DUJE (Dicle University Journal of Engineering) 11:2 (2020) Page 679-688

Research Article

Humanitarian Logistics Management After A Disaster: An Earthquake Case

Elifcan Göçmen 1,*, Yusuf Kuvvetli 2 1 Munzur University, Engineering Faculty, Department of Industrial Engineering, Tunceli , 0000-0002-0316-281X 2 Çukurova University, Engineering Faculty, Department of Industrial Engineering, Adana, 0000-0002-9817-1371

ARTICLE INFO ABSTRACT

Article history:

Received 11 December 2019 Post-disaster relief logistics includes logistics activities in the shortest time. Inventory routing problems Received in revised form have decided routing decisions considering inventory levels during the planning horizon at minimum 21 April 2020 cost. In this study, an inventory routing problem for the distribution after the disaster has been proposed. Accepted 23 May 2020 The problem aims the distribution of the supplies needed considering available inventory levels at Available online xxx minimum time. Distribution amount and the routes under the constraints of routing and inventory Keywords: amounts for affected people have been decided. An integer programming approach to solve the problem has been proposed and solved. The proposed model is solved for a case of Van earthquake which Post-disaster relief logistics, occurred at 2011 in Turkey. The results from the case study show us that determining the inventory and Inventory-routing problems, routing decisions simultaneously can provide less logistic activities. In addition to this, holding inventory Mathematical modelling, in the central depot can ensure to respond the emergency needs safely and quickly. Earthquake

Doi: 10.24012/dumf.658184

* Corresponding author Elifcan, Göçmen  [email protected]

Please cite this article in press as E. Gocmez, Y. Kuvvetli, “Humanitarian Logistics Management After A Disaster: An Earthquake Case”, DUJE, vol. 11, no. 2, pp. 679- 688, June 2020. DUJE (Dicle University Journal of Engineering) 11:2 (2020) Page 679-688

Introduction rescue centres [5]. A disaster planning of medical needs is provided. The model Disasters are sudden, dangerous events and determines the storage location, inventory cause catastrophe in human life. They have levels, and distribution decisions. The study is affected nations in recent decades. Thus, to applied for an earthquake scenario [6]. A mixed manage effective humanitarian operations is an integer model is developed for location important part of a disaster relief. Disaster inventory problem. They aim to minimize the management is the process of taking measures response time. The model is established for 9 beforehand and inspecting the effects of a warehouses and 3 inventory levels [7]. A two disaster. Humanitarian logistics is sub-part of stage approach is proposed for an earthquake. logistics that is relevant of the disaster They firstly try to solve location inventory management. This area is suitable for problem and then vehicle routing is handled. mathematical approach and several By the uncertain situations, they use robust applications. approach. They also meta heuristic methods Organizations pay more attention to increase [8]. the efficiency of logistics systems. They are Disaster management also requires giving aware that the inventory routing decisions decisions about routing problems. based on their logistics network are critical. Transportation of aids for the affected people is The inventory-routing problems (IRPs) have ensured by the effective routes. Many studies been one of the most important problems. about routing/distribution problems are Several applications of the IRP have been conducted by many researchers. A documented [1]. Humanitarian logistics is a mathematical model is developed for good area for the applications of the IRP and it emergency logistics planning. They integrate has received interest both from academics and two network flow problems, the first one linear the practitioners. It includes disaster relief and and the second one integer. They needed support for developing regions [2]. Quick heuristic solutions for the second problem [9]. response to the urgent need after disasters is A problem is presented about bioterrorism critical for emergency logistics [3]. Managing emergencies. They decomposed the problem the emergency logistics is difficult because of into two stages. In the first stage, they plan the this critical structure. Disaster management has routes in any emergency; in the second stage gained interest after the 1999 Marmara they decide the delivery quantity. They use Earthquake in Turkey. Post disaster relief mathematical formulations to solve the regulations were organized and distribution of problems [10]. Many studies about location aids to affected people was suitably ensured. problems are conducted by many researchers. This study has been carried out to decide the Humanitarian logistics network is designed routes considering the inventory levels at under mixed uncertainty involving multiple minimum cost after a disaster. warehouses, local distribution centres. In the Disaster management requires solving several first step, locations of warehouses and centres problems to help the affected people. These are determined and then, a distribution decision problems include location, routing and is given to minimize total distribution time, inventory decisions. Many studies about total cost of unused inventories. The study is location-inventory problems are conducted by applied in Tehran for potential earthquakes many researchers. They use exact formulations [11]. A location-allocation problem is proposed or/and heuristic algorithms to solve the to minimize response time. Ambulance problem. A model is proposed that decides the locations near demand points are positioned location of distribution centres and supplies to [12]. A humanitarian supply chain design is be stocked at the centres [4]. The location- developed. They use a p-median model for inventory problem of rescue services is small instances and a tabu heuristic for large investigated. In the post disaster, they assign instances. The heuristic method has given better the relief items between demand points and results. The results also show that integration of 680

