science.ai simple simulator for break-even article processing charges
(APC)
Authors


Ballesteros, Sebastien “Sebastien Ballesteros” (science.ai )
Bogich, Tiffany (L) “Tiffany L Bogich” (science.ai )
Affiliations

science.ai – New York, NY, USA
Abstract
We present a simple simulator to compute the article processing charge (APC) that a journal
should set to cancel science.ai cost.
Introduction
Article processing charges (APCs) are commonly used as a business model to sustain open
access journals (Björk & Solomon, 2012). Here we present a simple model allowing to build a
simulator for break-even APC. We define the break-even APC (𝐹0 ) as the minimal APC required
to compensate science.ai cost, 𝐶.
Model
𝐹0 is defined in Equation 1:
Equation 1. Break-even APC (𝐹0 ) where 𝐴 is the number of articles with paid APCs for the time period when the cost (𝐶) was
computed
𝐹0 =
𝐶
𝐴
science.ai monthly cost (𝐶) is defined as Equation 2:
Equation 2. science.ai cost (𝐶). 𝑃 is science.ai monthly price and 𝑈 the number of active users in a given month
𝐶 =𝑃∗𝑈
As science.ai practices a fair billing policy, only active users are charged. Active users are
defined as the number of unique editors and production editors involved in ongoing
submissions on a given month. Note that reviewers and authors are never counted as active
users.
We compute the number of active users under the assumption that active users will be used to
their fullest capacity before new active users are added as defined in Equation 3:
Equation 3. Number of active users as a function of 𝑄𝑒 , the number of ongoing submissions at equilibrium, 𝐸, the number of
editors needed to process a submission, 𝑆 the number of submissions that an active user can process concurrently.
𝑄𝑒 ∗ 𝐸,
𝐸,
𝑈={
𝑄𝑒
𝑄𝑒 𝑚𝑜𝑑 𝑆
(⌊ ⌋ + ⌈
⌉ ) 𝐸,
𝑆
𝑆
if 𝑄𝑒 < 1
if 𝑄𝑒 < 𝑆
otherwise
We compute 𝑄𝑒 as the equilibrium value of Equation 4:
Equation 4. Dynamic of submissions (𝑄) where 𝜇 is the rate of incoming submission and 𝑇 the time to process a submission.
𝑑𝑄
1
=𝜇−
𝑄
⌈𝑇⌉
𝑑𝑡
To compute 𝐴, we assume that a fraction 𝛼 of submissions end up with paid APCs (see Equation
5).
Equation 5. Dynamic of submissions with paid APCs (𝐴), where 𝛼 is the proportion of submissions for which an APC is collected
and 𝜇 the submission rate.
𝑑𝐴
= 𝛼𝜇
𝑑𝑡
We can then express the break even APC (𝐹0 ) in terms of our basic parameters (Equation 6).
Equation 6. Break even APC expressed in terms of basic model parameters
𝐹0 =
𝑃 ∗ 𝑈(𝑄𝑒 = 𝜇⌈𝑇⌉, 𝐸, 𝑆)
𝛼𝜇
Examples
Using the model defined in the previous section we can compute break-even APCs for common
parameter values (see Table 1) and across a range of submission rates and processing times
(Figure 1).
Table 1. Example values of break even APCs for common parameter values.
Break even
APC (𝑭𝟎 )
Submission
rate (𝝁) per
month
Processing
time (𝑻) in
months
Number of
editors
needed to
process 1
submission
(𝑬)
Proportion
of
submissions
for which an
APC is
collected (𝜶)
2
3
Number of
submissions
that an
active user
can process
concurrently
(𝑺)
8
5
2.57𝑃
2.5𝑃
35
6
1.5
0.25
2.67𝑃
1𝑃
12
0.5
2
1
2
2
3
1
0.5
0.7
5𝑃
6
3
3
5
0.4
6.67𝑃
8𝑃
3.15P
3
1
14
2
2
2
2
4
3
6
3
5
0.1
0.5
0.408
0.2
0.4
Figure 1. The break even APC divided by the science.ai monthly price for submission rates (𝜇) ranging from 1 to 100 submissions
/ month) and for processing times (𝑇) of 1, 2, 3, and 4 months. We assume common parameter values of: 𝑆 = 3, 𝐸 = 2, and
𝛼 = 0.5 in all plots. Code from: Supporting Code 1.
Discussion
We presented a simple model to compute the break even APC. Future versions of this work will
present more complex models taking into account different types of editorial workflows where
processing time and human resource requirements vary by stage.
Supporting Information
#Parameters fixed
E=2
#
S=3
#
alpha=0.5
#
T=c(1,2,3,4)
#
number of editors per submission
max number of simulataneous submissions per editor
proportion of submissions that are paid
processing time (months)
mu=seq(1,100,1) # number of new submissions per month
#function to calculate F0/p
f0p<-function(mu=2,t=2,a=0.5,e=2,s=3){
qe<-mu*ceiling(t)
if (qe<1) {F0=e*qe}
else if(qe<s) {F0=(e/(a*mu))}
else F0=(((floor(qe/s)+ceiling(qe%%s/s))*e)/(a*mu))
return(F0)
}
sim<-vector("numeric",length=length(mu))
par(mfrow=c(2,2))
#vary mu (i) and T (k)
for(k in 1:length(T)){ #vary T
for(i in 1:length(mu)){ #vary mu
sim[i]=f0p(mu[i],t=T[k],s=S,e=E,a=alpha)
}
#plot f0/p for each T across the range of mu
plot(mu,sim,type="l", bty="n", xlab="mu (monthly)", ylab="F0/P",
main=paste("T=",T[k],"month"),log="x",ylim=c(0,8),cex.lab=1.2,cex.axis=1.2)
}
Supporting Code 1. R code to calculate the breakeven APC divided by science.ai price for submission rates (𝜇) ranging from 1 to
100 submissions / month) and for processing times (𝑇) of 1, 2, 3, and 4 months.
References
Björk, B.-C., & Solomon, D. (2012). Pricing principles used by scholarly open access publishers.
Learned Publishing, 25, 132-137.