An agent-based model for resource allocation during relief distribution Open Access

Humanitarian assistance providers face several bottlenecks in distributing relief (e.g. water, food, and shelter) to the right person, at the right time, and at the right cost. The major challenge in achieving the goals of humanitarian logistics (HL) is the mismatch between demand and supply and resource management (i.e. transportation, warehouses). Prepositioning, which refers to the storage of inventory at or near the location where it will be used, has been suggested as a possible logistics strategy for minimizing the gap between supply and demand in the aftermath of a disaster (Pan American Health Organization (PAHO), 2001; Thomas, 2003). In contrast, transportation management after a disaster is often conducted on an ad hoc basis. PAHO (2001) recommends contracting fleet management for the transportation of relief goods.

HL consist of several actors/agents, and the conflicts among the stakeholders of a relief chain place additional stress on limited resources. Typically, no single stakeholder of HL has sufficient resources to respond effectively to a major disaster (Bui et al., 2000). Therefore, stakeholders must depend on each other even though they may have different interests, mandates, capacities, and logistics expertise (Balcik et al., 2010).

In investigating the various interests of stakeholders, we first present the mandates of various aid organizations. For example, Oxfam focusses on water distribution and sanitation, the United Nations High Commissioner for Refugees (UNHCR) and the International Federation of Red Cross and Red Crescent (IFRC) focus on shelter, and the World Food Program (WFP) focusses on food. Furthermore, while United Nations Children’s Fund (UNICEF) and Save the Children focus on children (Kovacs and Spens, 2009), WFP (and many other aid organizations) does not have a particular interest in a beneficiaries group. Although these organizations have entirely different targets, their common aim is to reach more victims impartially.

On the other hand, logistics providers also play an important role in relief distribution by providing services outside of their regular service area, and they generally aim to reduce transport-related costs. Logistics providers may also have their own preference; for example, during the relief efforts after Hurricane Katrina, many of the vehicles and drivers who were expected to distribute relief supplies abandoned New Orleans after hearing reports of violence (Holguín-Veras et al., 2007). To enable coordination among the different agencies, the United Nations Joint Logistics Centre (UNJLC) was formed in 2002 as an umbrella organization to handle operational logistics in the disaster relief environment and to encourage the best use of limited logistics resources (Kaatrud et al., 2003).

As a hypothetical example, consider a large-scale earthquake that has caused varying degrees of damage in different areas. This disaster generates enormous relief demand in a given condition of limited resources. The coordinator faces difficulties in allocating available relief because of resource constraints. We propose a model for assisting logistics coordinators in allocating resources in different zones based on the stakeholders’ interests. In this study, this problem is called resource allocation. This study presents a fleet allocation model that considers multiple stakeholders who attempt to maximize their own interests after a large-scale disaster. We adopt the framework of an agent-based model (ABM) to integrate the various HL stakeholders. The ABM is a popular approach in modeling decision-making systems because it allows flexibility in representing various parameters in a dynamic environment. The ABM easily adapts to changes in the environment because it allows changes in the behavior of a system with minimum influence on the processes happening in that system. Therefore, this framework is highly suitable for dynamic situations.

This study presents an ABM for fleet allocation across various zones after a large-scale disaster. The model has several distinctive features compared to existing research. First, the proposed model is capable of assigning each function to a particular agent in HL. The functionality and relationship among HL stakeholders is complex, and not well documented in the literature. Therefore, we explore the ontology of stakeholders in HL. It shows that aid organization and carrier have significant roles in relief distribution. Second, we also propose a decomposition approach to solve the fleet allocation problem. This approach groups the demand points and makes the computation tractable. Finally, we propose a novel approach for measuring the logistics performance. Besides contributing to the progress of HL modeling, the paper can be helpful for aid organizations in making decisions on transport contract. Herewith, the model is beneficial for relief distribution coordinator for selecting distribution policies.

The remainder of the paper is structured as follows. A review of the literature on resource allocation is presented in Section 2. In Section 3, we explain the task chains and explore the stakeholders’ interest. This section also presents the architecture of ABM for coordinated relief distribution and deployment strategies. Section 4 presents a numerical analysis of the Great East Japan Earthquake using the proposed model and reports the results. Finally, Section 5 presents the conclusion of the paper and a summary of the study outcomes.

