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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.17 No.4 pp.850-863
DOI : https://doi.org/10.7232/iems.2018.17.4.850

# A Logistical Relief Distribution Preparedness Model: Responses to a Probable Tsunami Case Study in West Sumatra, Indonesia

Reinny Patrisina*, Nikorn Sirivongpaisal, Sakesun Suthummanon
Department of Industrial Engineering, Faculty of Engineering, Prince of Songkla University, Hat Yai, Thailand.
Department of Industrial Engineering, Faculty of Engineering, Andalas University, Padang, Indonesia.
Department of Industrial Engineering, Faculty of Engineering, Prince of Songkla University, Hat Yai, Thailand.
* Corresponding Author, E-mail: reinny.patrisina@gmail.com
April 8, 2017 November 17, 2017 March 5, 2018

## ABSTRACT

Preparedness to establish an efficient and effective relief response is essential in reducing severity and fatality in a disaster. This study presents a two-stage mixed-integer programming model applied in a 3-tier of a relief distribution network consisting of permanent warehouses, local distribution centers, and refugee camps for a disaster relief operation at the operational level. A mixed delivery strategy is considered in order to obtain an efficient logistics planning strategy to respond to a disaster. Stage-1 is a location-allocation model to determine the sites of local distribution centers setup in the initial response period, together with the aggregate amount of relief items that should be delivered during the response period. It has an objective to minimize the total logistics cost as well as unfairness cost regarding unfair distribution among affected people. Stage-2 develops further the relief distribution plan that minimizes total route travel cost according to outputs of the previous stage. The model is tested on a fictitious but probable tsunami in West Sumatra, Indonesia. The proposed model should be helpful to disaster relief managers in employing it to increase performance of such a disaster relief operation, should there be a need.

## 1. INTRODUCTION

Disasters, besides causing casualties, also influence social and economic fundamentals of the affected are as at the same time. With respect to the serious impacts of a disaster, it is imperative to make a country be more resilient against it. Good strategies in disaster management inclusive of mitigation, preparedness, responses, and recovery will enhance disaster resilience building at all levels (Altay and Green III, 2006).

Nothing could be done to stop a disaster happening, but improving services to millions of affected people could be improvised. Since disasters could not be avoided, after the best mitigation efforts have been done, the next best thing is to be prepared for another one. Most disasters that cause both material and immaterial damage can be correlated, in part, to the lack of preparedness (Nirupama and Etkin, 2012).

An effective and efficient logistics in the immediate aftermath of a disaster is critical for effective relief operations to prevent human loss and suffering (Moe and Pathranarakul, 2006). Logistics activities encompass up to 80% of activities and become a central in any disaster response operation (DRO) (Van Wassenhove, 2006). Logistics concerning humanitarian is called humanitarian logistics. Humanitarian logistics is 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 the point of origin to the point of consumption for the purpose of alleviating the suffering of vulnerable people (Thomas and Kopczak, 2005).

Regarding disaster operations, humanitarian logistics involves both pre (preparedness) and post-disaster (response) operations (Manopiniwes and Irohara, 2014). Prior to a disaster, humanitarian logistics concern strategic planning, decision making on the locations of permanent warehouses for storing relief prepositioning stocks and the type and amount of relief goods that would be stored at the warehouse. After a disaster, humanitarian logistics plays an important role in operational planning; distributing relief goods to disaster victims in the affected areas is required to alleviate fatality rates and severity. Distributing relief items also has a significant effect to the success of rescue operations (Baldini et al., 2012); only then that survivors get their hands on the available help.

This action has to be performed instantly right after the disaster; delays are not tolerated. There will be no time for long discussion or to make decisions when it is already too late to develop a relief operation plan that has not been set before. The operation plan encompasses locations of temporary facilities that are established in the aftermath and during the response period for a relatively much shorter time such as local distribution centers (LDCs); the amount of the goods that would be delivered through the relief network; and routing of vehicles in transporting relief goods to survivors in the affected areas.

Balcik and Beamon (2008) stated that designing a relief network and its operation have important roles in obtaining an effective and efficient response. Anaya- Arenas et al. (2014) found that study in humanitarian logistics especially which integrate both location and distribution problems in post-disaster situation is limited. Yi and Özdamar (2007)combined relief delivery with casualty transportation in DROs. A location-routing model is introduced to determine health care sites set up at postdisaster, as well as loading and routing of a vehicle in distributing relief supplies from supply centers to distribution centers in the affected areas. Nolz et al.(2010) proposeda metaheuristic approach for planning water distribution tours in disaster relief. Similarly, Naji-Azimi et al. (2012) integrated a tour-covering and site selection problem for delivery of relief goods during the response time.

