Outpatient Appointment Scheduling with Variable Interappointment Times

Algorithm 1

Simulation-based heuristic algorithm.

Input: N, b, n_p (p = 1⋯b), c_w, c_d, c_v, service time distributions, and h.

Output: a_p (p = 1…b).

Initialization: a_p = 1 for p = 1⋯b;

 Evaluate 𝐶;

 OldMinExpectedTotalCost = 𝐶.

Begin

Step  1  For 𝑝=1⋯𝑏

  𝑎_𝑝=𝑎_𝑝+1;

  Evaluate 𝐶;

  ExpectedTotalCost(p) = 𝐶;

  𝑎_𝑝=𝑎_𝑝−1;

 End For

 Step  2  Find p such that ExpectedTotalCost(p) is the minimum;

  𝑎_𝑝=𝑎_𝑝+1;

  𝑁𝑒𝑤𝑀𝑖𝑛𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑𝑇𝑜𝑡𝑎𝑙𝐶𝑜𝑠𝑡=𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑𝑇𝑜𝑡𝑎𝑙𝐶𝑜𝑠𝑡(𝑝).

  Step  3  If NewMinExpectedTotalCost < OldMinExpectedTotalCost

  OldMinExpectedTotalCost = NewMinExpectedTotalCost;

  Go to  Step  1;

 else

  𝑎_𝑝=𝑎_𝑝−1;

  Return 𝑎_𝑝(𝑝=1⋯𝑏);

 End If

End