برنامه ریزی موجودی و هماهنگی در تلاش های امداد رسانی

This research proposes a stochastic programming model to determine how supplies should be positioned and distributed among a network of cooperative warehouses. The model incorporates constraints that enforce equity in service while also considering traffic congestion resulting from possible evacuation behavior and time constraints for providing effective response. We make use of short-term information (e.g., hurricane forecasts) to more effectively preposition supplies in preparation for their distribution at an operational level. Through an extensive computational study, we characterize the conditions under which prepositioning is beneficial, as well as discuss the relationship between inventory placement, capacity and coordination within the network.

Coordinating emergency supplies during the aftermath of a disaster is one of the main challenges associated with immediate response efforts. Information about available resources is often unknown and contributions of suppliers can be unpredictable (Kovacs and Spens, 2007). Adding to the challenge is the fact that the disaster relief environment in large-scale, catastrophic events often involves many actors such as non-governmental organizations (e.g. Red Cross); various local, state, and federal government agencies (e.g. FEMA); faith based organizations (e.g. churches); and firms in the private sector (e.g. local grocers). Some organizations function autonomously providing specialized products (e.g. food, water) or services (e.g. medical assistance, sheltering.). Others work within a larger collaborative structure led by either the governmental authority of the affected area (NRF, 2008) or a coordinating agency such as the United Nations Joint Logistics Center (Kaatrud et al., 2003 and Balcik et al., 2010). Most scholars agree that coordination can improve effectiveness of initial response efforts (e.g. Stephenson, 2005, Van Wassenhove, 2006, Chandes and Pache, 2010 and Balcik et al., 2010). However, coordination can also be quite challenging as evidenced by the Indian Ocean tsunami. The relief operation for this particular disaster was described as “chaotic” due to the large influx of new and inexperienced organizations and volunteers, an overwhelmed government, and an absence of regulatory measures to control and manage the entry of volunteers and goods (Van Wassenhove, 2006). A number of quantitative models in the disaster relief literature have addressed issues related to inventory management such as inventory placement/prepositioning, determining quantities of relief supply to stock in advance of a disaster, and determining how the inventory should be distributed post-disaster. However, inventory coordination during disaster relief efforts has largely been unexplored. There is some evidence that inventory coordination in the form of sharing information and/or warehouse space occurs during disaster relief efforts (Balcik et al., 2010). For example, the UN Humanitarian Response Depot supports strategic stockpiling efforts of the UN, international, governmental and non-governmental relief organizations (www.hrdlab.eu). The state of Florida has a logistics warehouse to coordinate the efforts of state and federal responders (SLRC, 2012). However, many non-governmental organizations that participate in disaster relief have their own warehouse network where they stock supplies. For example, Feeding America, a non-profit hunger relief organization, has warehouses across the United States where they receive donated food. Some faith based organizations (e.g. Church World Service, United Methodist Committee on Relief) that participate in disaster relief activities through the Voluntary Organizations Against Disasters (VOAD) own warehouses that stock relief supplies. Coordination among these various participants requires accurate information as well as frequent communication regarding the availability of their resources. Better planning and information regarding disaster resources will help to eliminate redundancy, duplication of effort and potentially unused supply. In this paper, we address inventory management decisions in the context of coordination. Specifically we consider the problem of prepositioning local and external supplies within a cooperative distribution network prior to an upcoming natural disaster, such as a hurricane. The term local refers to supplies that are stored close to the affected area and perhaps managed by a local governmental authority. External supplies refer to those goods available from an outside agency. We define a cooperative distribution network as a group of entities who normally act autonomously, but under severe disaster conditions, try to come together to provide assistance and aid to the affected population. We explore a specific coordination structure characterized by two parameters: reserve capacity (warehouse space) and inventory commitment (relief supplies) and identify conditions under which coordination and supply allocation decisions are beneficial. We take into consideration road congestion resulting from (i) pre-disaster evacuation activities and (ii) post-disaster road damage. Prepositioning is not a new concept, as the military has used this for quite some time (Johnstone et al., 2004). However, it is becoming more widely studied and applied in the context of emergency response (e.g. Duran et al., 2011; Lodree and Taskin, 2009 and Rawls and Turnquist, 2010 ). The majority of the research on prepositioning occurs at the strategic level addressing long-term supply network decisions such as where to establish supply locations, and how much material to stock there. The best location is weighed against disaster uncertainty (demand for resources) through the use of probability distributions that represent the likelihood of potential disaster scenarios. The majority of the data used to determine these probability distributions are historical in nature; that is they do not often incorporate information such as forecasted hurricane paths that affect the probability a particular site will be affected by a disaster. The model presented in this paper incorporates forecasted hurricane path and intensity to determine how best to preposition supplies in an established single commodity supply network where one or more of the nodes is in a high-risk path for a particular event. This situation could arise either when strategic prepositioning decisions have been made, or when an existing network is already used to service the community. Since the network under consideration already exists, the problem we consider makes no location decisions. We instead consider the relocation of supplies in advance of a disaster to minimize the possible destruction of those goods, and to aid the distribution of supplies to service those affected by the disaster after it occurs. In our context, relocation of supplies can be considered repositioning rather than prepositioning. However we adopt the term prepositioning as the supplies are positioned prior to the occurrence of the disaster event. We consider uncertainty in demand and available supply and use a stochastic linear programming model to determine the placement of supply within the network to minimize the number of people who cannot be served post-disaster. In addition, we address the uncertainty in the location of the disaster using short-term forecasts such as those available prior to hurricanes. This paper makes the following contributions to the literature. The problem we consider is in the preparedness domain (vs. post-response). To the best of our knowledge, this is the first paper in the preparedness domain to consider inventory coordination in emergency planning. Secondly, we consider uncertain supply as well as uncertain demand. It should also be noted that the majority of papers consider historical information to determine where to preposition supplies. In contrast, we consider short-term forecasts to determine where to preposition supplies so as to prevent damage to supplies, while also considering timely service to those affected by the disaster. Lastly, we examine the impact of coordination in the network to provide improved response post-disaster. The coordination decisions considered determine (1) how much supply from external suppliers to preposition, (2) how much local (internal) supply to reposition, and (3) where the external/internal prepositioning activity should take place in the network. Since the first 72 h following a disaster are critical (Salmeron and Apte, 2010), coordination is characterized as a function of the response time and average fill rate. Lastly, we explore the impact of the coordination decisions from a cost and service perspective. The remainder of the paper is organized as follows. In Section 2 a review of related literature is presented. The model and assumptions are presented in Section 3. Section 4 outlines the numerical study considered in this work, including the specific research questions that are addressed and assumptions made regarding the data used. Computational results are reported in Section 5, followed by concluding remarks in Section 6.

