathematical models the authors employ the sample average approximation (SAA) scheme.

The determination of a pre-positioning network configuration for CARE International (a humanitarian organisation) is found in Duran et al (2009). (Humanitarian pre-positioning itself can be defined as the locations of inventory at or near the disaster location; see Ukkusuri & Yushimito, 2008: 18). With the objective of enhancing CARE's ability to deal with fast-onset disasters, the authors propose a mixed-integer programming (MIP) inventory location model. The allocation of particular regional demand to certain inventory is also addressed in the model. To verify the model robustness, a sensitivity analysis is performed subsequently.

Another location-type of research in disaster logistics is that on transfer point location. In this case, a transfer point is a place to which ‘goods' (including the victims of certain disasters) need to be transported from the demand points and from which they subsequently have to be sent to certain facility location(s). Previous works by Berman et al. (2007, 2008) fall into this type. By considering the p-median case, p-centre case, and maximal covering case, respectively, they develop a transfer point location problem (TPLP) model in the first paper and a multiple TPLP model in the second paper. The former paper is concerned with the problem of finding the optimal location of a transfer point given the facility location (for instance, a hospital) as well as the set of points need to be connected to that facility (for example, casualty points). The extended version of the model which deals with multiple locations of transfer points is proposed in the latter paper.

2.4.4 Research on Evacuation Process Routing Problems

In term of disaster-induced evacuation characteristics, Chiu and Zheng (2007) propose two categories: short-notice and no-notice disasters. Furthermore, their paper presents a model formulation and solution for simultaneous mobilization destination, traffic assignment, and departure schedule for multi-priority groups (SMDTS-MPG in short) intended for real-time emergency situation in no-notice disaster context. To tackle this type of problem, they formulate a cell transmission model (CTM)-based linear programming model which is subsequently transformed into matrix form in order to enable the model applicable for other similar problems with larger networks.

The problem of evacuation planning in an emergency situation can also be found in Saadatseresht et al.'s (2008) paper. They develop a three-step approach for evacuation planning: safe area assignment, optimum path discovery, and the selection of optimal safe areas for each building block. They declare that the third step is a kind of spatial multi-objective programming (MOP). By combining this third step with multi-objective evolutionary algorithms (MOEA) and the GIS technique as solution methods, they further conclude that the spatial MOP can assist the process of evacuation planning in the form of finding an appropriate way for allocating the fatalities to the safe areas.

Considering the panicky of the people in a disaster situation, Yuan and Wang (2008) develop a single-objective path selection model as well as a multi-objective one. The former is then solved by applying a modified version of Dijkstra algorithm, whilst an ant colony optimization algorithm is chosen to solve the latter. At the end of the paper, they plan to build a model which takes more actual factors into consideration.

The determination of rescue path in the presence of uncertainties following the occurrence of a disaster is addressed by Chiou and Lai (2008). They offer an integrated multi-objective mathematical programming model which contains three sub-models: rescue shortest path model (which is solved by employing Azevedo's algorithm on finding the K-shortest path), post-disaster traffic assignment model (which is overcame by using Frank-Wolfe method), and traffic controlled arcs selection model (which is resolved by applying a genetic algorithm). Since these three sub-problems are inter-related, they are subsequently integrated and solved simultaneously. To demonstrate the applicability of the model, the authors use the case of Chi-Chi earthquake in Taiwan as a computational experiment. The application shows the efficiency of the proposed model in terms of reducing the impacts on the ordinary trips and the quantity of police officers needed in traffic control enforcement, respectively.

Two papers of Lu et al. (2003, 2005) deal with the development of a capacity constrained routing in evacuation planning context. These two papers point out the lack of previous optimal methods in terms of computational complexity and its possibility to be absent from scalability to large transportation networks. They also criticise previous heuristic approaches as neglecting the capacity constraints of the evacuation networks and its likeliness to give infeasible solutions. With the weaknesses of both approaches, the authors propose time series-modelled capacity constrained heuristic routing approach to overcome the evacuation planning problem. Despite the latter paper could be seen as giving better result compared with the former one, it is still declared as having the following limitations: (1) it neglects the fact that maximum capacity of an edge probably depends on the traffic flow amount of that edge, and (2) it requires that the arc travel time reflects traffic delays at intersections; in other words, traffic delays at intersections are not treated separately.

For certain evacuation practices, the evacuees could choose their evacuation routes despite the existence of a set of optimal-system evacuation paths recommended by evacuation management agencies. In order to improve the performance of evacuation systems in such situations, Chiu and Mirchandani (2008) propose an evacuees' behaviour-based feedback information routing (FIR) strategy.

The incorporation of evacuation routes, vehicle capacities, and delay/ preparation time for each type of vehicles into the evacuation route planning optimisation after flash flood occurrences is addressed by Yusoff et al. (2008). To cope with this situation, the authors develop an algorithm namely vehicle priority selection (VPS) which requires the presence of the following: (1) A transportation network with source node, intermediate nodes, destination nodes, and arcs/ edges, (2) Source node comprises the number of evacuees and various type of available vehicles with certain capacities, (3) Information contained in destination nodes is their locations and maximum capacities, (4) Each directed arc is signified by its distance and travelling time needed for each type of vehicles. It should be noted, however, that the scalability of this algorithm to larger networks has not already been explored.

The inclusion of congestion and time delays on road links in the context of multi-objective evacuation routing in transportation networks is investigated by Stepanov and Smith (2009). To cope with optimal route assignment, the authors develop an integer programming formulation, whereas M/G/c/c state-dependent queuing models are used to handle congestion and time delays on road networks. They incorporate total travel distance, clearance time and blocking probabilities/ congestion level as performance measures of the proposed plan. Using the 1st shortest evacuation routes policy as a benchmark, the performance of the proposed approach is subsequently evaluated by using simulation approach. The comparison of these two approaches leads to the conclusion that the proposed method has a higher performance in terms of congestion level as well as clearance time despite its lower level of performance in respect with the total travelled distance.

