Scheduling with Learning Effects and/or Time-Dependent Processing Times to Minimize the Weighted Number of Tardy Jobs on a Single Machine

Algorithm 2

Initialization: 𝑍^∗=∞, 𝑙=0.

   while  𝑙≤𝑛  do

     Step  1. Apply Algorithm 1. Denote the optimal job sequence by 𝜋^∗(𝑙)=([1],[2],…,[𝑛]) and the minimum cost by 𝑍^∗(𝑙).

     Step  2. If 𝑍^∗(𝑙)≤𝑍^∗, then set 𝑍^∗=𝑍^∗(𝑙), 𝑙^∗=𝑙, 𝜋^∗=𝜋^∗(𝑙).

     Step  3. 𝑙=𝑙+1.

   end