Satisfaction of survivors is not less important in a relief operation; allocating more relief aids to a group of survivor while others receive smaller or nothing, and/or delivery relief supplies in the early response period while others get assistance later would cause not only dissatisfaction that could trigger a chaotic situation but also death and misery. One of the rules in disaster management is equity where every survivor has the right to survive and should be treated equally (Balcik et al., 2008; Geale, 2012; Holguín-Veras et al., 2013). Humanitarian logistics cares about rapid responses, sufficient relief supplies, and distribution equity among disaster victims as well as minimizing cost (Huang et al., 2012; Baldini et al., 2012). There are some literatures that also combine both location and distribution issues in the aftermath and involve distribution equity in their study. Afshar and Haghani (2012) formulated a location-routing model applied in Federal Emergency Management Agency (FEMA)’s logistics structure. The formulated model decides the locations of temporary depots functioning as transit points before relief goods are deployed to distribution points actuating as demand points and the amount of delivery through the relief network using multi-type of vehicles. Distribution equity is involved by setting the lowest satisfaction level for each demand point. Rennemo et al. (2014) developed a three-stage stochastic programming for disaster response planning. The initial stage addresses determination of the location of distribution centers, as well as an allocation of relief goods under uncertain demand and vehicle capacity. The last two stages concern with the last mile distribution problem. However, in their model all distribution points are served from distribution centers. The second stage decisions are made on the load and the route of vehicles by assuming that the demand and the capacity of heterogeneous vehicle fleets are known. Their route model assumed that the vehicles are not required to return to their starting points after distributing the relief items. Torre et al. (2012) classified this model into a model which has no concept of depot (no depot).This model demands greater resources than a single depot model where the route of a vehicle starts and finishes at a single depot as well as the ability to communicate routing decisions to vehicles throughout a region. Actually, communication is one of obstacles especially in the beginning of a disaster because it is hard to perform. The last stage includes network uncertainty by revising the predefined route when it involves an inaccessible distribution point. Fairness is involved by prioritizing delivery where higher utility is given to higher priority demand points. Ahmadi et al. (2015) proposed a multi-depot location-routing model in both strategic and operational level considering specified relief time for each vehicle.

Homogeneous vehicles are used to deliver relief supplies. Each demand point is served by only one specific vehicle, and that could be inadequate. Unmet demand is involved by penalizing demand shortage. Manopiniwes and Irohara (2017) presented a stochastic programming model that integrates facility and stock prepositioning problem and transportation planning. The model is applied to three tiers of a relief distribution network encompassing one main warehouse, distribution centers, and shelters/communities that are used to distribute one type of relief items. Using a number of homogeneous vehicles, relief items will be transported from main warehouses to distribution centers, then from these points, the supplies will be dispatched to shelters/communities. A movement of affected people to shelters during the response period is considered since it affects a number of supplies that would be sent to the shelters. All demands at shelters/ communities are allowed to be fulfilled by more than one centers and no demand shortage occurs. The equity involves by restricting maximum response time.

