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Stock and flow of a population held over time

Source: R/stkflw.R
stkflw.Rd

Person-days divided by the length of a period give the average daily population (a stock: how many are held at once); divided by the people admitted or released, the average length of stay (how long each stays). The two share a numerator and days = adp * t = people * alos (Little's law in the words of corrections planning; Lakner 1976), so any two of people, days, average daily population and average length of stay give the rest, except days with the average daily population, which carry the same information. When the length of stay moves, the stock and the flow can move in opposite directions; pshare is the share of the change in days (on the log scale) that the change in people accounts for, the rest coming from the length of stay. See proof("stkflw").

Usage

stkflw(
  people = NULL,
  days = NULL,
  adp = NULL,
  alos = NULL,
  t = 365,
  prd = NULL,
  from = NULL,
  to = NULL,
  expo = NULL,
  per = 1e+05,
  base = "first",
  rel = NULL,
  early = NULL
)

Arguments

people, days, adp, alos

Two of: the people admitted or released in each period (positive), the person-days (from 0), the average daily population (from 0; or a list with the periodic headcounts of each period, whose means are taken), and the average length of stay (positive). A clpre list from clprep() is taken too (as people): its elements fill the arguments by name.

t

The length of each period in days: one positive number or one per period.

prd

NULL (1, 2, ...) or the label of each period.

from, to

NULL, or the first and last day of each period (dates or date strings); then t is the days from one to the other, counting both.

expo

NULL, or the population at risk: one positive number or one per period, for rates per per.

per

The rates are per per people: one positive number.

base

Changes against the "first" period or the "previous" one.

rel, early

NULL, or the releases of each period and the days by which every release is brought forward.

Value

An object of class stkflw, a list: flow, a data frame with one row per period (period, t, people, days, adp, alos, their percent changes peochg, aloschg, dayschg, adpchg, pshare, with expo flowrate, stkrate, frchg, srchg, and with rel cut, cutpct); mean, the means over the periods of people, days, adp and alos; base and per.

Details

Given the releases of each period and a number of days by which every release is brought forward, cut is the stock that removes in a steady state, rel * early / t (releasing everyone six months early removes six months of releases at once), and cutpct that share of the average daily population.

References

Lakner, E. (1976). A Manual of Statistical Sampling Methods for Corrections Planners. University of Illinois at Urbana-Champaign.

Little, J. D. C. (1961). A proof for the queuing formula: L = lambda W. Operations Research, 9(3), 383-387. doi:10.1287/opre.9.3.383

Examples

stkflw(people = c(5200, 4800, 4300), days = c(310000, 318000, 330000),
       prd = 2021:2023)
#> stkflw: stock and flow, changes against the first period
#>  period   t people   days      adp     alos     peochg  aloschg  dayschg
#>    2021 365   5200 310000 849.3151 59.61538   0.000000  0.00000 0.000000
#>    2022 365   4800 318000 871.2329 66.25000  -7.692308 11.12903 2.580645
#>    2023 365   4300 330000 904.1096 76.74419 -17.307692 28.73218 6.451613
#>    adpchg    pshare
#>  0.000000        NA
#>  2.580645 -3.141506
#>  6.451613 -3.039708
# admissions implied by a population and a length of stay
stkflw(adp = 900, alos = 61)$flow$people
#> [1] 5385.246