Table 1.
Description of model parameters and assumed values based on expert elicitation and estimates.
Fig 1.
Reefs in AIMS dataset dispersed along the coast of Queensland.
Total set of 2816 reefs are size-scaled by area. A subset of the 50 randomly chosen reefs used for the case study are coloured by cluster, with the remaining reefs coloured grey. Port locations are coloured black. Reprinted from [36] under a CC BY license, with permission from d-maps.com, original copyright 2021.
Fig 2.
Proportional survival plot of asymptotic, linear, logistic, and pseudo-gamma functional forms against growth time.
c = 25, 0.2, 15, 10 respectively. pmin = 0, pmax = 0.1 (black dashed line), t0 = 0.2.
Fig 3.
A spatial plot of optimal solution for parametrized base case.
Reef clusters are sized by demand quantity and coloured by optimal port assignment–Cairns in purple, Townsville in brown, Airlie Beach in orange, Mackay in green, and Rockhampton in red. Optimal facility locations are coloured black sized by their production quantity, and indicated as proportion of total coral produced. Reprinted from [36] under a CC BY license, with permission from d-maps.com, original copyright 2021.
Fig 4.
A proportional frequency histogram of each potential facility location appearing in optimal solutions based on 100 random subsets of 50 reefs.
Fig 5.
Frequency of potential facility locations included in optimal solutions for 100 random subsets of 50 clustered reefs.
Bars are grouped by facility location and coloured by the number of optimal facilities. This plot excludes Bundaberg and Gladstone which appear in less than 5% of optimal solutions.
Table 2.
Cost parameter sensitivity analysis.
The base case scenario is listed, as well as solutions with cost parameter scaling variations resulting in optimal solutions with a different number of optimal facilities to the base case scenario. Facility locations are Bundaberg (B), Gladstone (G), Rockhampton (R), Mackay (M), Airlie Beach (A), Townsville (T), and Cairns (C).
Fig 6.
Maximum proportional survival variance.
Optimal number of facilities (numbered in bars), total cost ($ million), and optimal growth time (years) relative to change in the maximum proportional survival limit for the base asymptotic survival function (c = 25, t0 = 0).
Table 3.
Maximum proportional survival variance sensitivity.
Sensitivity analysis results of maximum proportional survival rate on asymptotic survival function servicing base case subset of 50 reefs. The total cost, facility number and location, residence time, and production quantity are displayed for each. Locations are represented by the first letter of the names: Bundaberg (B), Gladstone (G), Rockhampton (R), Mackay (M), Airlie Beach (A), Townsville (T), and Cairns (C).
Fig 7.
Impact of change in gradient (c) and horizontal shift (t0) on optimal solutions for different survival curve relationships.
The asymptotic, linear, logistic, and pseudo-gamma distributions are plotted in panels a, b, c; d, e, f; g, h, i; and j, k, l; respectively. Column 1 (panels a, d, g, j) show total cost of the optimal solution, represented by the objective value from $70 million to $300 million. Column 2 (panels b, e, h, k) show growth time (years) from 0 to 1 year in 0.02 increments. Column 3 (panels c, f, i, l) show optimal number of facilities from 3 to 6.