Based on the literature review which present an optimization model for a location and routing problem, the proposed model has similar features to the model in Yi and Özdamar (2007), Afshar and Haghani (2012), and Rennemo et al. (2014) which considered heterogeneous relief vehicles for delivering multi-items over multiplanning periods. However, this study differs from theirsin several ways. First, though the models involve at least 3-tier of relief (permanent warehouses at the first tier; LDCs as transit points at the second tier; and refugee camps, which are also called as demand points, at the third), no model applies a mixed delivery strategy. The proposed model in this study employs a mixed delivery strategy: survivors in the affected areas are permitted to be served not only by the transit points but also directly from the main warehouses. For the victims located even nearby to the source points, shipments are still have to go through the transit points, and thus are expensive and time-consuming. Each camp or demand point is supposed to be served by the closest facility as long as the supplies are available (Manopiniwes et al., 2014). We address unsatisfied demand in two ways: by giving a penalty cost to a shortage demand and a penalty cost for unfair distribution. Although shortage is normal in disaster relief operations, it is still expected that relief distribution is conducted fairly, whereas the penalty to the shortage demand could not guarantee distribution equity. Giving a penalty cost to unequal distribution is still required to distribute supplies fairer. In addition, both shortage and unfairness in relief distributed system can lead to more pain and severity towardthe victims. In the proposed model, distribution equity is modeled by allocating aid supplies proportionally among camps based on demand amounts. Firstly, the satisfaction level of each camp is measured. Then the maximum difference of satisfaction level between two camps is calculated. Distinct to this study, Afshar and Haghani (2012) addressed equity by setting a minimum level of service for each victim over planning period and Rennemo et al. (2014) delivered the items to demand points based on its priority, while Yi and Özdamar (2007) did not take into account equity in distributing relief items. Moreover, the proposed routing model assumes that relief items are distributed by a set of heterogeneous vehicles on routes starting and finishing at the same point (single depot) and it is allowed to perform multi-tours under its service time. This depot concept can ease vehicle coordination and suitable for a disaster situation where resources are limited and information is hard to obtain, compared to multi-depot concept used in Yi and Özdamar (2007) and Afshar and Haghani (2012), and Rennemo et al. (2014) that does not have the concept of a depot. Thus, this study attempts to formulate a 2-stage mixedinteger programming model applied in a 3-tier of a relief distribution network consisting of permanent warehouses, local distribution centers, and refugee camps for a disaster relief operation at the operational level. A mixed delivery strategy is considered in order to obtain an efficient logistics planning strategy to respond to a disaster. Stage-1 is related to the location-allocation decisions. It has an objective to minimize the total logistics cost as well as unfairness cost regarding unfair distribution among affected people. Then, using the outputs of the previous stage, Stage-2 is aimed to determine the routes of vehicles at post-disaster phase. Specifically, this study applies the proposed model to the case of an assumed tsunami disaster in Indonesia in order to illustrate the benefit of assisting disaster managers in improving preparedness activities.

## 2. STATEMENT OF PROBLEM

Immediately after a disaster takes place, a number of aids items would be transported to survivors in the affected area in order to save lives and alleviate suffering. Identifying the location of the LDCs that would be established in the early phase of response period as well as developing a relief operation plan are vital in achieving an effective and efficient response (Balcik and Beamon, 2008). Though these decisions will be applied in a postdisaster period,whereas time is a critical issue in emergency response, preparedness for conducting an effective and efficient should be performed as early as possible. Then, its activities will strengthen the disaster preparedness (Vaillancourt and Haavisto, 2015) and timely and efficient delivery of relief aids could be performed.

In this current study, we present two problems involved in humanitarian logistics at response phase.The problems are solved in two stages.The first problem of our study, solved in Stage-1,is related to a locationallocation problem. The key decisions involved are the location of LDCs and the aggregate amount of items dispatched through the proposed relief network by minimizing the logistics operation costs as well as the unfairness cost regarding unfair distribution among survivors. To a disaster-prone area, prior to a disaster, some permanent warehouses, usually located in the big cities or capital cities, have normally been established and the goods have been prepositioned in the warehouses. In the initial response period, especially before humanitarian organizations or donors arrive, survivors will be supplied from the warehouses and depend on it (Vaillancourt and Haavisto, 2015). Their locations are possibly away from the affected areas so that for certain locations, direct shipping from the warehouses to the recipients at the refugee camps in the affected areas are costly and time-consuming. Thus, during the first response time, it would be beneficial to set up LDCs located between the warehouses and the disaster areas to function as transit points in distributing survival goods to the survivors. For an efficient relief response, the goods can be either allowed to be distributed either directly or indirectly via LDCs from the warehouses to the recipients. In addition, this study concerns with equity in distributing relief goods to survivors. Each survivor has the same right to be saved and getting aid supplies (Balcik et al., 2008). Hopefully, none of the affected people would receive nothing or close to nothing if resources run out as well as none of the recipients would receive more than others.In this study, fair distribution is defined as allocating relief goods equally among group of survivors.The penalty cost is applied for preventing uneven dispatch of items among beneficiaries. Actually, this cost is hard to quantify since it is related to the value of human life and the social cost but it needs to be defined, and the value increases with the standard of living (Altay et al., 2013). This Stage-1 will apply the model of a location-allocation from our earlier work, Patrisina et al. (2015). Then outputs of the first stage model will be inputs for the second problem. The second problem, Stage-2, corresponds to the development of a relief distribution planin order to minimize the total route travel cost using the output of the previous stage. The important decisions includeroutes of vehicles in transporting relief goods to survivors in the affected areas and the number of items that will be carried by each vehicle in its tour.Since this current study covers both a location-allocation problem and routing problem, whereas Patrisina et al. (2015) only involved a location-allocation problem, then it will be an extended to Patrisina et al. (2015).

