A Dynamic Programming Approach to Determining Optimal Forest Wildfire Initial Attack Responses
A Dynamic Programming Approach to Determining Optimal Forest Wildfire Initial Attack Responses
复制标题
确定最佳森林野火初始攻击响应的动态规划方法
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发表时间：
2003
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通讯作者：
M. Wiitala
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作者：
M. Wiitala
提出了一种基于确定性动态规划运筹学技术的数学优化模型，用于快速搜索可选方案，寻找经济有效的初始攻击资源集来扑灭野火。在选择初始攻击资源以进行有效的初始响应时，需要考虑的因素包括运输和使用成本、线路建设生产率、响应时间、资源互补性、发现时的火灾规模、火灾蔓延速度、火灾损害、清理成本和火灾效益。调度优化模型在制定预先计划和实时调度以及评估新的初始攻击技术的经济效益等方面具有广泛的应用。多年来，迅速而有力的初步反应被认为是成功扑灭森林火灾的关键。为了实现这一目标，使用最接近的力量标准来选择被认为是初始攻击努力所必需的压制资源。许多早期的支持性研究都集中在寻找最接近力的自动化过程上（Mees 1978）。人们很少关注最初的攻击反应成本，以及与火灾规模相关的成本和资源损失可能造成的经济权衡。在过去的二十年中，维持一个足够规模的初始攻击组织以做出快速而有力的初始攻击反应的成本稳步而显著地增加。面对日益紧缩的预算，调度员对平衡初始灭火反应的成本和减少火灾规模的好处变得更加感兴趣。作为回应，研究人员开始探索形式化的方法来帮助调度员选择最有效的初始攻击抑制响应。甚至在关注经济效率之前，Parks（1964）就提出了寻找经济上最优抑制努力的解析解。当效率问题变得更加紧迫时，帕拉尔和维克森（1982）重新审视了帕克斯的模型。他们提供了一种利用控制理论中的优化技术的替代解决方案。这两个模型都集中在最有效的规模和时间的总体抑制努力。两种模型都没有考虑到个体灭火资源在响应时间、线路建设率和其他重要消防特征方面的差异对调度决策的重要性。由于这些考虑因素过去是，现在仍然是分派决策的重要方面，因此这两个模型都无法运行。在随后的研究发展中，考虑了资源差异对调度决策的重要性。在这一领域的一次尝试是由维塔拉（1986）发起的，他率先使用动态规划来寻找成本效益高的调度。库尔兹（1989）也采用了类似的方法来派遣水轰炸机和用直升机运送机组人员。尽管Wiitala（1986）试图考虑所有初始攻击抑制成本，但Kourtz（1989）的动态规划算法只最小化了运输成本。库尔兹（1989）没有正式考虑资源损失或其他类型的压制相关成本，也没有考虑攻击强度的经济性。这篇论文的缩略版在1999年4月5日至9日在加州圣地亚哥举行的“火灾经济学、规划和政策：底线”研讨会上发表。美国农业部太平洋西南研究站运筹学分析师，林务局，1221西南Yamhill街，200套房，波特兰，俄勒冈97205。e -mai 1: mwi - i - ta / r6pnw_ Portland@fs.fed.us美国农业部林业局总技术代表PSW-GTR-173。1999. 在确定适当的灭火响应时，注重效率的调度员要考虑所有的成本和损失。必须在扑灭努力的费用和与火灾规模有关的费用和损失之间取得平衡。然而，由于分散在许多位置上的大量初始攻击资源具有广泛的特征，找到具有成本效益的调度是一项困难的任务。对于每个可用的抑制资源，调度员必须知道它的位置、运输成本、线路建设成本、线路建设速度和响应时间。同样重要的是资源之间的线构建交互以及影响资源性能强度和持续时间的任何约束。即使只有30种不同的资源可供选择调度，可以有效控制火灾的组合数量也可以轻松达到数百万种。有这么多的选择，如果没有计算机和运筹学技术的帮助，确定最有效的组合来调度火灾几乎是不可能的。本文提出了一种运筹学技术，可以帮助具有效率意识的调度员快速确定合适的初始攻击响应。这个目标分两个步骤实现。第一步给出了野火调度优化问题的一般数学表达式。第二步对一般数学优化问题进行了重新表述，允许使用确定性动态规划技术实现经济高效的调度。由于有许多可用于响应火灾的资源，可能的调度数量可能非常大。每次调度都有自己的火线建设轨迹、控制时间和成本概况。此配置文件将取决于所派遣资源的类型、到达时间和生产速率。假设立即派遣资源并建立火线直至火势被控制，则控制成本J可以正式表示为：J =∑xi (C0i + C1i (t - bi)) + C2(a(t)) + C4(t) [1]
A mathematical optimization model, based on the operations research technique of deterministic dynamic programming, is offered as a method to search quickly through available options to find the economically efficient set of initial attack resources to suppress a wildfire. Considerations in selecting initial attack resources for an efficient initial response include cost of transportation and use, line construction productivity, response times, resource complementaries, size of fire upon discovery, rate of fire spread, fire damage, mop-up cost, and fire benefits. The dispatch optimization model has several applications, such as developing pre planned and real-time dispatches and evaluating the economic efficiency of new initial attack technologies. For many years a quick and strong initial response was deemed paramount to successfully suppressing a forest fire. To achieve this objective, the criterion of closest forces was used to select the suppression resources deemed necessary for the initial attack effort. Much of the early supporting research focused on automating the process of finding closest forces (Mees 1978). Little attention was given to the cost of the initial attack response and the economic trade-offs that could be made with costs and resources losses associated with fire size. Over the past two decades the cost of maintaining an initial attack organization of sufficient size to make quick and strong initial attack responses increased steadily and significantly. Facing ever tightening budgets, dispatchers became more interested in balancing the cost of the initial suppression response against the benefit of reducing fire size. In response, researchers began to explore formal methods to help dispatchers select the most efficient initial attack suppression response. Even before the concern with economic efficiency, Parks (1964) presented an