The Sphere project, which is a collaborative effort between hundreds of non-governmental organizations (NGOs) to establish standards in humanitarian practice, states that aid organizations should provide assistance impartially and according to the need (The Sphere project, 2004). It suggests minimum standards for a humanitarian response (e.g. ensuring each person has 2,100 calories of food daily). However, they do not address how to allocate goods when these quantities cannot be met (De la Torre et al., 2012).

Recently, several models have been proposed for relief allocation. Altay and Green (2006) provide a holistic review of the Operational Research/Management Science (OR/MS) model in disaster operation management until 2004. After that, Galindo and Batta (2013) extensively reviewed the progress on disaster operation management after 2004. Both resources confirm that quantitative modeling in HL is necessary for successful relief operation and allocation.

The importance of quantitative modeling of relief allocation to areas suffering from disasters was introduced couple of decades ago by Knott (1988). A simple linear programming model was implemented for supporting relief routing during famine in Africa. After that, a number of researchers tended to formulate the resulting relief transportation issues as multi-commodity, multi-modal flow problems with time windows (Haghani and Oh, 1996). Considering the multi-commodity supply problems under emergency conditions, three linear programming formulations are proposed by Rathi et al. (1992), where the routes and the supply amount carried on each route are assumed to be known in each of the given origin-destination pairs. Their purpose, in reality, is to assign a limited number of vehicles loading multiple types of goods in given pairs of origins and destinations such that the induced multi-commodity flow problem is solved with minimal penalties caused by delivery inefficiency (e.g. early and late delivery as well as shipping in non-preferred vehicles). Ozdamar et al. (2004) propose a logistics model to minimize total unsatisfied demand without considering equality of delivery. Beamon and Kotleba (2006) propose a relief inventory management model for stochastic demand that aims to reduce inventory cost for long-term support for victims in Sudan; while Das and Hanaoka (2014) extend the relief inventory model to consider stochastic demand and lead time for a large-scale disaster. Alongside, several researchers integrate pre- and post-disaster conditions to the model formulation. Balcik and Beamon (2008) formulate a facility location model for storing relief, and the model aims to maximize the demand coverage of the facility. Campbell and Jones (2011) incorporate facility failure risks in formulating facility locations and optimal stocking quantity. Several papers propose two-stage models aiming to minimize warehouse operation cost and post-disaster operation cost (Bozorgi-Amiri et al., 2013; Mete and Zabinsky, 2010; Rawls and Turnquist, 2010). Adivar and Mert (2010) introduce a fuzzy linear programming for relief collection from international communities after a disaster that minimizes logistics cost while maximizing credibility.

In Fiedrich et al. (2000), a dynamic combinatorial optimization model is proposed to find the optimal resource rescue schedule with the goal of minimizing the total number of fatalities during the search and rescue period, that is, the first few days after the disaster. The model proposed by Fiedrich et al. (2000) aims to merely deal with rescue resource allocation problems. Sheu (2007, 2010) introduce a novel approach of relief allocation depending on relief urgency. The model of Sheu (2007) consists of five steps:

1. demand calculation;

2. affected area grouping;

3. ranking of area group;

4. group-based relief distribution; and

5. dynamic relief supply.

Ozdamar and Demir (2012) propose a vehicle routing model that aims to minimize travel time and incorporates the idea of hierarchical cluster.

Humanitarian operations are characterized by multiple actors, feedback loops, time pressures, resource constraints, and uncertainty (Besiou et al., 2011). However, the above-mentioned models lack the properties of agents’ behaviors and exclude relief urgency. In HL models, it is generally assumed that aid organizations own the transport facilities and have enormous power to control vehicle routing even after disruption of transport network. However, these assumptions are not true for all situations. Pedraza-Martinez and Van Wassenhove (2013) find that most aid organizations do not have their own vehicles and tend to hire vehicles from on-spot market. In this regard, behaviors of aid organizations and carriers are required to be considered separately and exclusively. Therefore, we introduce an ABM for relief allocation. Herewith, our model incorporates the idea of relief urgency from Sheu (2007). We also extended the application of relief urgency to incorporate agent’s behavior. In addition, a novel approach is proposed to measure the logistics performance.

