Section: New Results

Machine Scheduling Problems

In [21] we consider the unrelated parallel machine scheduling problem with setup times to minimize a general objective function. In this work we present a novel exact algorithm that is capable of solving this problem $R|r_j,s_{ij}^k|\sum f_j\left(C_j\right)$ and the large class of problems that can be derived as particular cases from it. The proposed algorithm consists of a branch-cut-and-price approach that combines several features such as non-robust cuts, strong branching, reduced cost fixing and dual stabilization. To our knowledge, this is the first exact algorithm for unrelated machines with earliness and/or tardiness criteria that can solve consistently instances with more than 20 jobs. We report improved bounds for instances of problems $R|r_j,s_{ij}^k|\sum w_j^{\text{'}}{E}_j+w_j{T}_j$ and $R\left|\right|\sum w_j^{\text{'}}{E}_j+w_j{T}_j$ with up to 80 and 120 jobs, respectively.