In addition, our study compares the experiment results of relief logistics between the model with mixed delivery strategy and pure delivery strategy such applied in Ahmadi et al. (2015). Under the restriction on response time, this study also investigates the performance of relief operations by varying number of vehicles located at the supply points. Moreover, the effects of supplies and unfairness cost to the performance of humanitarian logistics operation are provided.

## 3. PROBLEM ASSUMPTIONS

The model is developed under several assumptions as follows.

### 3.1. Model of Stage-1

The problem is applied in a 3-tier of the relief distribution network including permanent warehouses, LDCs, and refugee camps, shown in Figure 1. The camps would receive supplies from either one of the warehouses or one of the LDCs, while the LDCs are allowed to get the relief items from more than one warehouses. The warehouses and LDCs are considered as supplies points since they would deliver the relief supplies to other points. Heterogeneous relief vehicles are used to carry the aids to survivors in the affected area.

The LDCs functioned as transit points between the permanent warehouses and the camps are opened in the initial response period and only be operated during the response period. Thus, we consider the cost for establishing the LDCs. Since the relief items should be shipped to survivors as quickly as possible, it is assumed that there is no holding cost at the LDCs and the capacity of the LDCs is unlimited. The transportation cost from warehouses to LDCs, from warehouses to camps, as well as from LDCs to camps are calculated for two ways since the vehicle needs to return to its origin points.Actually, an LDC may be located at the same location as a camp as long as the location is representative to be an LDC in term of location, size, and resources, while at the same time it is also functioned as a refugee camp. Then, from the LDC to the camp is connected by a dashed line such as from LDC J2 to Camp K5 in Figure 1. If the LDC J2 is selected to be opened, then at least there should be one camp other than Camp K5 served by LDC J2. Therefore, Camp K5 has two functions simultaneously, as a location for refugees to stay and as a location for an LDC. Since LDC J2 and Camp K5 are located at the same location, no transportation is required from LDC J2 to Camp K5.In the situation, the proposed LDC which is located at the same place with a camp is not selected to be opened, then this location is solely functioned as a refugee camp, a fixed cost for opening an LDC should not be induced. A shortage demand will be charged by shortage cost. In the case of unfair distribution, unequal allocation of supplies among the camps, each type of the item distributed will be penalized by unfairness cost.

### 3.2. Model of Stage-2

Heterogeneous fleets of vehicles located at the supply points are used to dispatch aids supplies to victims through the proposed relief distribution network obtained in Stage-1 during the planning period. The planning period will assure that all disaster victims get help during the time. After a specified time, it may be too late for them to receive a service (Galindo and Batta, 2013). Each vehicle is allowed to perform multi-trips during its working time.The total number of items that should be delivered to the camps could possibly be more than the vehicle capacity. To deal with this situation, split delivery is allowed. So, the camps can be visited many times during the planning period by the same or different vehicles, through the same or different route, using the same or different vehicle. Moreover, the vehicle can carry multi types of items as well as visiting one or more destination points at one-time delivery. Then the route travel costs in Stage-2 is not equal to the sum of transportation cost from one supply point to one destination point and back to its origin since each vehicle is assumed to move in a route; while a route encompasses several destination points, hence, the travel cost of the route is calculated by summing up the travel cost of all arcs included in a route.

## 4. MODEL FORMULATION

The 2-stage of mathematical programming model can be written using the following notations:

Index Sets:

• I set of permanent warehouses

• J set of potential LDCs

• K set of refugee camps

• P set of relief items

• Kbr set of destination points served from supply point b, obtained in Stage-1 on route r

• R set of routes rinitiating from supply point b to destination points under its service

• V set of relief vehicles

• T set of planning periods

• B set of supply points consisting of permanent warehouses ∪opened LDCs (Zj=1)

• A set of destination points consisting of camps∪opened LDCs (Zj=1)

Parameters:

• fj fixed cost for opening LDC j

• dpk the number of relief goods p required by camp k

• spi the number of available relief goods p at warehouse i

• M a big positive number

• hp shortage cost for relief goods p

• rp penalty cost of relief goods p when unfair distribution occurs

• ρ vehicle working hours

• cpij transportation cost of relief goods p from warehouse i to LDC j

• cpjk transportation cost of relief goods p from LDC j to camp k

• cpik transportation cost of relief goods p from warehouse i to camp k

• γbrv the total travel time for route r using vehicle v starting from supply point b