Consider a large-scale earthquake that has contributed to different degrees of damage. All victims need assistance in the aftermath of this disaster, and the circumstances require that limited resources be utilized with proper judgment. This section formulates a fleet allocation model for this type of situation. After explaining the task chains and our study focus, we explain the behaviors of stakeholders in last-mile distribution (LMD). This section concludes with an illustration of the ABM architecture and operation.

Figure 1 (top) provides an illustration of relief flow (modified from Balcik et al., 2008). First, the relief item transfers from various locations to a primary warehouse. Next, the relief item is shipped to tertiary hubs via a secondary hub. Finally, the tertiary hubs deliver the relief item to demand points (victims). The relief distribution from the tertiary hub to the demand point, known as LMD, is the most challenging section and requires special attention (Balcik et al., 2008). Therefore, LMD requires critical analysis when allocating logistics resources in each tertiary hub to maximize social benefit. This topic is the focus of this paper, and ABM is implemented for relief distribution in LMD.

Figure 1 (bottom) shows the task chains that are linked to relief allocation. This figure shows that the relief item is received in the tertiary hub from the secondary hub. Simultaneously, demand points request relief from the tertiary hub. The tertiary hub evaluates the relief request under the resource constraints and deploys relief to the demand point accordingly. Finally, the whole operation is evaluated with the aim of maximizing social benefit.

Social benefit from a project is often intangible, hard to quantify, and difficult to attribute to a specific organization. Fortunately, the social benefit of distributing relief can be linked to the relief delivery. Therefore:

(Equation 1) 

where, SB(x)=social benefit from x available resources.

Although social benefit is the aim of relief distribution, resource constraints often force decision makers to distribute relief depending on relief urgency. This study defines the effort of aid organizations as follows:

(Equation 2) 

Aid organizations that create a higher acknowledgement by providing relief tend to garner more donations, whereas those that squander their resources receive lower future donations (Cermak et al., 1991). For example, Lily Duke, an independent film producer, arrived in New Orleans after Hurricane Katrina with a single fleet of donated food. The residents of this highly damaged area were satisfied, and the media highlighted the effectiveness of relief distribution. Duke’s effort was considered an effective strategy for relieving victims’ suffering. Within three months of the disaster’s onset, Duke was operating three distribution centers that served 20,000 people a day (Sobel and Lesson, 2007). The value of the effectiveness of the relief distribution strategy is computed by acknowledgement. The acknowledgement value for Duke’s efforts is higher due to a larger numerator value in Equation (2).

Kovacs and Spens (2008) list donors, aid organizations, NGOs, governments, the military, logistics service providers, and suppliers as the stakeholders involved in this network. Oloruntoba and Gray (2006) add aid recipients (beneficiaries) to the list. Van Wassenhove (2006) adds the media as a stakeholder of disaster relief. This study investigates the ontology of stakeholders in the last-mile relief distribution, as shown in Figure 2. Note that, ontology is characterized as a formal, explicit specification of a shared conceptualization (Gruber, 1993). Ontology facilitates the knowledge sharing and re-use among various stakeholders in the particular domain of knowledge. The stakeholders include the aid organization, carrier, demand agent (DA), coordinator agent (CAO) and society (e.g. national authority, evaluation team, and media). Figure 2 shows the objectives and activities of each stakeholder and the details of Figure 2 are as follows.

Donors are not obliged to fund, and if they do, they often donate funds to aid organizations to increase their own social esteem (Cermak et al., 1994). In contrast, aid organizations want to generate more funds by gaining the trust of donors. The total fund of an aid organization is a function of the social benefit generated by the organization and the efficiency of the organization (Preston, 1989).

The AOA is a key player in HL, and is responsible for collecting funds from donors and for managing relief. The AOA aims to reach more victims. In the proposed model, the AOA is assigned the role of a tertiary hub.

The CAA follows the behavior of business logistics, and wants to maximize monetary profit. The CAA performs several activities, such as transporting, loading, and unloading. The goals of the CAA are to minimize transportation costs and waiting time. However, the CAA faces the constraint of fleet capacity and operator working hours.

