Application of a Humanitarian Relief Logistics Model to an Earthquake Disaster

Humanitarian relief is a key operation after a disaster for people who are isolated in disaster-affected areas and cannot get basic supplies for daily living. Because the demand can be large and unexpected, an efficient humanitarian relief logistics planning becomes extremely important. In a recent paper, Lin et al. (2009) proposed a logistics model for disaster relief operations. In this paper we demonstrate how to apply their model to a case study. The scenario that we have selected is that of an earthquake disaster in Southern California simulated using the HAZUS-MH software. A series of sensitivity analyses is conducted in the paper to provide insights on the influence of various parameter settings to the performance of a disaster relief operation – specifically we study the impact of the depot location, the number of vehicles, and the number of clusters chosen. For the simulated earthquake disaster, our analysis shows that geographic location for the depot is important, increasing the number of vehicles does improve the performance, and that reduction in the number of clusters does not guarantee an improvement in the logistics of humanitarian relief. Lin, Y-H, Batta, R., Rogerson, P.A., Blatt A. and Flanigan M. 3 INTRODUCTION AND LITERATURE REVIEW Humanitarian relief operations have drawn significant attention in the past decade because of the huge personal and financial costs associated with natural disasters (e.g. the Indian Ocean tsunami in 2004, the Pakistani earthquake in 2005 and hurricane Katrina in New Orleans in 2005). In the scenario of disasters, a humanitarian relief operation includes transporting supplies into the earthquake-affected areas where people are isolated and where daily supplies are not sufficient without shipments from outside. Because the demand for this scenario is often extremely large and unexpected, how to transport supplies from a major distribution center to clusters (destinations) that are located around the affected area becomes a difficult and large-scale logistics problem. The challenges include how many clusters we want to set up, how many vehicles we want to use, etc. In this paper, an actual earthquake event is studied through a simulation to provide insights on how to organize and execute effective and efficient humanitarian relief logistics planning. Even though humanitarian relief operations (or often called disaster relief operation) have attracted more research interest in the past few years, as early as 1996, Haghani and Oh (1) had proposed a multicommodity, multi-modal network flow model for disaster relief operations. The formulation of the problem was based on the concept of the time-space network and two heuristic algorithms were introduced. Furthermore, Fiedrich et al. (2) proposed a dynamic optimization model to find the best assignment of available resources to affected areas after an earthquake. Barbarosoglu et al. (3) developed a mathematical model for assigning helicopters tasks during a disaster relief operation. These two studies aimed at optimal resource assignments during the operation in order to make the operation more efficient. There are several studies in the literature from the perspective of the supplies or the supply chain inventory control. Horner and Downs (4) developed a flexible network flow model in a hurricane disaster relief to provide efficient transport linkages between critical elements of the relief goods’ supply chain. Ozbay and Ozguven (5) concentrated on development of the general humanitarian supply chain problem by proposing an efficient and quick-response humanitarian inventory management model that is able to determine the safety stock that will prevent disruptions at a minimal cost. Ukkusuri and Yushimito (6) considered the prepositioning of supplies for disasters and modeled it as a facility location problem accounting for the routing of vehicles and possible disruptions in the transportation network. In addition, the major interest of a disaster relief operation in academia is related to the logistics problem during and after the disaster. Ozdamar et al. (7) proposed the dynamic, time-dependent emergency logistics planning model for natural disasters. Sheu (8) introduced a hybrid method for the emergency logistics problem, which includes fuzzy clustering and multi-objective dynamic programming models. Additionally, a dynamic logistics coordination model for both evacuation and supplies support was formulated in Yi and Ozdamar (9). An analogous study was found in Yi and Kumar (10) in which the ant colony optimization approach was applied to dispatching commodities