Add objective: maximize net profit

Define an objective that maximizes net profit by combining profits with optional planning-unit and action-cost penalties.

Usage

add_objective_max_net_profit(
  x,
  profit_col = "profit",
  include_pu_cost = TRUE,
  include_action_cost = TRUE,
  actions = NULL,
  alias = NULL
)

Arguments

x: A Problem object.
profit_col: Character string giving the profit column in the stored profit table.
include_pu_cost: Logical. If TRUE, subtract planning-unit costs.
include_action_cost: Logical. If TRUE, subtract action costs.
actions: Optional subset of actions to include in the profit and action-cost terms. Values may match x$data$actions$id and, if present, x$data$actions$action_set.
alias: Optional identifier used to register this objective for multi-objective workflows.

Value

An updated Problem object.

Details

Use this function when decisions generate returns and the objective should optimize the resulting net balance after subtracting selected cost components.

Let:

$x_{ia} \in \{0,1\}$ denote whether action $a$ is selected in planning unit $i$,
$w_i \in \{0,1\}$ denote whether planning unit $i$ is selected,
$\pi_{ia}$ denote the profit associated with decision $(i,a)$,
$c_i^{PU} \ge 0$ denote the planning-unit cost,
$c_{ia}^{A} \ge 0$ denote the action cost.

In its most general form, the objective is:

$$ \max \left( \sum_{(i,a) \in \mathcal{D}^{\star}} \pi_{ia} x_{ia} - \sum_{i \in \mathcal{I}} c_i^{PU} w_i - \sum_{(i,a) \in \mathcal{D}^{\star}} c_{ia}^{A} x_{ia} \right), $$

where $\mathcal{D}^{\star}$ denotes the subset of feasible planning unit–action decisions included in the objective.

If actions = NULL, all feasible actions contribute to both the profit term and the action-cost term.

If actions is provided, the profit term and the action-cost term are restricted to that subset. The planning-unit cost term, if included, remains global.

If include_pu_cost = FALSE, the planning-unit cost term is omitted.

If include_action_cost = FALSE, the action-cost term is omitted.

Repeated calls

With alias = NULL, one explicit single objective can be defined per problem; a second unaliased definition raises an error. With an alias, objectives accumulate under distinct names; a repeated alias raises an error. Aliased definitions preserve an explicitly configured single objective. To compare alternatives, start from the problem before its objective was added.

References

Polasky, S., et al. (2008). Where to put things? Spatial land management to sustain biodiversity and economic returns. Biological Conservation, 141, 1505–1524. doi:10.1016/j.biocon.2008.03.022

Chan, K. M. A., Hoshizaki, L., and Klinkenberg, B. (2011). Ecosystem services in conservation planning: targeted benefits vs. co-benefits or costs? PLOS ONE, 6, e24378. doi:10.1371/journal.pone.0024378

Examples

# EXAMPLE: Maximise returns minus implementation costs
#
# Use the same west-to-east profit pattern as above, but now
# charge 9.5 monetary units for every selected action. Some
# locations may no longer generate a positive net return.
sim <- load_sim_multiaction()
returns <- sim$action_costs[, c("pu", "action")]
x_coord <- sim$planning_units$x[
  match(returns$pu, sim$planning_units$id)
]
returns$profit <- ifelse(
  returns$action == "protect", 12 - x_coord, 4 + x_coord
)

p <- create_problem(
  pu = sim$planning_units,
  features = sim$features,
  dist_features = sim$dist_features,
  cost = "cost"
) |>
  add_actions(sim$actions, cost = 9.5) |>
  add_profit(returns) |>
  add_objective_max_net_profit(include_pu_cost = FALSE, alias = "net_profit")

# Unlike gross profit maximisation, leaving a unit unmanaged
# can now be optimal when its best return is below its cost.
if (requireNamespace("rcbc", quietly = TRUE) &&
    requireNamespace("ggplot2", quietly = TRUE)) {
  solutions <- solve(set_solver_cbc(p, time_limit = 30, verbose = FALSE))
  get_objectives(solutions, format = "wide")
  plot_spatial_actions(solutions, layout = "single")
}