The DA, who performs demand estimation, orders relief items, receives relief items, and distributes relief items to victims, is assigned the role of a demand point, and represents the last key stakeholder in the supply chain. The DA receives relief from the tertiary hub and distributes it to victims. The DA attempts to bring in more relief to their demand point, and therefore exhibits very local-specific (i.e. selfish) behavior. The DA and AOA may be two distinct sections of the same organization. However, we classify them into two groups to distinguish their functionalities.

The SA does not have decision-making power in the relief chain. Society computes the value of acknowledgement and imposes it on aid organizations. However, the SA evaluates the aid organizations’ efforts, and may be a representative of an evaluation team.

The COA is responsible for coordinating the overall relief flow. The United Nations (UN) and aid organizations have established various committees and offices, such as the Office of the Coordinator for Humanitarian Affairs (OCHA) and the Inter-Agency Standing Committee (IASC), to improve coordination within the relief community (Reindorp, 2002; Kehler, 2004; Balcik et al., 2010). In addition, a national disaster management agency (e.g. the Federal Emergency Management Agency (FEMA) in the USA) may work as a COA.

The target relief item is consumed daily (i.e. it is a meal box). The demand for the product is generated every day and is considered unmet if not satisfied within a specified period. The unsatisfied demand incurs a penalty cost. The relief allocation includes a series of decisions including DA selection, delivery time, and fleet composition.

Figure 3 shows the relationships among agents. The ABM is used to assign a specific type of agent to each function in relief distribution. The CAA manages the transportation required for the entire planning period. The demand points are distributed among DAs (DA: i=1,  …,  n). A DA is responsible for only one demand point, and cannot exchange information with other DAs. This assumption reduces the modeling complexity and prohibits the possibility of relief transferring from one DA to another DA.

The COA is responsible for the coordination of local planning of the DA, AOA, and CAA. The AOA makes a contract with the CAA, and provides a fleet composition plan to the COA. The relationship between the AOA and COA resembles that of a client and server. The AOA, in the role of a client, submits a resource plan to the COA, and the COA returns the solution to the AOA. Finally, the SA evaluates the performance of the logistics system based on urgency-based mechanisms.

Next, we explain the simulation flow of the model. Figure 4 shows the steps in the simulation, which runs until it meets the termination criteria.

In Phase (1), the AOA submits a plan of fleet composition and relief quantity.

In Phase (2) the relief distribution to demand point is carried out in six steps. In step (2.1), the CAA calculates the possible minimum cost for relief transport subject to resource constraint and submits cost information to the COA. Equations (4) and (5) are the constraints for COA:

(Equation 3) 

Subject to,

(Equation 4) 

(Equation 5) 

where c_rk is the cost for route r with vehicle type k, y_rkt the binary variable for selecting route r, vehicle k on time t, and V_kt the available vehicle of type k in period t.

Here, objective Equation (3) minimizes the transportation cost for route r with vehicle type k. Equation (4) shows that CAA cannot utilize vehicles more than the available vehicles while Equation (5) is a binary constraint.

In step (2.2), the DA estimates demand using a method proposed by Sheu (2007):

(Equation 6) 

In this equation, a₁ represents the average hourly demand of target product. (Equation 7) represents the upper bound preset to regulate the temporal headway between two successive relief distributions to any given affected area without exceeding the corresponding maximum value. Z_1-α represents the statistical value when the tolerable possibility of time-varying relief demand shortage is set to be α. δ_i(t) represents the estimated number of victims in the affected area i in a given time interval t. STD_i(t) represents the time-varying standard deviation of relief demand associated with the delivered relief and affected area i.

In step (2.3), the DA places request for relief and the AOA collects information from all DAs to create a hierarchy of demand points to reach more victims. The AOA attempts to minimize the penalty cost differences among different demand points, as shown in Equation (7). The satisfaction rate is the ratio between the delivered amount and the demand that is presented in Equation (8) . The constraints for AOA are represented in Equations (8)-(11). Equation (9) is the demand constraint while Equation(10) is the relief supply constraint. Equation (11) is the available vehicle capacity:

(Equation 8) 

subject to:

(Equation 9) 

(Equation 10) 

(Equation 11) 

(Equation 12) 

where x_it is the amount of relief delivered to node i in period t, d_it the demand of relief during period t for demand point i, s_i the satisfaction rate of delivering relief, f the penalty cost for relief item shortage, F_t the available relief item in period t, and Cap_k the capacity of vehicle type k.

