Calculates the balancing cost measure, which is defined as the travel cost required to reach as many opportunities as the number of people in a given origin. Originally proposed by Barboza et al. (2021) , under the name "balancing time".

This function is generic over any kind of numeric travel cost, such as distance, time and money.

balancing_cost(
travel_matrix,
land_use_data,
opportunity,
travel_cost,
demand,
cost_increment = 1,
group_by = character(0),
fill_missing_ids = TRUE
)

## Arguments

travel_matrix

A data frame. The travel matrix describing the costs (i.e. travel time, distance, monetary cost, etc.) between the origins and destinations in the study area. Must contain the columns from_id, to_id and any others specified in travel_cost.

land_use_data

A data frame. The distribution of opportunities within the study area cells. Must contain the columns id and any others specified in opportunity.

opportunity

A string. The name of the column in land_use_data with the number of opportunities/resources/services to be considered when calculating accessibility levels.

travel_cost

A string. The name of the column in travel_matrix with the travel cost between origins and destinations.

demand

A string. The name of the column in land_use_data with the number of people in each origin that will be considered potential competitors.

cost_increment

A number. The cost increment that should be used when defining the travel cost distribution from which the potential balancing costs will be picked. For example, an increment of 1 tends to suitable for travel time distributions, meaning that the function will first check if any origins reach their balancing cost with a travel time of 0 minutes, then 1 minute, 2 minutes, 3, 4, ..., etc. A increment of 1 might be too big for a distribution of monetary costs, on the other hand, which could possibly benefit from a smaller increment of 0.05, for example, resulting in the function looking for balancing costs first at a cost of 0, then 0.05, 0.10, ..., etc. Defaults to 1.

group_by

A character vector. When not character(0) (the default), indicates the travel_matrix columns that should be used to group the accessibility estimates by. For example, if travel_matrix includes a departure time column, that specifies the departure time of each entry in the data frame, passing "departure_time" to this parameter results in accessibility estimates grouped by origin and by departure time.

fill_missing_ids

A logical. When calculating grouped accessibility estimates (i.e. when by_col is not NULL), some combinations of groups and origins may be missing. For example, if a single trip can depart from origin A at 7:15am and reach destination B within 55 minutes, but no trips departing from A at 7:30am can be completed at all, this second combination will not be included in the output. When TRUE (the default), the function identifies which combinations would be left out and fills their respective accessibility values with 0, which incurs in a performance penalty.

## Value

A data frame containing the accessibility estimates for each origin/destination (depending if active is TRUE or FALSE) in the travel matrix.

A data frame containing the accessibility estimates for each origin in the travel matrix. Origins marked with a NA balancing cost never reach as many opportunities as there is people residing in them, given the specified travel matrix.

## References

Barboza MH, Carneiro MS, Falavigna C, Luz G, Orrico R (2021). “Balancing Time: Using a New Accessibility Measure in Rio de Janeiro.” Journal of Transport Geography, 90, 102924. ISSN 09666923, doi:10.1016/j.jtrangeo.2020.102924 .

## Examples

data_dir <- system.file("extdata", package = "accessibility")

bc <- balancing_cost(
travel_matrix,
land_use_data,
opportunity = "jobs",
travel_cost = "travel_time",
demand = "population"
)