DUJE (Dicle University Journal of Engineering) 11:2 (2020) Page 679-688 post disaster decisions with pre disaster to prevent stock out. The network of the paper decisions is important [13]. A stochastic comprises centre depots, supply nodes and approach is proposed to decide inventory emergency nodes shown in Figure 1. The amounts before disaster and sufficient amounts centres must provide emergency products to the after the disaster. The problem includes demand points. uncertain demand, so a scenario based model is In this study, in order to solve problems caused provided [14]. A mixed integer programming by the disaster, an inventory routing model is approach is presented for blood supply. The proposed. The proposed model solved the model includes some constraints based on routes considering the inventory levels at uncertain demands, perishability products. minimum cost. As the greatest benefit, with this Minimum cost of supply chain, maximum system, delivery of aid materials at emergency demand meeting, minimum time between is markedly provided. production and consumption are expected in the objectives [15]. A disaster planning problem is presented by multi objective programming. Supply They aim to take the location, inventory, nodes Emergency nodes distribution decisions for a flood disaster in Centre Mexico [16]. Location warehouses, inventory Depot levels in the pre disaster are decided, routing decisions are given in the post disaster. They solve the problems by two meta heuristic approach [17]. A model for deciding the relief locations and transportation is formulated. They aim to minimize pre disaster costs and unmet demands [18]. Distribution and routing decisions are investigated for emergency conditions by meta heuristic approach [19]. A mixed integer linear programming model is formulated for location-routing problem. They Figure 1. The proposed network in the problem solve the problem by different meta heuristics [20]. The military supply is investigated by integer programming. Total supply chain costs and inventory levels are decided in the model Mathematical model [21]. The indices used for mathematical modelling of In the literature, inventory routing problems are the problem are as follows; mostly studied. However, in this study, the problem is applied firstly for the post-disaster Indices relief logistics. The reasons for this are as follows: 푖, 푗, 푣 푖푛푑푖푐푒푠 푓표푟 푠푢푝푝푙푦 표푟 푒푚푒푟푔푒푛푐푦 푛표푑푒푠 Managing products inventory after disasters is E 푖푛푑푖푐푒 for emergency area S 푖푛푑푖푐푒 for supply area critical to avoid the stock-out situation. 푘 푖푛푑푒푥 푓표푟 푠푢푝푝푙푦 표푟 푒푚푒푟푔푒푛푐푦 푣푒ℎ푖푐푙푒푠 The inventory component carries a time 푡 푖푛푑푒푥 푓표푟 푝푒푟푖표푑푠 dimension to the routing problems. In the 푁퐸 푠푒푡 표푓 푒푚푒푟푔푒푛푐푦 푎푟푒푎푠 humanitarian logistics, the distribution of the 푁푠 푠푒푡 표푓 푠푢푝푝푙푦 푎푟푒푎푠 supplies needed considering available inventory 퐾퐸 푠푒푡 표푓 푡푟푢푐푘푠 푓표푟 푒푚푒푟푔푒푛푐푦 푎푟푒푎푠 levels at minimum time. 퐾푠 푠푒푡 표푓 푡푟푢푐푘푠 푓표푟 푠푢푝푝푙푦 푎푟푒푎푠 푇 푠푒푡 표푓 푝푒푟푖표푑푠 푖푛 푝푙푎푛푛푖푛푔 ℎ표푟푖푧표푛 푇0 = 푇 ∪ {0}

Materials and Methods The parameters and decision variables used are Inventory routing problem concerned in this as follows; paper includes two sub problems: transportation of aid products and controlling inventory levels 681

