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Add objective: maximize profit

Source: R/add_objectives.R
add_objective_max_profit.Rd

Define an objective that maximizes total profit from selected planning unit–action decisions.

Usage

add_objective_max_profit(
  x,
  profit_col = "profit",
  actions = NULL,
  alias = NULL
)

Arguments

x

A Problem object.

profit_col

Character string giving the profit column in the stored profit table.

actions

Optional subset of actions to include. Values may match x$data$actions$id and, if present, x$data$actions$action_set. If NULL, all actions are included.

alias

Optional identifier used to register this objective for multi-objective workflows.

Value

An updated Problem object.

Details

Use this function when the objective is to maximize gross economic return, without subtracting planning-unit or action costs.

Let \(x_{ia} \in \{0,1\}\) denote whether action \(a\) is selected in planning unit \(i\), and let \(\pi_{ia}\) denote the profit associated with that decision, as taken from column profit_col in the stored profit table.

If all actions are included, the objective is:

$$ \max \sum_{(i,a) \in \mathcal{D}} \pi_{ia} x_{ia}, $$

where \(\mathcal{D}\) denotes the set of feasible planning unit–action decisions.

If actions is provided, only the selected subset contributes to the objective. Letting \(\mathcal{D}^{\star}\) denote the feasible decisions whose action belongs to the selected subset, the objective becomes:

$$ \max \sum_{(i,a) \in \mathcal{D}^{\star}} \pi_{ia} x_{ia}. $$

This objective considers profit only. It does not subtract planning-unit costs or action costs. For a net-profit formulation, use add_objective_max_net_profit.

See also

add_objective_min_cost, add_objective_max_net_profit

Examples

pu_tbl <- data.frame(
  id = 1:4,
  cost = c(1, 2, 3, 4)
)
feat_tbl <- data.frame(
  id = 1:2,
  name = c("feature_1", "feature_2")
)
dist_feat_tbl <- data.frame(
  pu = c(1, 1, 2, 3, 4),
  feature = c(1, 2, 2, 1, 2),
  amount = c(5, 2, 3, 4, 1)
)
actions_df <- data.frame(
  id = c("conservation", "restoration"),
  name = c("conservation", "restoration")
)
profit_df <- data.frame(
  pu = c(1, 2, 3, 4, 1, 2, 3, 4),
  action = c("conservation", "conservation", "conservation", "conservation",
             "restoration", "restoration", "restoration", "restoration"),
  profit = c(5, 4, 3, 2, 8, 7, 6, 5)
)

p <- create_problem(
  pu = pu_tbl,
  features = feat_tbl,
  dist_features = dist_feat_tbl,
  cost = "cost"
) |>
  add_actions(actions_df, cost = c(conservation = 1, restoration = 2)) |>
  add_profit(profit_df)

p1 <- add_objective_max_profit(p)
p1$data$model_args
#> $model_type
#> [1] "maximizeProfit"
#> 
#> $objective_id
#> [1] "max_profit"
#> 
#> $objective_args
#> $objective_args$profit_col
#> [1] "profit"
#> 
#> $objective_args$actions
#> NULL
#> 
#> 

p2 <- add_objective_max_profit(
  p,
  actions = "restoration"
)
p2$data$model_args
#> $model_type
#> [1] "maximizeProfit"
#> 
#> $objective_id
#> [1] "max_profit"
#> 
#> $objective_args
#> $objective_args$profit_col
#> [1] "profit"
#> 
#> $objective_args$actions
#> [1] "restoration"
#> 
#>