In step 2.4, the COA generates an urgency matrix for the system based on the technique for order of preference, similar to the ideal solution (TOPSIS) method (Deng et al., 2000, Sheu, 2010). The TOPSIS method is as follows.

A set of DAs is compared to a set of the criteria C=}C_j, j=1, …, m}; Five criteria are selected to form the hierarchy of demand points. These criteria are as follows (Sheu, 2010):

C1. The time-varying demand for the relief product.

C2. The population density associated with a given area.

C3. The ratio of frail population (e.g. children and older adults).

C4. The time difference between the present time and the last delivery.

C5. The damage condition of area. This value lies within 1 to 10.

Note that each criteria j is in different scales. For instance, C3 (i.e. j=3) is ratio-type data and C5 (i.e. j=5) is ordinal data (i.e. Likert scale). Let (Equation 13) be the value of criteria j for DA i. Therefore, (Equation 14) are normalized as:

(Equation 15) 

where, p_ij is the normalized value of criteria j for DA i.

An assessment matrix (P) for this problem can be obtained as:

(Equation 16) 

Next, each criteria weight can be measured by the entropy value (H_j) (Deng et al., 2000) as:

(Equation 17) 

Here k=1/lnn is a constant. This ensures 0H_j1.

The degree of divergence (g_j) of the average intrinsic information contained by each criterion is calculated as:

(Equation 18) 

The criteria weight (k_j) for each criterion is thus given by:

(Equation 19) 

After determining the rating of each criterion, the next step is to aggregate the ratings to produce an overall relief urgency for each zone. This aggregation process is based on the positive ideal solution (A+) and the negative ideal solution (A−), which are defined, respectively, as:

(Equation 20) 

(Equation 21) 

The members of vector A+are the positive ideal values of each criterion and the members of the vector A− are the negative ideal values of each criterion. Therefore, the lengths of vector A+ and A− are equal to the total number of criteria. Next, Equations (13), (17), and (18) are utilized to compute the weighted Euclidean distance between A_i and A+, and between A_i and A−, as:

(Equation 22) 

(Equation 23) 

Therefore, the overall relief urgency index (μ_i) of each zone can be computed by:

(Equation 24) 

A larger index value indicates a more urgent zone.

In step (2.5), the COA creates a joint evaluation matrix after incorporating information of the AOA and the CAA:

(Equation 25) 

where:

(Equation 26) 

The aid organization and carrier both adopt the weighted sum method (Zadeh, 1963) after incorporating the urgency index of relief for each DA. Equation (22) combines the objectives of the aid organization and the carrier. w₁ and w₂ are weight factors. Generally, w₁>w₂, which indicates a relatively high penalty cost. If w₁=w₂, then the carrier is reluctant to consider the victims’ suffering. If w₁<w₂, then the CAA exhibits opportunistic behavior. In the special case of w₂=0, the carrier provides voluntary transport to support aid organizations.

The COA then deploys the fleet to the DA. This deployment can happen in different ways, and this study presents a comparison of two deployment methods. The first is the enumeration method, and the second is the decomposition-type approach. The enumeration approach is popular for benchmarking the effectiveness of the proposed approach. It appears in many research papers (Aykin, 1995; Yu and Egbelu, 2008). Other approaches for this task include random demand points, drop solution, and drop and interchange solution (Aykin, 1995).

In this study, the enumeration approach is regarded as a simple myopic approach and the value of w₁is zero. In other words, this approach generates a DA hierarchy based on the distance from the nearest tertiary hub, and deploys the fleet to the nearest DA that requires relief. However, not all fleets can go to a particular DA since a fleet cannot deliver more relief than the requirement in a DA. Besides, the satisfaction rate (s_i) changes after a decision on the deployment of a fleet to a DA (i.e. before the arrival of a fleet at a DA). Thus, the urgency index (μ_i) changes after each deployment decision. The following discussion presents the decomposition algorithm used in this study.