to distribution centers and meanwhile evacuate injuries to medical centers. Balcik et al. (11) considered a humanitarian relief chain problem and focused on allocating relief supplies and determining delivery schedules for each vehicle. Recently, Lin et al. (12) proposed a logistics model to delivery critical supplies in a disaster relief operation. The significant feature of their study was prioritizing supplies and penalizing delivery delays cumulatively to emphasize the different urgent needs for human beings in daily supplies. Based on the Lin et al. (12) model and the solution approach, a real-world earthquake scenario is studied in this paper. An earthquake is simulated by the software HAZUS to estimate the damage and economic losses based on the location and magnitude of the 1994 Northridge California earthquake in the United States. The output of the simulation is converted to useful information required in the logistics model in Lin et al. (12). A series of sensitivity analyses are conducted to provide insights on the influence of various resource settings to the efficiency and effectiveness of emergency logistics planning, such as the depot location, the number of vehicles, and the number of clusters chosen. We summarize our contributions in this paper as follows. First, we demonstrate that the risk of a disaster can be simulated through a comprehensive software package provided by the federal agency. Second, we generate useful data required in the mathematical model directly from the simulation output. Third, sensitivity analyses of parameters in the model are conducted to justify their influence on the relief operation performance. Finally, discussions of limitations in this research are provided to provide guidance on how to improve the precision of the analysis by considering more real world scenarios. Lin, Y-H, Batta, R., Rogerson, P.A., Blatt A. and Flanigan M. 4 HUMANITARIAN RELIEF MODEL AND SOLUTION ALGORITHM Lin et al. (12) proposed a multi-objective, multi-item, multi-vehicle, and multi-period logistics model to optimize delivery schedules of critical supplies in a disaster relief operation. In this paper, we only use their first objective (minimization of total penalty cost) as the objective function to simplify the analysis. The model was developed particularly for delivering relief supplies to disaster-affected areas immediately after a disaster occurs and then lasting for several time periods by a set of vehicles through the existing transportation network. Relief supplies considered in this model contain medicine, water, and food that are identified as the most important and needed supplies for daily living. More importantly, urgency levels of these three supplies are assigned based on the importance for human beings, with medicine as the highest priority, followed by water and then food. The demand of all periods in all locations is assumed known at the beginning of the planning, and it remains unchanged during the planning horizon. The amount of supplies in the distribution center is assumed unlimited. For each assignment of the delivery, a vehicle is assigned a tour to travel and deliver supplies. A tour is defined as beginning at the distribution center, continuing to one or more locations, and then returning to the distribution center. The model constructed in their paper is an integer programming model, and it is described here for the sake of completeness. The inputs include: (a) T: the set of planning time periods {1,2,...,t,...,tmax}, and tmax: total number of planning time periods; (b) Jk: the set of locations which the vehicle will visit on tour k; (c) dijt: demand of the supply i at cluster j in time t; (d) tk: travel time required for the tour k; (e) toi: tolerated delay time of supply i; (f) ai: unit weight of supply i; (g) bi: unit volume capacity of supply i; (h) H: total working time available in a single period; (i) W: the maximum loading weight of a vehicle; (j) V: the maximum volume capacity of a vehicle; (k) piu: the penalty cost of item i at delay level u, and piũ: the penalty cost of item i if there is remaining unsatisfied demand after the operation periods. The outputs of this model are: (a) xijklt: amount of item i delivered to cluster j on tour k by vehicle l in period t for the demand occurred exactly in period t; (b) ijklmn: backorder amount of item i delivered at cluster j on tour k by vehicle l in period m to satisfy demand in period n, where n < m, and m, n  T; (c) yklt: equal to 1 when tour k is assigned to vehicle l in period t, and 0, otherwise. Then the formulation of the model is summarized as follows: Minimize dijt − xijklt + ωijklvt t+u v=t+1 l k ∙ piu tmax −to