2.4.5 Research on Relief Distribution and Evacuation Process Routing Problems

This research paper category deals with the simultaneous optimisation process of relief delivery and evacuation routing. As long as the author knows, there are three previous works on this category to date.

Yi and Kumar (2007) propose an ant colony optimization (ACO)-based meta-heuristics for solving the multi-commodity dispatch and victim evacuation problem arising in disaster relief activities. This paper could be seen as a dynamic VRP-type. In this paper, the original emergency logistics problem is decomposed into two phases of decision making, i.e. the vehicle route construction and the multi-commodity dispatch. The first phase builds stochastic vehicle paths under the guidance of pheromone trails while a successive maximum flow (SMF) algorithm is developed in the second phase for the products dispatch to various types of vehicle flows. Both sub-problems are solved in an iterative manner. The solution is then compared with the model solution produced by CPLEX using solution quality and computational time as the criteria.

Regarding the problem of delivering multi-commodity relief from supply points to the victims in affected areas and evacuating the wounded people from affected areas to medical centres, Özdamar and Yi (2008) propose a heuristics named path-builder. It is based on a greedy l-neighbourhood search method. The author further test the method's performance on 28 test problems which is generated randomly and is built on grid networks with integer arc travel times using CPLEX 7.5 and visual C++ as well. Based on this test, the authors come to conclusion that the solution quality might be acceptable in a continuous uncertainty-and-high information dynamics-surrounded environment.

The incorporation of fuzzy approach on similar problem of those in Yi and Kumar (2007) and Özdamar and Yi (2008) could be found in Yi and Özdamar (2009). Concerning the impreciseness of demand, supply, wounded people and hospital service level, the authors propose fuzzy approach to deal with parameters related to those aspects.

2.4.6 Research on Location-Routing Problems (LRPs)

Researches on this type of problem are not much. To the best knowledge of the researcher, there are only four papers on LRP in disaster logistics.

Commodities dispatch, evacuation and transfer of injured people to emergency units, selection of locations for temporary emergency centres and shelters in the affected regions, and an optimal medical personnel allocation on both temporary and permanent emergency units in nearby hospitals might take place simultaneously in logistics planning in disaster response activities. To overcome this type of problem, Yi and Özdamar (2007) develop a two-stage mixed integer multi-commodity network flow model. This model treats vehicles as integer commodity flows rather than binary variables in the first stage. In the second stage, a vehicle splitting algorithm that converts integer vehicle flows into binary vehicle routes is employed at first. It is further succeeded by solving a set of linear equations to assign a loading/ unloading schedule to each such journey. At the end of the second stage, detailed vehicle instructions are obtained. In the paper, the proposed procedure is then compared with the VRP based single-stage model built for the same problem. By using model size, number of binary/ integer variables, number of constraints, computation time, and iteration count as the criteria, the proposed model shows its dominance.

Mete and Zabinsky (2009), on the other hand, propose the use of stochastic programming (SP) approach and mixed integer programming (MIP) approach, respectively, to deal with the determination of medical supply location and distribution. Locations of medical supply and their inventory levels as well as aggregate transportation plans of medical supplies are determined by applying a two-stage SP, whereas detailed loading and routing of vehicles to deliver medical supplies to hospitals are obtained by employing an MIP approach.

Different from those two previous works, Ukkusuri and Yushimito (2008) are concerned with the humanitarian prepositioning problem. Regarding the need to provide critical goods to the victims after disaster occurrences, they propose the use of LRP to find out the optimal locations for pre-locating disaster relief materials. In their model, the reliability of available paths is taken into account. The model also assumes that the probability of path failure is independent to each other. The objective is to select the locations to pre-locate inventory under a possible disaster in such a way that the likelihood of the inventory achieving all demand points is maximised.

Han and Guan (2007), on the other hand, deal with the optimal supply location selection and routing for emergency material delivery. In the model built for the problem under study, every supply point is able to send a commodity to any customer. The traffic jam caused by heavy traffic is also included in the model.

2.5 Disaster Response as Part of Disaster Management

As previously mentioned, disaster response is a part of disaster management. It could be defined as the employment of a set of measures during the initial occurrence of certain disastrous events, including those to save casualties' lives and prevent further property damage (Barbarasoğlu & Arda, 2004). According to Tierney et al. (2001), disaster response also includes such measures taken a short period prior to and during disaster occurrences.

Disaster response is usually performed under disaster response plan which has previously already been determined (Altay & Green III, 2006). It incorporates the evacuation process of threaten populations (Altay & Green III, 2006; Yi & Kumar, 2007; Chiu & Mirchandani, 2008; Tierney et al., 2001), logistics support (Yi & Kumar, 2007; Yi & Özdamar, 2007; Özdamar & Yi, 2008), and fatality management (Altay & Green III, 2006), to name a few.

Logistics support in disaster response could take various forms. Some of them are the activation of emergency operations centre, the establishment of shelters and the provision of mass care service, and the provision of emergency rescue and medical care service (Altay & Green III, 2006; Tierney et al. 2001; Brandeau et al., 2009).

Despite the evolving focus from disaster response to disaster risk reduction in recent years (see, for example, Tompkins et al., 2008), disaster response is recognised as still having a vital role (see, for instance, Brandeau et al., 2009). The presence of certain disasters that hard to predict (such as earthquake) or happen enormously (such as tsunami or hurricane) suggests that the role of disaster response is even more obvious (see, e.g., Liang et al., 2001; Tolentino Jr., 2007; Klein & Nagel, 2007).