First, the decomposition approach decomposes the entire problem into several sub-problems by forming a group of demand points with a predefined maximum number of nodes per group. This approach allocates fleets to different sub-groups to maximize the benefit from available resources. It is reasonable to assume that the number of fleet vehicles is greater than the number of tertiary hubs. Therefore, a portion of the fleet is assigned to each sub-problem. The proposed approach is described in the list below. Pseudo-code of the decomposition-type approach is as follows (modified from Lin et al., 2011):

1. Randomly select a demand point that is not included in any group.

2. Find the nearest demand point (not currently included in any group) to the last assigned demand point in the group, and repeat the process until the predefined number of demand points in a group is met or there is now ungrouped demand point left.

3. Find the average distance of the group member from tertiary hub, put the new group to lowest distance tertiary hub (J _h).

4. IF there is a demand point that does not belong to any group, Go to step a.

5. Else equally assign a number of vehicles L _h to each group h∈H, where H={1,  …  h} is the collection of groups (Equation 27) and (Equation 28). The original problem has now been decomposed into h sub-problems with assigned demand points and vehicles, respectively and each sub-problem is labeled as SP _h.

6. For each sub-problem SP _h, all feasible tours are enumerated and constructed using the shortest time principal.

7. For each sub-problem, construct the mathematical model based on L _h , J _h and the corresponding de demand points in the sub-problem; Solve SP _h by a solver and get the objective value z _h and the total objective value (Equation 29). If (iteration) i=0, set the best total objective value (Equation 30).

8. Find a pair of groups (p, q) that has the minimum and maximum objective value, respectively.

9. IF L _p>2, then remove a random number of vehicle v from L _p where 1vL _p−1 and assign to L _q.

10. Go to step f, update z_p, z_q, and z_all.

11. IF (Equation 31) update (Equation 32), Go to step f

12. ELSE set i=i+1.

13. IF (Equation 33). Go to step a.

14. ELSE find the next maximum objective value group, stop and exit.

Levels a-d of the algorithm decompose the original problem into several sub-problems. In other words, these steps categorize the demand points in several sub-groups. The number of sub-groups is identical to the number of tertiary hubs. Each sub-group of a demand point is assigned to a particular tertiary hub according to the rule of the algorithm. In Level e, the fleet is distributed among the sub-problems (i.e. tertiary hubs). At the first iteration, the fleet is allocated evenly to each sub-problem. The objective values of sub-problems and overall objective values are obtained in Level g. Levels f-n aim to improve the solution by adjusting the vehicle assignments among groups.

If the fleet carries more load than required in the target area, it visits another demand point after delivering to the initial target demand point. In step (2.6), after distributing all relief, the fleet returns to the tertiary hub.

Phase (3) is a logical condition in which the COA checks the work status. Phase (4) is performed once in each cycle, and is an evaluation of the efforts. In step (4.1), the SA calculates the difference between the requested and supplied relief.

In step (4.2), the value of the relief effort is calculated. Holguín-Veras and Perez (2010) propose a methodology of calculating the deprivation cost that assumes that the deprivation cost increases with a late delivery:

(Equation 34) 

We propose a new formulation for deprivation cost after incorporation of the relief urgency index:

(Equation 35) 

If there are two strategies for relief distribution, say strategy 1 and strategy 2, and they generate deprivation costs dc_i1 and dc_i2, respectively. Then, the social benefit is:

(Equation 36) 

where dc_i is the deprivation cost, n_i the shortage of relief, Δt the time gap between two deliveries, and ω, ξ, the parameter.

The following equation provides the acknowledgement value:

(Equation 37) 

In Phase (5), the COA suggests that the AOA should change the fleet composition to minimize the deprivation cost.

In Phase (6), the model checks the termination criteria. The operation terminates after meeting all demands or meeting the stopping criteria. If the termination criteria are satisfied, the mission ends in Phase (7).

