مدل هایی برای مسیریابی امداد: عدالت، بهره وری و اثر بخشی

In humanitarian relief operations, vehicle routing and supply allocation decisions are critically important. Similar routing and allocation decisions are studied for commercial settings where efficiency, in terms of minimizing cost, is the primary objective. Humanitarian relief is complicated by the presence of multiple objectives beyond minimizing cost. Routing and allocation decisions should result in quick and sufficient distribution of relief supplies, with a focus on equitable service to all aid recipients. However, quantifying such goals can be challenging. In this paper, we define and formulate performance metrics in relief distribution. We focus on efficacy (i.e., the extent to which the goals of quick and sufficient distribution are met) and equity (i.e., the extent to which all recipients receive comparable service). We explore how efficiency, efficacy, and equity influence the structure of vehicle routes and the distribution of resources. We identify trends and routing principles for humanitarian relief based on the analytical properties of the resulting problems and a series of computational tests.

Recent disasters have increased attention on the effectiveness of humanitarian aid; there is increased pressure from donors on relief agencies to show that pledged aid and goods are reaching those in need quickly (Van Wassenhove, 2006). This has led to a larger focus on improving humanitarian relief logistics. The recent large scale disasters and relief efforts (e.g., 2004 Asian tsunami, 2005 Pakistan earthquake, 2010 Haiti earthquake) highlight the need for improved logistics in the field. For example, following the Tsunami, the amount of pledged relief overwhelmed the relief agencies’ ability to properly store and distribute the aid (Russell, 2005). Given the trends in the impact of disasters on vulnerable populations and economies worldwide and the criticality of logistics in humanitarian relief operations, it has been increasingly highlighted that Operations Research (OR) can help improve the logistics of humanitarian aid (Van Wassenhove, 2006). This paper focuses on last-mile distribution in a humanitarian relief chain from a distribution center to beneficiaries (Balcik et al., 2008). Relief supplies must be delivered quickly in sufficient amounts. Given limitations in transportation resources and relief supplies, and damaged infrastructure, it is challenging to plan last mile operations (Balcik et al., 2008). Distribution decisions are often made ad hoc, which may lead to inefficient use of resources, slow response, and inadequate or inequitable relief deliveries. The classical vehicle routing problem (VRP) minimizes total transportation costs; in humanitarian relief, one is primarily concerned with whether the routes are able to deliver the aid quickly. Focusing on relief response times, Campbell et al. (2008) show that the choice of objective affects how aid is distributed. With alternative objectives of minimizing the last arrival time and minimizing the sum of arrival times, the authors demonstrate that superior service times may be achieved than those resulting from a traditional VRP objective. They show that minimizing total routing costs results in solutions with longer response times. Equitable aid distribution among recipients is also a critical consideration in humanitarian relief (Beamon and Balcik, 2008). However, equity may be hard to define both in practice and for modeling purposes. In this paper, we characterize equity in terms of the disparity between service levels among aid recipients, where service levels are characterized by delivery speed and amount. Even so defined, it is not clear how equity should be modeled. Furthermore, it is not obvious how different and potentially conflicting objectives of equity, efficacy and efficiency affect the route structures in the relief context. Balcik et al. (2008) present an analysis of last mile operations and show how modeling these operations with all the associated complexities can make it difficult to study the underlying differences in route design that occur. Our goal in this paper is to simplify the modeling of last mile distribution to a more stylized setting where we can more easily gain insights into the effects of equity and other considerations in relief distribution. We refer to this problem setting as the last-mile delivery problem (LMDP). The LMDP designs vehicle routes and distribution schedules for a fleet of vehicles delivering supplies from a distribution center, yet unlike Balcik et al. (2008), we focus on a single period problem where each vehicle performs at most one trip to deliver one commodity type. Although more restricted than Balcik et al. (2008), our problem setting still captures many critical characteristics of the last mile environment; in particular, the LMDP in this paper would well address relief operations in rural areas where each vehicle can perform only one trip per period and supplies are distributed in the form of standard packages/pallets. Relief organizations often make daily distribution plans rather than considering multiple days ahead, especially during the initial phases of the emergency due to the chaotic environment and lack of reliable information (Mantyvaara, 2010). An example of LMDP routes is presented in Fig. 1. The demand of a site can be satisfied by more than one vehicle in the LMDP, similar to the Split Delivery Vehicle Routing Problem (SDVRP). The SDVRP is motivated by the potential savings in costs due to splitting demand among multiple vehicles (Dror and Trudeau, 1989). Split deliveries in last mile relief distribution can allow one to quickly serve large demands using limited resources. Our problem setting allows us to analyze the impact of different objectives on route structures and the performance of aid distribution, in terms of (i) efficiency (transportation costs), (ii) efficacy (quick and adequate response), and (iii) equity (fairness as measured by deviations between recipients in efficacy). The incorporation of equity in particular leads to unique challenges.We develop a set partitioning model for the LMDP to incorporate alternative objectives, based on efficiency, efficacy and equity metrics. Analytical properties of the LMDP models are examined. A numerical study of small instances, in which it is possible to obtain optimal solutions for each of the objectives, is conducted to develop insights into route characteristics. Our analysis shows that there exist substantial differences among solutions that attempt to minimize efficiency compared to those that are concerned with efficacy and equity. Heuristics are developed to solve large instances of the LMDP variations. This paper is organized as follows: in Section 2, we review the relevant literature. Section 3 gives a detailed description and analysis of the LMDP variations. Section 4 proposes heuristics for the LMDP variations. Section 5 discusses practical implications of this work and future directions.

