Parameter |
Value |
Range |
Necessity |
Patient Characteristics |
\(\text{Mean}\) |
|
\((0,∞)\) |
Optional |
\(\text{SCV}\) |
|
\([0.1,1.5]\) |
Required |
\(q\) |
|
\([0,\frac{3-2\cdot\text{SCV}}{5})\) |
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 no-show probability.
|
\(v\) |
The walk-in 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.
|