The ABM adopted in this study is implemented in the open-source tool, NetLogo. In the proposed model, several optimization sub-models are included. The optimization is solved by another open-source tool, R. Here, the RNetLogo package is used to connect two open-source tools. The ABM was tested on an Intel (R) Core (TM) i3-3,220 PC operating at 3.30 GHz. The following section describes the test concept and the results.

The Great East Japan Earthquake destroyed an enormous number of roads and buildings. The most severely affected prefectures were Fukushima, Miyagi, and Iwate, which had pre-disaster populations of 2.35, 1.33, and 2.03 million, respectively. In this case study, we collected data for five of the most-affected cities in these three prefectures. Miyagi prefecture lost 3.11 percent of its population (10,739 victims) to the disaster. Iwate prefecture had fewer fatalities, but lost 4.35 percent of its population. Fukushima had a much smaller number of fatalities (Vervaeck et al., 2011; Holguín-Veras et al., 2012). Table I shows the victims-in-shelters, fatalities (percent), frail population, and density for the five most-affected cities in each prefecture. Victims-in-shelters and fatalities (percent) are post-disaster data. In contrast, frail population and density are pre-disaster data. The NetLogo computes the transportation time from the tertiary hub to the demand point internally. The demand point keeps the record of each delivery time. In the TOPSIS method, time of last delivery, which is a dynamic parameter, is a criterion for computation of the urgency index. In this analysis, the 15 shelters are the demand points. For the network setting, three tertiary hubs were placed in three prefectural offices. Fleet compositions of 9, 12, 15, 18, 21, 24, and 27 were used. The parameter value for Equation (6) a ₁ is 3, and the standard deviation is assumed to be 10 (Table II).

This case study was analyzed using the decomposition approach and the enumeration approach. The decomposition approach employs Equation (22) as an objective function in step 2.5 of the simulation flow stated in Figure 4. In the decomposition approach, w ₁ and w ₂ are assumed to have an identical value (i.e. 0.5). On the other hand, the enumeration approach employs Equation (22) for w ₁ equivalent to zero.

Table III represents the result of the TOPSIS method for calculating the hierarchy of each demand point in terms of the relief urgency index. Here, A1-A15 represent cities in the three prefectures. Among them, A8 (Ishinomaki) is the most urgent demand point and A5 (Shinchi-machi) is the least urgent demand point at Day 0. In the case of relief shortage, the AOA serves the demand points sequentially, starting from A8. However, the urgency index of each demand point changes after each decision on the deployment of fleet. At Day 0, Criterion 5 in the TOPSIS method (i.e. the time difference between the present time and the last delivery) is equal for all points. The urgency index of demand points is computed after each fleet deployment.

The average deprivation cost of the complete planning period was calculated to compare the two deployment methods, and Table IV presents the results. The decomposition approach dominates the enumeration approach for all fleet compositions. This model generates routes and allocates the fleet to deliver relief to all demand points. If one demand point does not receive relief for two consecutive days, the deprivation cost increases exponentially. In the decomposition approach, the fleet visits each point at least once per day, whereas in the enumeration approach, the fleet distributes relief to closer demand points and other demand points are left un-served.

We compute relief shortage in each method. The relief shortage depends on the available capacity of the fleet. This is directly plausible because HL fleet management assumes that all vehicles operate with full truckloads under operational time constraints. Figures 5 and 6 show the changes in total shortage and transportation cost as the fleet volume changes in the enumeration and decomposition approaches, respectively. According to both Figures, the relief shortage decreases linearly as the fleet volume increases. This implies that the fleet maximizes its utilization capacity. The fleet moves from one demand point to another demand point until it delivers all carrying relief. This system is in line with the model proposed by Ozdamar et al. (2004), in which the fleet gets a call from its last position rather then returning to the depot to get a new order. In contrast, the transportation cost changes every operational day in the decomposition approach and remains unchanged in the enumeration approach. This implies that the fleet must run longer distances to meet the demands of the most urgent demand points in the decomposition approach. This proves that the urgency index has an effect on the selection of the target demand points. This study employs a linear cost function of distance for transportation cost. Therefore, it is natural that an increase in resources would lead to a higher transportation cost and a lower deprivation cost. We successfully simulate this phenomenon in the virtual world to analyze the effects of transportation measures.

