Patient Characteristics Schedule Characteristics Background Information Objective Function Parameter Value Range Necessity $$\text{Mean}$$ $$(0,∞)$$ Optional $$\text{SCV}$$ $$[0.1,1.5]$$ Required $$q$$ $$[0,\frac{3-2\cdot\text{SCV}}{5})$$ Optional $$w$$ $$[0,1]$$ Optional $$n$$ $$[2,35]$$ 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 $\min_{t_1,\ldots, t_n} \omega\sum_{i=1}^n \mathbb{E}I_i^{k_1} + (1-\omega)\sum_{i=1}^n \mathbb{E}W_i^{k_2}$ $$k_1 = 1$$ & $$k_2= 1$$ $$k_1 = 1$$ & $$k_2= 2$$ $$k_1 = 2$$ & $$k_2= 1$$ $$k_1 = 2$$ & $$k_2= 2$$ $$\text{Mean}$$ The mean service time. $$\text{SCV}$$ The variance divided by the squared mean. $$q$$ The no-show probability. $$w$$ 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. $$n$$ & $$ω$$ 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.