• cbrv the travel cost for route r using vehicle v starting from supply point b, calculated by summing up the travel cost of all arcs included in the route

• capbv capacity of vehicle v located at supply point b

Decision Variables of Stage-1:

• Zj binary variable that equals to 1 if LDC j is selected to be opened and 0 otherwise

• Upk satisfaction level to relief goods p of camp k

• Ep the maximum difference of satisfaction level to relief goods p due to unfair distribution among camps

• Xpij the aggregate number of relief goods pdelivered from warehouse i to LDCj

• Xpjk the aggregate number of relief goodsp delivered from LDCj to camp k

• Xpik the aggregate number of relief goods p delivered from warehouse i to camp k

• Ljk binary variable that equals 1 if camp k is served by LDC j, and 0 otherwise

• Lik binary variable that equals to 1 if camp k is served by warehouse i and 0 otherwise

Decision Variables of Stage-2

• βpbarvt the number of relief goods p would be delivered from supply point b to any destination point a through route r using vehicle v during period t

• αbrvt binary variable that equals to 1 if vehicle v starts its service from supply point b through route r on period t and 0 otherwise

Using the above definitions, the models are formulated as follows.

### 4.1. Stage-1: Location-Allocation Decisions

Minimize(12)

$( ∑ j ∈ J f j Z j ) + ∑ p ∈ P ( ∑ i ∈ I ∑ j ∈ J X p i j c p i j + ∑ j ∈ J ∑ k ∈ K X p j k c p j k + ∑ i ∈ I ∑ k ∈ K X p i k c p i k ) + ∑ p ∈ P { h p [ ∑ k ∈ K ( d p k − ( ∑ i ∈ I X p i k + ∑ j ∈ J X p j k ) ) ] } + ( ∑ p ∈ P r p E p )$
(1)

Subject to

(2)

$∑ j ∈ J X p i j + ∑ k ∈ K X p i k ≤ s p i ∀ p ∈ P , ∀ i ∈ I$
(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

The objective of the model (Equation (1)) is to minimize the total relief logistics costs including the total set up cost, the total cost for transporting aid supplies to disaster victims in disaster areas through the relief distribution network, the total shortage cost, and the total penalty cost respect to uneven distribution among group of recipients. Equation (2) is to ensure that the total inflow to LDC j is the same as the total outflow from the LDC j. Equation (3) represents that the total amount of relief items distributed from any permanent warehouse should be less than or equal to the total amount of available supplies at a warehouse.Equations(4) and (5) describe that the total number of relief items delivered to any camp could not exceed its required demand. Equations(6) and (7) ensure that no camp would be assigned to LDC j as well as no supplies would be dispatched from LDC j unless the LDC j is opened. Equation (8) allows that each camp as a demand point to be served by only one of supply points either by one of permanent warehouses or one of opened LDCs. Equations(9) and (10) are used to measure the satisfaction level of each camp and inequitable relief distribution among camps. Equations(11)-(13) are non-negative constraints, while Equation (14) is integer constraints regarding the location decision and the assignment decisions.

### 4.2. Stage-2-Vehicle Assignment and Routing Decisions in Relief Distribution Plan Development

The first stage of a mixed-integer programming model provides the amount of item pthat would be allocated from warehouse i to LDCj(Xpij), from LDC j to camp k(Xpjk), and from warehouse i to camp k(Xpik). In order to dispatch relief vehicles according to the previous solutions, Xpij, Xpjk, and Xpik would be converted to a relief transportation plan for the vehicle loading and routing problem. These amounts will be recognized as Xpba that isthe relief goods p would be allocated from supply point b(warehouse i∪opened LDC j) to any destination point a (opened LDCj∪campk).

Minimize

(15)

Subject to

(16)

$∑ p ∈ P ∑ a ∈ K r b β p b a r v t ≤ c a p b v α b r v t ∀ r ∈ R , ∀ b ∈ B , ∀ v ∈ V , ∀ t ∈ T$
(17)

(18)

(19)

$α b r v t ∈ { 0 , 1 } ∀ b ∈ B , ∀ r ∈ R , ∀ v ∈ V , ∀ t ∈ T$
(20)

The objective (15) of Stage-2 is tominimize the total route travel cost. Equation (16) is to ensure that the total amount of relief goods p shipped to any camp is equal to the amount of relief goods allocated to the camp at the first stage. Equation (17) defines that the total amount of relief items that will be distributed by each vehicle should be less than or equal to its capacity.Equa-tion (18) restricts the total travel time of a vehicle. Finally, Equations (19) and (20) represent non-negative and integer constraints, respectively.