We have developed a model that illustrates how to perform inventory management coordination in the event of an extreme event such as a hurricane. Our model confirms that the optimal solutions we obtain are intuitive. This is helpful in that a planner's intuition can help guide the repositioning of inventory to safe locations to avoid supply loss. In particular, shelters should coordinate with the closest non-affected warehouses when determining what quantities should be positioned and how those supplies should be distributed to the affected counties based on the desired response time. Our model is helpful in that it can quantify the value of coordination within disaster relief efforts and provides solid backing for this rationale. We characterize the level of service that can be achieved under different coordination mechanisms. In particular, we have identified the amount of relief supply that is necessary to satisfy the needs of the affected population after the event, based on a management determined threshold level. This model is flexible enough to incorporate effects of non-availability of warehouses as a result of multiple areas being affected by a hurricane, as well as other forms of collaboration. While we have only considered two collaboration cases in the experiment (limited and no coordination), other collaborative mechanisms can be explored by adjusting the capacity and inventory parameters of the non-affected warehouses. The non-affected warehouses could also serve as inventory locations of potential donors and other governmental suppliers. We can also consider multi-state disasters by carefully selecting the affected area based on the forecast path over a 5 day period. A key challenge of this approach is estimating the demand as a result of the different hurricane scenarios. Better forecasting as it relates to the relationship between demand and hurricane intensity is critical as this determines the optimal solution.