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Parameters 퐸 푠 퐶푘 (퐶푘 ): 퐶푎푝푎푐푖푡푦 표푓 푒푚푒푟푔푒푛푐푦 (푠푢푝푝푙푦)푣푒ℎ푖푐푙푒 푘 (푢푛푖푡) 퐸 푠 푙푖 (푙푖 ): 푚푖푛푖푚푢푛 푖푛푣푒푛푡표푟푦 푙푒푣푒푙 표푓 푒푚푒푟푔푒푛푐푦 (푠푢푝푝푙푦) 푛표푑푒 푖 (푢푛푖푡) 퐸 푠 푔푖 (푔푖 ) 푚푎푥푖푚푢푚 푖푛푣푒푛푡표푟푦 푙푒푣푒푙 표푓 푒푚푒푟푔푒푛푐푦 (푠푢푝푝푙푦)푛표푑푒 푖 (푢푛푖푡) 퐸 푠 푓푘 (푓푘 ): 푓푖푥푒푑 푢푠푎푔푒 푐표푠푡 푓표푟 푒푚푒푟푔푒푛푐푦(푠푢푝푝푙푦) 푣푒ℎ푖푐푙푒 푘 (푚표푛푒푦/푝푒푟푖표푑) 푝 ∶ 푣푎푟푖푎푏푙푒 푐표푠푡 푓표푟 푡푟푎푛푠푝표푟푡푎푡푖표푛 (푚표푛푒푦/푑푖푠푡푎푛푐푒) ℎ ∶ ℎ표푙푑푖푛푔 푐표푠푡 푓표푟 (푚표푛푒푦/(푢푛푖푡 ∗ 푝푒푟푖표푑) 퐸 푠 푑푖푗 (푑푖푗): 푑푖푠푡푎푛푐푒 푏푒푡푤푒푒푛 (푖, 푗) 푒푚푒푟푔푒푛푐푦 (푠푢푝푝푙푦)푝푎푖푟 (푑푖푠푡푎푛푐푒) 퐷퐸(퐷푠): 푚푎푥푖푚푢푚 푡표푢푟 푙푒푛푔푡ℎ 푓표푟 푒푚푒푟푔푒푛푐푦(푠푢푝푝푙푦) 푣푒ℎ푖푐푙푒푠 푟푖푡: 푑푒푚푎푛푑 표푓 푒푚푒푟푔푒푛푐푦 푛표푑푒 푖 푎푡 푝푒푟푖표푑 푡 (푢푛푖푡) A(B): number of emergency (supply) nodes Decision Variables 푆 퐸 퐼푖푡 (퐼푖푡): 퐼푛푣푒푛푡표푟푦 푙푒푣푒푙 표푛 푠푢푝푝푙푖푒푟 (푒푚푒푟푔푒푛푐푦)푛표푑푒 푖 푎푡 푝푒푟푖표푑 푡 (푢푛푖푡) 푆 퐸 푄푖푘푡 (푄푖푘푡): 푃푖푐푘푒푑 푎푚표푢푛푡 (푑푒푙푖푣푒푟푦 푎푚표푢푛푡)푓푟표푚(푡표) 푠푢푝푝푙푖푒푟 (푠푢푝푝푙푦) 푛표푑푒 푖 푎푡 푝푒푟푖표푑 푡 푤푖푡ℎ 푣푒ℎ푖푐푙푒 푘 (푢푛푖푡) 퐸 푆 푋푖푗푘푡 (푋푖푗푘푡): 퐿표푎푑 표푛 푡푟푎푣푒푙푙푖푛푔 (푖, 푗) 푒푚푒푟푔푒푛푐푦 (푠푢푝푝푙푖푒푟)푝푎푖푟 푎푡 푝푒푟푖표푑 푡 푤푖푡ℎ 푣푒ℎ푖푐푙푒 푘 (푢푛푖푡) 1, 푖푓 푎 푑푒푙푖푣푒푟푦 푚푎푑푒 푡표 (푖, 푗)푠푢푝푝푙푖푒푟 푝푎푖푟 푆 푌푖푗푘푡 = { 푎푡 푝푒푟푖표푑 푡 푤푖푡ℎ 푣푒ℎ푖푐푙푒 푘 0, 표푡ℎ푒푟푤푖푠푒 1, 푖푓 푣푒ℎ푖푐푙푒 푘 푖푠 푢푠푒푑 푓표푟 푠푢푝푝푙푦 표푛 푝푒푟푖표푑 푡 푈푆 = { 푘푡 0, 표푡ℎ푒푟푤푖푠푒 1, 푖푓 푎 푑푒푙푖푣푒푟푦 푚푎푑푒 푡표 (푖, 푗)푒푚푒푟푔푒푛푐푦 푝푎푖푟 퐸 푌푖푗푘푡 = { 푎푡 푝푒푟푖표푑 푡 푤푖푡ℎ 푣푒ℎ푖푐푙푒 푘 0, 표푡ℎ푒푟푤푖푠푒 1, 푖푓 푣푒ℎ푖푐푙푒 푘 푖푠 푢푠푒푑 푓표푟 푑푒푙푖푣푒푟푦 표푛 푝푒푟푖표푑 푡 푈퐸 = { 푘푡 0, 표푡ℎ푒푟푤푖푠푒