## 5. NUMERICAL EXPERIMENT

### 5.1. Data Sets

To illustrate the proposed model, this study has ap-plied it to a predicted tsunami triggered by an earthquake in the western coast of West Sumatra, Indonesia within the next few decades. Based on the geological record, Sieh (2006) who have studied the Sumatran megathrust sectors for more than a decade found that an 8.4 magnitude earthquake struck, followed by a tsunami, devastated Padang city, West Sumatra in 1797, and another of 9.0 magnitude, also with tsunami, in 1833. The findings were affirmed using biological records on giant coral heads and from monitoring the motion of earth’s crust at this zone by GPS stations continuously.

It was concluded that the sectors have been squeezed for more than two centuries and the megathrust is predicted to crack again in 50 years from 2005. This predicted disaster has gained much attention from the government of Indonesia and other disaster stakeholders. The local government agency which is responsible for disaster management (BPBD Sumatera Barat) along with other institutions such as social welfare, health, and public works, the military, scientists, privates, and non-governmental organizations have developed a tsunami contingency plan for West Sumatra (BPBD Sumatera Barat, 2013). The worst possible scenario is an earthquake with a magnitude of 8.8, at a depth of 30 km, 150 km from south-west of Padang City, shown in Figure 2. A million individuals living in seven coastal cities in West Sumatra (Agam, Mentawai, Padang, Pariaman, Padang Pariaman, Pasaman Barat, and Pesisir Selatan) will be exposed to the disaster, while potential losses are estimated to be not less than the 2004 Indian Tsunami (Sieh, 2006). In this study, all the affected cities excluding Mentawai are considered since that region consists of islands situating apart from others.

Based on the scenario of possible disasters, this study has developed a humanitarian logistics plan at the operational level with regards to locations of the LDCs, pre-determined routes, distribution plans for relief goods to the affected areas during the initial response time (the first 72 hours). Using the relief network applied in Patrisina et al.(2015), three permanent warehouses - Pusdalops; Provincial; and Bukittinggi - 17 potential locations of LDCs, and 34 camps are considered, presented inFigure 3. The cost for setting up an LDC is assumed approx. 500 USD such in Kusumastuti et al. (2013).

Three types of relief goods (rice, instant noodle, and preserved food) are considered. Prior to the assumed disaster, the warehouses are assumed to have stored relief prepositioning stocks, explained in Table 1.

The dimension of a box of instant noodle is chosen as the basic unit for computing equivalent volume. Penalty cost is given to a shortage demand and unfair distribution. The shortage cost per equivalent volume is set at 300, 200, and 370 USD respectively for rice, noodle, and preserved food, while the cost of unfairness for each item is assumed to be 10,000-time its shortage cost.

Two types of truck are used for transporting the goods: 6-wheel truck of 4 tons (627 unitsequivalent) and 4-wheel truck of 1.5 tons (208 units equivalent). Both types of trucks are assigned to the warehouses, and only the small trucks to the LDCs. The variable transportation costs per equivalent volume for the 6-wheeler and the 4-wheeler per kilometer are, respectively, 0.0005 and 0.0007 USD. The working hours of the vehicles in a single planning period is assumed to be 24 hours (T=24hours) since the initial response time is very critical. The route travel distance is measured using Google map.

### 5.2. Computational Results

The case study is solved using LINGO 15.0 on a PC with Intel® Core™ i7-4790 3.6 GHz processor, and 4.00 GB RAM. The problem is solved in two stages. First is to select locations of LDCs and to determine the aggregate number of relief goods that will be delivered from the supply points (warehouses and LDCs) to the refugee camps. Based on the first stage decisions, pre-determined routes are identified, and its travel cost and times are calculated. The number of allocated supplies obtained in Stage-1 as well as the pre-determined routes is used as inputs to determine load and routing of a vehicle in the second stage.

The optimal solution to Stage-1 results in a deci-sion to open 6 LDCs as transit points in distributing re-lief goods during the response period. A total of 19 refu-gee camps from 34 camps will be served from the opened LDCs and the others will be supplied directly from the warehouses. The warehouses serve the LDCs and the closest camps, as long as they have stocks while the further ones are served by the LDCs located close to them.

Based on the result from Stage-1, pre-determined routes, route travel times, and costs are identified. Eighty possible routes for delivery relief supplies during the response operations are identified, starting at a warehouse or opened LDCs through a sequence of LDCs or camps (Table 2).The route travel time is calculated based on travel distance assuming that the speed of vehicle is fixed at 30 km per hour for all vehicles.

