A Multistage Stochastic Programming Approach to the Optimal Surveillance and Control of the Emerald Ash Borer in Cities

Abstract

Emerald ash borer (EAB), a wood-boring insect native to Asia and invading North America, has killed untold millions of high-value ash trees that shade streets, homes, and parks and caused significant economic damage in cities of the United States. Local actions to reduce damage include surveillance to find EAB and control to slow its spread. We present a multistage stochastic mixed-integer programming (M-SMIP) model for the optimization of surveillance, treatment, and removal of ash trees in cities. Decision-dependent uncertainty is modeled by representing surveillance decisions and the realizations of the uncertain infestation parameter contingent on surveillance as branches in the M-SMIP scenario tree. The objective is to allocate resources to surveillance and control over space and time to maximize public benefits. We develop a new cutting-plane algorithm to strengthen the M-SMIP formulation and facilitate an optimal solution. We calibrate and validate our model of ash dynamics using seven years of observational data and apply the optimization model to a possible infestation in Burnsville, Minnesota. Proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. Our comparative analysis shows that the M-SMIP model outperforms six different heuristic approaches proposed for the management of EAB. Results from optimally solving our M-SMIP model imply that under a belief of infestation, it is critical to apply surveillance immediately to locate EAB and then prioritize treatment of minimally infested trees followed by removal of highly infested trees. Summary of Contributions: Emerald ash borer (EAB) is one of the most damaging invasive species ever to reach the United States, damaging millions of ash trees. Much of the economic impact of EAB occurs in cities, where high-value ash trees grow in abundance along streets and in yards and parks. This paper addresses the joint optimization of surveillance and control of the emerald ash borer invasion, which is a novel application for the INFORMS society because, to our knowledge, this specific problem of EAB management has not been published before in any OR/MS journals. We develop a new multi-stage stochastic mixed-integer programming (MSS-MIP) formulation, and we apply our model to surveillance and control of EAB in cities. Our MSS-MIP model aims to help city managers maximize the net benefits of their healthy ash trees by determining the optimal timing and target population for surveying, treating, and removing infested ash trees while taking into account the spatio-temporal stochastic growth of the EAB infestation. We develop a new cutting plane methodology motivated by our problem, which could also be applied to other stochastic MIPs. Our cutting plane approach provides significant computational benefit in solving the problem. Specifically, proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. We calibrate and validate our model using seven years of ash infestation observations in forests near Toledo, Ohio. We then apply our model to an urban forest in Burnsville, Minnesota, that is threatened by EAB. Our results provide insights into the optimal timing and location of EAB surveillance and control strategies.

Optimizing surveillance and management of emerald ash borer in urban environments

“…We have not considered the preventive removal of all trees at a survey site, which is applied in practice to avoid the need to monitor all trees because this strategy has been shown to provide worse solutions compared to the optimization model in the study of Kıbış et al (2020). Specifically, Kıbış et al (2020) have performed a comparative analysis of a previous version of our multistage stochastic optimization model with stage removal and monitor-and-remove strategies currently employed by the cities of Minneapolis and Saint Paul for the management of EAB. Their results show that significant benefits are obtained by using the complex multistage stochastic programming model as opposed to the simple approaches currently employed, including preventative removal without surveillance and prophylactic removal of some ash tree population after surveillance.…”

“…To account for EAB spread, we apply a distance-dependent estimation of spread probabilities at four 1-km distance classes from the infested sites, as opposed to the 1-level spread considered in Kıbış et al (2020). This spread model captures the short-range spread of EAB in urban environments, as suggested by records from previous EAB surveys in Twin Cities, Minnesota (Osthus, 2017).…”

“…In this section, we present a revised version of the multistage stochastic mixed-integer formulation originally proposed by Kıbış et al (2020) for the optimal surveillance and control of EAB. This modified formulation improves over the former one by addressing critical issues regarding the surveillance uncertainty as well as the dynamic probabilities of uncertain surveillance outcomes.…”

“…Onal et al (2019) present a multiperiod simulation‐optimization framework to find the optimal search path for locating and controlling the infestation of a biological invader. Kıbış et al (2020) addressed the problem of joint optimization of surveillance and control decisions with a multistage stochastic mixed‐integer programming (MSS‐MIP) formulation that extended the time horizon to five stages and applied that model to the management of EAB in Burnsville, Minnesota, USA. MSS‐MIP combines the complexity of stochastic programming with a mixed‐integer programming model and represents an NP‐hard combinatorial problem.…”

“…In our multistage model, the number of variables, constraints, and scenarios increases exponentially for each additional time period. Therefore, to improve on the solution time and memory, we apply cutting planes and a preprocessing algorithm adapted from Kıbış et al (2020). These cutting planes helped improve the solution time by a factor of 10+ compared to the standard approach without using cutting planes.…”