Model 푇 퐾푒 푇 푁푒 푁푒 퐾푒 푇 푁푒 퐸 퐸 퐸 퐸 퐸 min 푧 = ∑ ∑ 푓푘 ∗ 푈푘푡 + ∑ ∑ ∑ ∑ c ∗ 푙푖푗 ∗ 푌푖푗푘푡 + ∑ ∑ ℎ ∗ 퐼푖푡 푡=1 푘=1 푡=1 푖=0 푗=0 푘=1 푡=1 푖=0 푖≠푗 푇 퐾푠 푇 푁푠 푁푠 퐾푠 푇 푁푠 (1) 푆 푆 푆 푆 푆 + ∑ ∑ 푓푘 ∗ 푈푘푡 + ∑ ∑ ∑ ∑ c ∗ 푙푖푗 ∗ 푌푖푗푘푡 + ∑ ∑ ℎ ∗ 퐼푖푡 푡=1 푘=1 푡=1 푖=0 푗=0 푘=1 푡=1 푖=0 푖≠푗 퐾푒 퐸 퐸 퐸 퐸 퐼푖푡 = 퐼푖푡−1 − 푟푖푡 + ∑ 푄푖푘푡 t ϵ {1. . T}, i ϵ {1. . Ne} (2) 푘=1 푁푠 퐾푠 푁푒 퐾푒 푆 푆 퐸 푆 퐸 퐼0푡 = 퐼0푡−1 − 푟0푡 + ∑ ∑ 푄푖푘푡 − ∑ ∑ 푄푖푘푡 t ϵ {1. . T} (3) 푖=1 푘=1 푖=1 푘=1 퐸 퐸 퐸 푋푖푗푘푡 ≤ 퐶푘 ∗ 푌푖푗푘푡 i ϵ Nc, j ϵ Nc | i ≠ j, t ϵ {1. . T}, k ϵ Ke (4) 푁푒 푁푒 퐸 퐸 퐸 ∑ 푋푗푖푘푡 − ∑ 푋푖푣푘푡 = 푄푖푘푡 k ϵ Ke, t ϵ {1. . T}, i ϵ {1. . Ne} (5) 푗=1 푣=1 푖≠푗 푖≠푣