analytic solution for finding the economically optimal suppression effort. When the efficiency issue became more pressing, Parlar and Vickson (1982) revisited Parks' model. They offered an alternative solution using optimization techniques from control theory. Both models focused on the most efficient size and timing of the general suppression effort. Neither model considered the importance to the dispatch decision of differences among individual suppression resources in response times, line building rates, and other significant fire fighting traits. Because these considerations were and remain important aspects of the dispatch decision, neither model became operational. In subsequent research developments, resource differences important to the dispatch decision were considered. A foray in this area was initiated by Wiitala (1986) in pioneering the use of dynamic programming to find cost-effective dispatches. A similar approach was taken by Kourtz (1989) for dispatching water bombers and for delivering crews by helicopter. Although Wiitala (1986) attempted to account for all initial attack suppression costs, the dynamic programming algorithms by Kourtz (1989) minimized only transportation cost. Kourtz (1989) did not formally consider resource loss or other types of suppression related costs nor the economics of the strength of the attack. An abbreviated version of th i s paper was p resen ted at the Symposium on Fire Economics, Planning, and Policy: Bottom Lines, April 5-9, 1999, San Diego, California. Operations Research Analyst, Pacific Southwest Research Station, Forest Service, U.S. Department of Agriculture, 1221 SW Yamhill St., Suite 200, Portland, Oregon 97205. e -mai l : mwi i ta la / r6pnw_ Portland@fs.fed.us USDA Forest Service Gen. Tech. Rep. PSW-GTR-173. 1999. 115 Session III Optimal Forest Wildfire Responses---Wiitala In determining an appropriate suppression response, the efficiency-minded dispatcher considers all costs and losses. A balance must be struck between the cost of the suppression effort and those costs and losses associated with fire size. However, finding the cost efficient dispatch is a task made difficult by the availability of numerous initial attack resources dispersed over many locations that exhibit a wide range of characteristics. For each available suppression resource the dispatcher must know its location, transportation cost, line building cost, line construction rate, and response time. Also important are line building interactions between resources and any constraints affecting the intensity and duration of a resource's performance. Even with a modest 30 different resources from which to choose a dispatch, the number of combinations that can feasibly contain a fire can easily range into the millions. With so may choices, identifying the most efficient combination to dispatch to a fire is nearly impossible without assistance of computers and operations research techniques. This paper presents an operations research technique that can help the efficiency-minded dispatcher quickly identify an appropriate initial attack response. This objective is accomplished in two steps. The first step sets forth a general mathematical formulation of the wildfire dispatch optimization problem. The second step reformulates the general mathematical optimization problem to permit using the technique of deterministic dynamic programming to achieve an economically efficient dispatch. Model Formulation With many resources available to respond to a fire, the number of possible dispatches may be very large. Every dispatch will have its own fireline building trajectory, containment time, and cost profile. This profile will depend on the types, arrival times, and production rates of dispatched resources. Assuming resources will be sent immediately and will build fireline until the fire is contained, the cost of containment, J, can be formally stated as: J = ∑ x i (C0i + C1i (t − bi )) + C2(a(t)) + C4(t) [1]