Table 2 The solution of LRCVaR-OPSM based on a hybrid clustering of patient-physician characteristics.

Input

Samples of patient-physician characteristics \(\varvec{x}\); the number of clusters \(K\); a significance level \(\alpha\); the range of

parameter \(t,\) \(\mathscr {T}_{k,d} = \left[ -\max \left\{ y_{k,d}^{(1)}, y_{k,d}^{(2)}, \ldots , y_{k,d}^{(S)} \right\} , 0 \right]\).

Output

Outpatient physician scheduling plan \(\{\chi _{i,w,d} \mid i \in \mathscr {J}, w \in \mathscr {W}, d \in \mathscr {D} \}\).

Steps

1. For the clustering model, perform the following steps:

  (a) Employ the EM algorithm to estimate the hybrid clustering of patient-physician characteristics defined in Eq. (1).

  (b) According to Eq. (2), for each \(i \in {\mathscr {J}}\) and \(k \in {\mathscr {K}},\) estimate the service capacity ratio \(\hat{a}_{i,k}.\)

2.    For each \(k \in {\mathscr {K}}\) and \(d \in {\mathscr {D}},\) perform the following steps:

  (a) Use a fixed step size of 1 to discretize the interval \({\mathscr {T}}_{k,d}.\)

  (b) For each \(t \in {\mathscr {T}}_{k,d},\) evaluate \(\min _{t \in {\mathscr {T}}_{k,d}} \left\{ \alpha ^{-1}\delta _{k,d}^{(t)} - t \right\}.\)

3.    Solve the LRCVaR-OPSM with reformulated service capacity constraint (18), and return the optimal solution \(\chi _{i,w,d}^*.\)