Identify the steady-state solution with the closest treatment capacity or renege rate to a given target

This function performs either a linear programming or binary search method to identify a solution that satisies multiple constraints (1, arrivals = departures, 2, percentile on waiting list waiting within given time is equal to given value, 3, renege rate is equal to given value)

Usage

optimise_steady_state(
  referrals,
  target,
  renege_params,
  target_time = 4 + (68/487),
  percentile = 0.92,
  method = c("lp", "bs"),
  s_given = NULL,
  bs_tolerance = target * 0.05,
  bs_max_iterations = 10
)

Arguments

referrals: numeric of length 1; value representing the steady-state number of referrals.
target: Numeric. The desired renege rate to be achieved. The value must be between 0 and 1 and represents the proportion of all departures that are reneges.
renege_params: numeric; proportion (0 ≤ r_m &leq; 1) of waiting patients reneging in the m-th month of waiting, where r₂ = 0.1 refers to 10% of those in the second month of waiting reneging.
target_time: numeric of length 1; the target waiting time, in months, to achieve the specified percentile.
percentile: Numeric value between 0 and 1 indicating the desired percentile (default is 0.92).
method: character length 1; "lp" for linear programming, or "bs" for binary search
s_given: numeric vector, length equal to length(renege_params); values must be between 0 and 1 and must represent the proportion of total treatments that are applied to each compartment. This is used as a constraint in the optimisation and the output should follow the same profile
bs_tolerance: Numeric. Acceptable deviation from `target` for convergence. Defaults to 10% of `target`.
bs_max_iterations: Integer. Maximum number of iterations for the binary search. Defaults to 10.

Value

A list containing:

p1: The value of p1 found to achieve the target waiting time.
time_p: The interpolated waiting time at the specified percentile.
mu: The total number of treatments required when the solution is found.
wlsize: The total size of the waiting list when the solution is found.
waiting_list: The data frame with historical data formatted and waiting list sizes calculated.
niterations: The number of iterations performed in the binary search.
status: Converged indicates a solution was found, and Not converged indicates no solution was found.
method: The method the solution was identified.

Examples

if (FALSE) { # \dontrun{
optimise_steady_state(
  referrals = 100,
  target = 0.1,
  renege_params = runif(24),
  method = "lp",
  s_given = c(0.4, 0.2, 0.1, rep(0.05, 6), rep(0, 15))
)

optimise_steady_state(
  referrals = 100,
  bs_target = 0.2,
  renege_params = runif(24),
  method = "bs"
)
} # }