i−u+1 t=1 tmax −to i u=1 j i + dijt t j − xijklt + ωijklmt m>t t l k j ∙ piu i (1) Subject to: tkyklt k ≤ H ∀l,∀t (2) xijklt ≤ Myklt ∀i,∀j ∈ Jk ,∀k,∀l,∀t (3) ωijkltn ≤ Myklt ∀i,∀j ∈ Jk ,∀k,∀l,∀t,∀n < t (4) xijklt l k t + ωijklmt t m>t l k ≤ dijt t ∀i,∀j (5) ai xijklt + ωijkltn n<t j i ≤ W ∀k,∀l,∀t (6) bi xijklt + ωijkltn n<t j i ≤ V ∀k,∀l,∀t (7) xijklt ≥ 0 ∀i,∀j ∈ Jk ,∀k,∀l,∀t (8) ωijklmn ≥ 0 ∀i,∀j ∈ Jk ,∀k,∀l,∀m ∈ T,∀n ∈ T (9) xijklt = 0 ∀i,∀jJk ,∀k,∀l,∀t (10) ωijklmn = 0 ∀i,∀j ∉ Jk ,∀k,∀l,∀m ∈ T,∀n ∈ T (11) yklt ∈ 0,1 ∀k,∀l,∀t (12) Lin, Y-H, Batta, R., Rogerson, P.A., Blatt A. and Flanigan M. 5 A brief explanation of the formulation is as follows. The objective function (1) is a penalty function that aims to minimize unsatisfied demand during the humanitarian relief operation including the sum of penalty cost incurred in various severe delay levels for different supplies within the operation and the penalty cost accrued if there is remaining demand of different types of supplies that cannot be delivered by the end of the operation. Equation (2) indicates that the total travel time of all tours for any single fleet in the same period cannot be violated available working hours in a single period. Equations (3) and (4) show that delivery units of items only can exist if corresponding tours are selected. Equation (5) shows that the total delivery amount of items cannot exceed the demand during the planning periods. Equations (6) and (7) are loading weight limit and the total volume limit of a fleet, respectively. Equations (8) – (11) are used to ensure that vehicles can only stop and deliver to clusters on tours assigned to them. Finally, equation (12) indicates yklt is a binary variable, indicating that if a tour k is selected at time t to fleet l. One of the challenges in the model is how to determine tours. One scenario is to enumerate all possible tour combinations of all visiting locations, though this becomes impossible when the size of the problem increases. The authors (12) suggested two heuristic approaches to keep the number of tours manageable in order to make the model tractable. One of the approaches, named Vehicle Assignment Heuristic (VAH), is suitable because of its ability of parallel computations. In short, the idea of VAH is that the original problem is divided into several sub-problems with manageable size and thus will make the enumeration of tours possible and practicable. The original problem can be solved by solving these small size problems in parallel. On the average, for the problem sizes examined, the VAH can find the solution within 7% of the optimality in 33 seconds. Due to the requirement of quick response in humanitarian relief logistics operations, we use the VAH as the solution algorithm in this paper. EARTHQUAKE DISASTER SIMULATION AND DATA COLLECTION The simulation of the earthquake disaster is executed by the software HAZUS-MH, which is developed by FEMA and is a risk assessment methodology for analyzing potential losses in floods, hurricane winds, or earthquakes. In this paper, the earthquake model in HAZUS-MH MR3 patch 2 version is employed, and it is simulated in the desktop computer with 2.00 GB RAM and with Intel Pentium D 3.40 GHz processor. In addition, the interface and analysis of running HAZUS-MH is on the geographic information system software ArcGIS 9.2 version. More information about the earthquake model in HAZUS-MH can be found at this website (www.fema.gov/plan/prevent/hazus) and in the user manual (13). Earthquake Scenario and Study Region We selected the Northridge earthquake in California because, in the past 20 years, it was the most catastrophic earthquake in the continental United. The Northridge earthquake occurred on Jan. 17, 1994 at 4:31 AM PST in Reseda, California, which is a neighborhood in the city of Los Angeles, California. The epicenter was at 3412’47’’N, 11832’13’’W and it had a recorded depth of 17 km. The earthquake had 6.7 moment magnitude and one of earthquakes with the highest ground accelerations in an urban area in North America. The study region is the Los Angeles County, California. The geographical size of this region is 4,086.9 square miles and it contains 2,054 census tracts. There are over 3,133,000 households in the region and a total population of 9,519,338 people (2000 Census Bureau data). There are an estimated 2,118,000 buildings (approximately 96.00 % of the buildings are associated with residential housing) in the region with a total building replacement value (excluding contents) of 691,005 million dollars. The replacement value of the transportation and utility lifeline systems is estimated to be 25,498 and 7,421 million dollars, respectively.