The selected routes and the number of items deli-vered during the initial response periods are presented in Table 3. When the total amount of delivery for the camps in the route is greater than the vehicle capacity, the camps on that route are visited more than once through the same or different route, using the same or different vehicle, and at the same or different period. For example, in the first period, from J2, K1 is visited once, directly from J2; in the second and the third period, from J2, K1 is visited twice - once directly from J2, and once indirectly in the route J2-K4-K3-K1.

Since the opened LDCs are located at camps: J2 at K5, J3 at K7, J8 at K15, J10 at K19, J12 at K24, and J13 at K25, no vehicle is assigned to deliver the relief supplies from the LDCs to those camps. The items that is remaining at the LDCs is allocated to the camps where the LDCs are located.

The performance of relief operations within the first 72 hours after the disaster with varying number of vehicles located at supply points (warehouses and LDCs) are shown inFigure 4. From the figure, at least ten vehicles are required to be located at the supply points in the first 72 hours (3T) of the feasible aftermath relief operations: 3 six-wheelers plus 1 four-wheeler are to be at the warehouses and 6 four-wheelers at the LDCs. Assigning more vehicles (e.g., an increase of 25% capacity) provides negligibly better performance in terms of the total variable travel cost (4%). Whereas the cost spent in providing more vehicles are more than what is gained from the slightly better performance.

To compare to a longer operation time, to deliver the same amount of relief supplies, a shorter planning period requires more vehicles.Figure 4describes that if the initial response period is restricted to 48 hours (2T), at least seven vehicles (3 six-wheelers plus 4 four-wheelers) are needed to be assigned to the warehouses and seven vehicles (7 four-wheelers) to the LDCs with the total capacity of 4,169 in unit equivalent. In case the number and capacity of available vehicles less than those numbers, the supplies would be not completely distributed during the 2T of relief operation period. Therefore, Figure 4 only shows a single point for explaining “variable and total costs” with 2T case. This information should be useful to a disaster manager in determining the number of vehicles that should be located at each supply point and the amount of budget that should be prepared to serve disaster victims in a specified operation time.

### 5.3. Comparison of The Two Delivery Strategies

Performances of two relief distribution strategies are evaluated: The proposed strategy (mixed strategy) in allowing the disaster victims to be served either directly from the permanent warehouses or indirectly via the LDCs, versus a pure strategy such presented in Ahmadi et al. (2015) where the survivors are only supplied by the LDCs. The evaluations are performed using the model of location-allocation in Stage-1. For a pure strategy, it requires adjusting the model firstly before a computation is taken place. Patrisina et al. (2015) used ten different amount of demands in their study, and these are employed in this evaluation; defined as the ten scenarios. Figure 5 shows that a lower total transportation cost is obtained when victims are able to get supplies from one of the warehouses/LDCs than when they are forced to be wholly supplied from the LDCs. This result validates our intuition in that permitting demand points or camps to gain aids supplies from either permanent warehouses or transit points is helpful in the reduction of transportation cost, as well as travel distance and time. Furthermore, in the computation, it was found that the mixed strategy needs less number of LDCs to be set up immediately after the disaster (it requires only 1 to 6 LDCs) compared to that required by the pure strategy of 7 to 9 LDCs.

### 5.4. Effect of Supplies and unfairness Cost

Prior to a disaster, permanent warehouses are sup-posed to have at least three days of relief prepositioning stocks to be distributed during an immediate response. Lack of supplies could increase the chances of losing more lives and severity (Galindo and Batta, 2013). Gen-erally, aid supplies from donors start coming in on the third day, increasing for a few more days, getting stable for a while, then subsequently decrease to the end of the response period (Ahmadi et al., 2015).

This study investigates the effect of supplies and unfairness cost to the performance of humanitarian logistics operation measured by the greatest differences of satisfaction among recipients (unfairness). The number of available stocks at warehouses (spi) varies between 10% and 100% of the required demand, while the penalty cost for unfairness (rp) ranges from 0 to 1,000 times the shortage cost (hp). Since we compare the total amount of supplies to the total demand then it is denoted as supply index inFigure 6. For example, supply index = 0.1 means that the available stocks only can fulfill 10 % of all required demand. Then ten computations with ten different supply indexes are performed for each unfairness cost. After that, the average unfairness of three relief items caused byunfair distribution among camps is recorded.