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퐾푒 푁푒 퐾푒 푁푒 퐾푒 푁푒 퐸 퐸 퐸 ∑ ∑ 푋0푗푘푡 − ∑ ∑ 푋푖0푘푡 = ∑ ∑ 푄푣푘푡 t ϵ {1. . T} (6) 푘=1 푗=1 푘=1 푖=1 푘=1 푣=0 푁푒 푁푒 퐸 퐸 ∑ 푌푖푗푘푡 − ∑ 푌푗푣푘푡 = 0 k ϵ Ke, t ϵ {1. . T}, i ϵ Ne (7) 푗=1 푣=1 푖≠푗 푖≠푣 푁푒 푁푒 퐸 퐸 퐸 퐸 ∑ ∑ 푌푖푗푘푡 ∗ 푑푖푗 ≤ 퐷 ∗ 푈푘푡 k ϵ Ke, t ϵ {1. . T} (8) 푖=0 푗=0 푖≠푗 푁푒 퐸 퐸 ∑ 푌0푖푘푡 = 푈푘푡 k ϵ Ke, t ϵ {1. . T} (9) 푖=1 푁푒 퐸 퐸 ∑ 푌푖0푘푡 = 푈푘푡 k ϵ Ke, t ϵ {1. . T} (10) 푖=1 퐸 퐸 퐸 푊푖푘푡 − 푊푗푘푡 + 퐴 ∗ 푌푖푗푘푡 ≤ 퐴 − 1 i ϵ {1. . Ne}, j ϵ {1. . Ne}, t ϵ T, k ϵ Ke (11) 퐸 퐸 퐸 푙푖 ≤ 퐼푖푡 ≤ 푔푖 t ϵ T, i ϵ Ne (12) 퐸 푆 퐼0푡 = 퐼0푡 t ϵ T (13) 퐾푠 푆 푆 푆 퐼푖푡 = 퐼푖푡−1 − ∑ 푄푖푘푡 t ϵ {1. . T}, i ϵ {1. . Ns} (14) 푘=1 푁푠 푁푠 푆 푆 푆 ∑ 푋푗푖푘푡 − ∑ 푋푖푣푘푡 = −푄푖푘푡 k ϵ Ks, t ϵ {1. . T}, i ϵ {1. . Ns} (15) 푗=1 푣=1 푖≠푗 푖≠푣 퐾푠 푁푠 퐾푠 푁푠 퐾푠 푁푠 푆 푆 푆 ∑ ∑ 푋0푗푘푡 − ∑ ∑ 푋푖0푘푡 = ∑ ∑ −푄푣푘푡 t ϵ {1. . T} (16) 푘=1 푗=1 푘=1 푖=1 푘=1 푣=0 푆 푆 푆 푋푖푗푘푡 ≤ 퐶푘 ∗ 푌푖푗푘푡 i ϵ Ns, j ϵ Ns | i ≠ j, t ϵ {1. . T}, k ϵ Ks (17) 푁푠 푁푠 푆 푆 ∑ 푌푖푗푘푡 − ∑ 푌푗푣푘푡 = 0 k ϵ Ks, t ϵ {1. . T}, i ϵ Ns (18) 푗=1 푣=1 푖≠푗 푖≠푣 푁푠 푁푠 푆 푠 푠 푆 ∑ ∑ 푌푖푗푘푡 ∗ 푑푖푗 ≤ 퐷 ∗ 푈푘푡 k ϵ Ks, t ϵ {1. . T} (19) 푖=0 푗=0 푖≠푗 푁푠 푆 푆 ∑ 푌0푖푘푡 = 푈푘푡 k ϵ Ks, t ϵ {1. . T} (20) 푖=1 푁푠 푆 푆 ∑ 푌푖0푘푡 = 푈푘푡 k ϵ Ks, t ϵ {1. . T} (21) 푖=1 푆 푆 푆 푊푖푘푡 − 푊푗푘푡 + 퐵 ∗ 푌푖푗푘푡 ≤ 퐵 − 1 i ϵ {1. . Ns}, j ϵ {1. . Ns}, t ϵ T, k ϵ Ks (22) 푆 푆 푆 푙푖 ≤ 퐼푖푡 ≤ 푔푖 t ϵ T, i ϵ Ns (23) amount from the supply area sent to the disaster The objective function (Eq. 1) minimizes the area and the need finally. The Eq. 4 ensures that total costs consist of fixed usage costs of the vehicle capacity couldn’t be exceeded. Eq. vehicles, transportation and holding costs of 5 and Eq. 6 allow the balancing of the helps both emergency and supply area. Inventory distributed. While Eq. 5 ensures the distribution balances regarding incoming products and carried out for each point by vehicle, Eq. 6 outgoing demands are ensured by Eq. 2 and 3. allows the total distribution by the depot. Eq. 7- The Eq. 2 allows the balancing the inventory 10 ensures the routing constraints. Eq. 7 allows amount by considering the needs occurred in the routing. Eq.8 provides that the route length the disaster region. The Eq. 3 calculates the cannot exceed the maximum tour length. Eq.9

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DUJE (Dicle University Journal of Engineering) 11:2 (2020) Page 679-688 and 10 ensure that the tour must start in the Table 1. The provided post disaster activities (AFAD depot and finish in the same depot. Eq. 11 is a report) sub tour elimination constraint. Eq. 12 holds the Post disaster For first 24 For first 72 inventory levels between the upper and lower activities hours hours limits. Eq. 13 is a transfer constraint which Number of staffs 3221 4615 provides to transfer main supply depot’s Number of total 523 794 inventory levels to main emergency node’s vehicles inventory level. Eq. 14 balances the inventory Number of 37585 103021 levels on supply nodes. Eq. 15 and 16 provide materials the pick-up amounts for supply nodes and main depot, respectively. Eq. 17-22 are routing Accordingly, the model for the first 72 hours constraints for supply nodes. While Eq. 17 of relief work (3 days) is resolved. The results forces to avoid from exceed capacity, Eq.19 are given in Table 2, Figures 2-3. forces to avoid from exceed of the maximum tour length. While Eq. 18 provides the routes, Table 2. Inventory levels on emergency nodes Eq. 20 and 21 ensures the tour must be start and Node Period 1 Period 2 end of the main depot. Eq. 22 is a sub-tour Malazgirt 16 5 elimination constraint for supply nodes. Finally, Bitlis 16 5 Eq. 23 ensures the held inventory levels should Patnos 12 4 be in a range of lower and upper limits. Adilcevaz 48 16 Erciş 97 699 Results and discussion

