Table 1. Summary of the model parameters and variables.
Symbol | Parameter / variable name | Description |
---|---|---|
Parameters: | ||
j | Potential survey sites in a defined regulated area | j ∈ J |
J | Size of the defined regulated area | J > 0 |
s | Stochastic spread scenarios | s ∈ S |
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.