Defensive Resource Allocation: The Roles of Forecast Information and Risk Control

Abstract

In defensive resource allocation problems, the defender usually collects some forecast information about the attacker. However, the forecast information may be incorrect, which means that there could be a risk associated with the defender using it in their decision making. In this article, we propose a forecast and risk control (FRC) framework to manage the risk in defensive resource allocation with forecast information. In the FRC framework, we introduce a new measure of risk and three types of defense plans: riskless defense plan, risky defense plan, and risk‐control defense plan. Several desirable properties based on the concepts of reward and penalty show that the risk‐control defense plan is a general form to support defensive resource allocation. Subsequently, we study a specific defensive allocation problem with forecast information and develop an optimization model that considers the forecast information and the defender's risk tolerance level in order to obtain the risk‐control defense plan with maximum reward. Furthermore, we provide some numerical analysis to illustrate the effects of forecast information and risk tolerance level on the risk‐control defense plan. Finally, a numerical case study is presented to demonstrate the usability of a risk‐control defense plan.

Науково-Методичний Апарат Оцінювання Уразливості Системи Охорони Державного Кордону

“…У роботі Yucheng Dong, Xia Chen, Kyle Hunt, Jun Zhuang [6] подано структуру прогнозування та контролю ризиків для обґрунтування розподілу ресурсів в оборонній сфері. Така концепція в цілому застосовується для обґрунтування розподілу ресурсів у Державній прикордонній службі України під час підготовки до оперативно-службової діяльності на наступний рік.…”

Assessing the option water‐saving willingness of irrigation areas considering farmers’ risk tolerance

“…Considering the risk tolerance of subjects, Ceder et al (2013) and Holden and Quiggin (2017) respectively explored tourists' travel route preferences and farmers' choice of maize varieties using cumulative prospect theory. For defense resource allocation, Dong et al (2021) proposes an optimization model that incorporates forecast information and the subject's risk tolerance to obtain the optimal risk control scheme. In terms of agricultural water management, considering the heterogeneous risk tolerance of decisionmakers for water scarcity, Yue et al (2022) proposed an interval linear programming model to identify the nonstationary disturbance of water allocation in irrigation areas.…”

“…Risk tolerance can be interpreted as the willingness or ability of decisionmakers to take risks. (Dong et al., 2021; Holden & Quiggin, 2017; Linner et al., 2019). Considering that the interests of farmers are attached to the irrigation area, heterogeneous risk tolerance will affect their OWSW when they face the group decision of water‐saving in the irrigation area.…”

Counterterrorism resource allocation during a pandemic: The effects of dynamic target valuations when facing a strategic terrorist

“…In the counterterrorism literature (Aziz et al., 2020; Dong et al., 2021; Institute for Economics & Peace [IEP], 2014; Wang & Bier, 2016), the total valuation of a target usually consists of two parts: casualties and the property damages, and the former part directly depends on the population flow at a specific target. Given that the primary motivation behind many terrorist attacks is to inflict casualties (Phillips, 2013), the value of a specific target should closely depend on the number of people who are occupying that target.…”