Van Province in Turkey is examined for post Table 1 shows the amount of inventory at each disaster management. After the earthquake, point. When these quantities are evaluated, due several rescue operations, aids are provided to the inventory being kept, the demand that shown in Table 1. The staffs include search and will be generated on the third day can be met rescue staffs and health personals. For first 24 from the stock and thus the lower logistics costs hours, %81 of all the staffs is sent to the region. are ensured with the solution of the model. The vehicles sent to the region are trucks, ambulances and airplanes. For first 24 hours, %94 of all the vehicles is sent to the region. The materials are tents, blankets and stoves which are sent to the region for first 24 hours with % 77 rate. The relief work after the Van earthquake in 2011 is took place for the solution of the model. The proposed mathematical model is solved in GAMS mathematical modelling language on computers with 3.6 GHz processor and 16 GB RAM.

(a)

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(b) (b) Figure 2. Routes on emergency nodes at (a) first period and (b) second period.

Figure 2 shows routes created between emergency points. The most important contribution of inventory keeping is seen in the formation of routes. Routes have been created only two days of the planning period.

(c) Figure 3. Routes on supply nodes at (a) first period (b) second period and (c) last period.

Figure 3 shows routes between supply points. Considering the inventory quantities in each period, the needs are met from the nearest (a) points. The result of establishing routes together between need and supply points is seen in the results. According to this, while there is no routing in the last period, supply is provided for the central depot requirement. Thus, it is possible to reduce the cost of routing.

Sensitivity analysis

Model parameters are estimated in this section. Measuring the sensitivity of the model against possible forecast errors is important. For this reason, the sensitivity of the model to the following conditions is examined:

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• Emergency vehicle capacity the tour length does not change the solution for • Supply vehicle capacity the emergency vehicle. However, shortening • Emergency tour length the length of the tour increases the costs for • Supply tour length supply vehicles. This is why a vehicle must • Holding cost / routing cost travel a longer way when the tour lengths Emergency vehicle capacity and supply vehicle shorter. When the duration of the solution is capacity values are set to 1000. A graph of the examined, the increase in the length of the variation of this value between 500 and 1500 is emergency tour increases the duration of the shown in Figure 4. Accordingly, it is seen that solution significantly. In terms of supply the change in the value of Supply Vehicle vehicles, it increases firstly and then decreases. capacity is more effective on the solution. This is an expected situation because long distances can be transported to these distribution points. Emergency vehicle capacity does not react very much to change. From the perspective of the solution times, it can be said that the decrease of vehicle capacities reduces the solution time.

Figure 5. The effect of tour lengths to the solution

When the parameter effects of the parameters are examined, the last parameter is the ratio of the holding and routing costs. This ratio is one Figure 4. The effect of changes in the vehicle capacities of the most important parameters in terms of to the solution times solution duration of holding or transportation in every period. When the results presented in Figure 5 shows the influence of the tour length Figure 6 are examined, objective function cost on the resolution time. Accordingly, increasing increases. However, when the solution

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DUJE (Dicle University Journal of Engineering) 11:2 (2020) Page 679-688 durations are examined, it is observed that the This study presents a mathematical model increase does not affect the solution times after approach, for larger applications heuristic a significant reduction in the solution at a methods can be applied. Some uncertain certain point. This point can be considered as conditions require stochastic or fuzzy the point at which the balance between holding approaches. Future works should address long- and routing is completely broken. term economic development programs. Also, mitigation, preparation, response and recovery phases of the emergency management should be handled to reduce the impact of the hazards. Limitation of the study is that the model developed is only applied for a region and for post disaster processes. Future work may include national preparedness in the pre disaster stage and the results may be generalized for whole country.

References

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