Parameter 
Value 
Range 
Necessity 
Patient Characteristics 
\(\text{Mean}\) 

\((0,∞)\) 
Optional 
\(\text{SCV}\) 

\([0.1,1.5]\) 
Required 
\(q\) 

\([0,\frac{32\cdot\text{SCV}}{5})\) 
Optional 
\(v\) 

\([0,1]\) 
Optional 
Schedule Characteristics 
\(n\) 

\([2,35]\) 
2 out of 3 
\(ω\) 

\([0.05,0.99]\) 
2 out of 3 
\(T\) 

\((n\cdot\text{Mean},∞)\) 
2 out of 3 
\(Δ\) 

\([0,∞)\) 
Optional 
Objective Function

\[
\min_{t_1,\ldots, t_n} \omega\sum_{i=1}^n \mathbb{E}[I_i^{k_1}] +
(1\omega)\sum_{i=1}^n \mathbb{E}[W_i^{k_2}]
\]






Background Information 
Parameter 
Details 
\(\text{Mean}\) 
The mean service time.

\(\text{SCV}\) 
The variance divided by the squared mean.

\(q\) 
The noshow probability.

\(v\) 
The walkin probability.

\(n\) 
The number of patients that need to be scheduled.

\(ω\) 
The weight factor in the objective function.

\(T\) 
The targeted expected session end time.

\(Δ\) 
The arrival times will be rounded to multiples of \(Δ\).
If entered then the actual expected makespan will differ due to rounding.

2 out of 3 
Basic Functionality 
\(n\) & \(ω\) 
The optimal schedule will be computed for these parameters, which also gives
the corresponding expected makespan.

\(n\) & \(T\) 
The optimal schedule will given such that exactly \(n\) patients are served
in expectation within \(T\) giving the implied value of \(ω\).

\(ω\) & \(T\) 
The optimal schedule will be given such that for the value of \(ω\) a maximum number of patients \(n\) are served
in expectation within \(T\).

The webtool solves the minimization problem (\(t_1, \ldots, t_n\) are the patients' arrival epochs)
\[
\min_{t_1,\ldots, t_n} \omega\, \sum_{i=1}^n \mathbb E[I_i^{k_1}] +
(1\omega)\, \sum_{i=1}^n \mathbb E[W_i^{k_2}].
\]
\(I_i\) is the idle time prior to the \(i\)th patient's arrival and \(W_i\) the \(i\)th patient's waiting time.