Figure 6 explains that if the number of items stored at the warehouses is enough to fulfill all demands (supply index = 1), distribution equity would occur at any penalty cost. In case the total demands exceed the prepared stocks, a shortage will persist. This situation is of high potential in creating an uneven distribution, especially when the unfairness cost is set to an rp of less than 100hp. As seen in Figure 6, at rp=0 and at the supply indexes between 0.1 and 0.9, the levels of unfairness are equal to one. It means that there is a camp that receives no supply while at least one of the camps get allof it needs. Though the unequal distribution takes place, the contribution of the total penalty cost caused by unfair distribution to the total cost is zero since the value of the difference of satisfaction level (Ep) is multiplied by the value of zero. It seems that no penalty cost would be charged if the unequal distribution takes place. Then, the transportation cost is the only consideration in determining the amount of supplies delivery from one supply point to one destination point. The lowest total cost is achieved by transporting the available relief supplies to the nearest camp firstly then to the next nearby ones while the farthest one would be the last location that would receive the aid supplies as long as the stocks are still available. On the contrary, at rp = 100 hp and rp=1,000hp, the figure showed that of any supply index, no unfairness applies. This amount of unfairness cost will enforce relief operations to perform fairer as the total penalty cost from uneven distribution contributes more to the total cost than the extra cost expended for dispatchinga number of supplies to victims in remote areas. While at rp=hp and rp=10hp, in the situation where the number of stocks increases, Figure 6 shows that the unfairness goes up till one point, continuing constantly, and then decline. The additional relief stocks are transported to the camps located around supply points since it provides fewer additional total cost contributed by the transportation and the penalty cost than to distribute the additional one equally to all camps in order to even the relief distribution. The fact, it would increase the satisfaction level of the nearest camps while the distant ones remain unchanged so that the gap in satisfaction among the camps would increase. Though the unfairness is increased, the increase of the total penalty cost caused by the unfair distribution is still less than the increase of transportation cost for dispatching the additional supplies to the farther camps to reduce satisfaction differences among the camps.

### 5.5. Practical Implementation

Although this study is applied to a probable future tsunami in West Sumatra, Indonesia, the proposed model should be appropriate for other types of disasters such as earthquakes, hurricanes, and floods in any area. However, to a disaster hazard-prone area, a disaster scenario ought to be developed, and the predicted impact generated, to prepare for an immediate response if a disaster does happen. The estimated number of vulnerable people in an area is indicative of the amount of relief items required. Based on information regarding locations and the amount of relief prepositioning stocks, the initial distribution plan is developed under the assumed disaster scenario: the proposed relief network, the number of items to be delivered through the network, the alternative routes and their travel times, and the required number of vehicles. Moreover, the plan would also provide estimation of the operational costincluding the total establishing cost and the transportation cost. Thus, the amount of operational budget in responding to a disaster could be allocated. This activity will streng-then disaster preparedness and help a disaster manager perform an efficient and effective disaster relief operation.

During the response time, with updated information on infrastructure conditions, required demands and the number of available supplies and vehicles, the proposed model is repeatedly applied to rapidly revise previous relief network designs and distribution plans.

Delivery capability is affected by the number and type of the vehicle fleets assigned to the supply points. The more vehicles are available, the shorter the relief time needed to dispatch relief items to people in affected areas.

In practice, a response period can take a week or two, or a month. Increasing the planning period will increase the problem size; shorten planning period will improve the accuracy of the relief operations. Too short period, however, will increase the problem size drastically and prolong the computation time as well.

## ACKNOWLEDGMENTS

This research was funded by Andalas University of Indonesia and Prince of Songkla University of Thailand. The authors gratefully appreciate their combined supports. The authors would like to thank the two anonymous reviewers for the very useful comments and suggestions which help us improve the quality of our paper. Moreover, the authors would also like to thank BPBD Sumatera Barat and Disaster Risk Reduction Indonesia of Padang (DRRI Padang) for providing us with information and understanding of disaster relief environment.

## Figure

The proposed relief network design.

Possible scenario of an earthquake that triggers a tsunami in West Sumatra, Indonesia (EOS, n.d).

Locations of Warehouses, potential LDCs, and Camps (Patrisina et al., 2015).

Transportation cost vs. the number of vehicles required in various operational plan in the initial response period.

Comparison of two relief distribution strategies.

Logistics performance with various supplies and unfairness cost.

## Table

The amount of relief items at warehouses.

Vehicle Route Information

Visited LDCs/camps and the amount of delivery in the initial response period (in unit equivalent)

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