The enumeration approach and the decomposition approach produce the same total relief shortage. However, the effectiveness of relief from two approaches is different. We compare the effect of decomposition approach and that of enumeration approach and compute the value of acknowledgement gap, which is based on the difference between the deprivation costs of the enumeration approach and decomposition approach. The denominator in Equation (28) is computed by the transport cost differences between the enumeration and the decomposition approach. The absolute value of acknowledgement gap is considered here. The formula is shown in the following equation:

(Equation 38) 

According to Figure 7, the acknowledgement gap decreases exponentially as fleet number increases from 9 to 12, 15, 18, 21, 24, and 27. This implies that the decomposition approach is more effective when resources are limited. The decomposition approach and the enumeration approach both generate identical benefit if there are sufficient resources, and the acknowledgement value is similar to the benefit-cost ratio computation.

Finally, all agents follow their own preferences in attempting to maximize their own objectives. The AOA aims to minimize the differences among various demand points. On the other hand, the CAA wants to deliver in shorter distances. The CAO finally reaches a solution for both parties. Table IV shows the combined effects of each agent’s preferences observed through changes in deprivation cost. The DA strives to obtain more relief, whereas the social agent evaluates the efforts of the aid organization based on relief urgency.

A simulation model can be used to help emergency logistics decision makers better understand the dynamics of an emergency response situation. A decision maker wants to know the effects of resource allocation. The ABM is a good tool for analyzing the effects of resource allocation. This approach is much less risky than actually waiting for another disaster to happen and then test the model in a real-life situation. This model allows actors to investigate the effects of transport measures and to understand the mechanisms of demand management in a dynamic environment.

Relief distribution aims to maximize the overall social benefit. To solve the problem of integrated transport operation and demand point selection, the proposed ABM includes five types of agents: AOA, CAA, DA, SA, and CAO.

The ABM was tested using data obtained from the Great East Japan Earthquake. This study shows the benefits of an alternative relief distribution method, examines the effects of resource allocation, and analyzes the improvement strategies of relief distribution from a more strategic viewpoint. The results of this study lead to the following conclusions:

• TOPSIS uses both qualitative and quantitative parameters to compute a relief urgency index. This method helps determine effective resource allocation.

• The decomposition approach generates more social benefit because it considers relief urgency in a relief allocation situation.

• The fleet allocation strategy greatly affects relief distribution. The proposed model demonstrates the fleet allocation. The enumeration approach generates benefits for victims staying near the depot.

• The decomposition approach helps achieve higher social benefits.

Finally, the proposed ABM not only improves the analysis of the effects of transportation measures, but can also be used to design the fleet contract for future relief response from a more strategic viewpoint. The model proposed in this study considers linear cost function and operational time constraint. Future research can investigate various types of contracts and their effects on social benefit. Herewith, data limitation always restricts the applicability of model after disaster. More studies are required to overcome data and associated limitation during relief distribution.

Dr Rubel Das is a Doctoral Student in the Department of International Development Engineering at the Tokyo Institute of Technology, Tokyo, Japan. He received his Bachelor of Engineering in Civil Engineering from the Bangladesh University of Engineering and Technology and his Masters of Engineering in Transportation Logistics from the Tokyo Institute of Technology. Dr Rubel Das is the corresponding author and can be contacted at: rubeldas2013@gmail.com

Shinya Hanaoka is an Associate Professor at the Graduate School of Science and Engineering, Tokyo Institute of Technology. He is also a Visiting Professor at the Kobe University. He has worked as a Researcher for the Institute for Transport Policy Studies in Tokyo (1999-2003), an Assistant Professor for the Asian Institute of Technology (2003-2007), and a Visiting Researcher for the Institute for Transport Studies, University of Leeds (2002). He has authored and co-authored numerous journal articles and has participated in private and government-funded transport research projects. His research interests include transport logistics, transport development studies, air transport, and transport infrastructure management.

This work was supported by the Grant-in-Aid for Scientific Research C (24510184) awarded by the Japan Society for the Promotion of Science. Finally, the authors would like to thank the anonymous referees and the journal editorial board for their helpful comments and suggested improvements.