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. 2017 Jul 31;12(7):e0181482. doi: 10.1371/journal.pone.0181482

Table 1. Summary of the model parameters and variables.

Symbol Parameter / variable name Description
Parameters:
j Potential survey sites in a defined regulated area jJ
J Size of the defined regulated area J > 0
s Stochastic spread scenarios sS
S Total number of stochastic spread scenarios 2400*
Nj Number of host trees at a site j Nj ≥ 0**
θjs Proportion of trees at a site j in a scenario s that are infested θjs ∈ [0; 1]***
β Proportion of a site's area that is surveyed β ∈ [0; 1]
γ Pest detection rate after inspecting a tree γ ∈] 0; 1]
d, 1—D Probability of eradication success d ∈] 0; 1]
d0 Probability value that denotes eradication failure 1e-64
p Minimum proportion of the scenarios where eradication is expected to succeed with the probability d (safety margin) P ∈] 0; 1]
α Confidence level that defines the value in the program costs distribution that can be exceeded only in (1 –α)*100% of worst scenarios 0.99
cj Tree survey cost $6.83 tree-1
tj Tree removal cost $1000 tree-1
F Weighting parameter that defines decision-making preferences towards minimizing the expected cost vs. minimizing the cost in the right tail of the cost distribution in the objective function equation F∈ [0; 1]
Decision variables:
xj Binary survey selection of a site j xj ∈ {0,1}**
Rjs Number of host trees removed at a surveyed site j in a scenario s Rjs ∈ [0; Nj]***
gs Binary indicator variable that specifies eradication success (or failure) for a scenario s gs ∈ {0,1}****
ws Auxiliary decision variable for a linearized formulation of CVaRα ws ≥ 0
ζ Auxiliary decision variable for a linearized formulation of CVaRα ζ ∈ ℜ

* The number of scenarios was chosen based on the optimality gap analysis.

** The parameter / variable value is site-specific.

*** The parameter / variable value is site and scenario-specific.

**** The parameter / variable value is scenario-specific.