This paper formulates efficacy and equity metrics and shows that there is a significant difference between solutions that focus on both efficacy and equity and solutions that focus on the traditional commercial concern of efficiency. In the following sections, we discuss the implication of our findings. 5.1. Practical implications The results from this paper provide several insights for relief operations. In practice, relief organizations tend to utilize a vehicle fleet consisting of many small vehicles, unlike in commercial settings where large vehicles are available and may be preferable to achieve economies of scale. The organizations acquire transportation resources locally as maintaining and shipping large vehicles long distances, especially overseas, can be very expensive and time consuming. Further, local drivers are more knowledgeable of the regions’ geography and customs. Characteristics of the post-disaster transportation network affect vehicle selection decisions; for instance, remote locations in a rural area may only be accessed by small trucks. Observation 1 suggests that operating a large number of small vehicles has the additional benefit of resulting in more effective and equitable aid distribution at the expense of a modest increase to traveling and operating costs (e.g., costs of fuel, drivers, etc.). While having a large fleet of small vehicles is beneficial in improving the efficacy and equity of relief deliveries, operating and coordinating a large fleet might be difficult for relief logisticians in the field. For instance, the logistics coordinator of the Finnish Red Cross was responsible for coordinating a fleet of 150 trucks from a single warehouse during the relief operations after the Pakistan earthquake in 2005 (Mantyvaara, 2010). While there is an increasing effort to develop and improve the logistics software in the relief sector, the current software is mostly used for tracking, monitoring and reporting purposes and lacks modules that would support operational decisions. Indeed, routing and delivery scheduling decisions are made mostly according to the insights and experiences of the logisticians. Our heuristics described in Section 4 are efficient and easy to understand, and hence could be a valuable decision support tool to manage large scale last mile operations, if embedded in such software. Observations 2 and 3 focusing on route shape dependent on objective and node demand represent a first step to developing even simpler rules-of-thumb so that a coordinator may make decisions without advanced computing resources. In humanitarian relief environments, there may be large differences between the needs of populations at different locations. Although Formulation (1) does not explicitly differentiate populations in terms of their vulnerabilities, our heuristic approach can easily incorporate the criticality and urgency of the needs at different locations. Specifically, relief supply deliveries can be prioritized by modifying βi and τ values so that vehicles can reach more vulnerable locations first. While setting the β values, it is also important to evaluate the characteristics of the relief network. As discussed earlier, while splitting may help achieve more equitable and effective solutions, it also increases travel costs. Moreover, in regions where the transportation network is damaged and security is a concern, or when access to certain locations is problematic for other reasons such as poor weather conditions, relief organizations may prefer satisfying the demand of a location in a single delivery if possible. In such cases, a small β value leading to few splits may be more reasonable. 5.2. Future work One avenue of extension to this work is to analyze the LMDP variations under uncertainty, both in relaxing demands and travel times. In the chaotic environment that follows the immediate aftermath of a disaster there is significant uncertainty. For instance, demand is not immediately known and can only be roughly estimated. Also, travel times between two locations can be uncertain due to damaged infrastructure and unreliable information regarding the road conditions. Therefore, insights into the behavior of efficiency, efficacy, and equity under a stochastic setting would be valuable. Another avenue of focus is to use the insights gained to generate rule-of-thumb solutions that are easy to find and simple to implement. Because relief agencies often lack technology and computational resources, solutions which may be implemented by hand would be valuable. Rule of thumb solutions would also be quick to calculate and in planning stages could serve as an approximation for costs until more sophisticated solutions are found. Our analysis of stylized distribution problems is an important first step in this area. To gather insight on how to address concerns of efficiency, efficacy and equity, the LMDP has been separated into three variations. However, in practice, agencies must handle these concerns concurrently. Therefore, it may be important to consider a multi-objective variation of the LMDP which combines the three factors into a single objective.