A Row-and-Column Generation Method to a Batch Machine Scheduling Problem

This paper studies a batch machine scheduling problem in which decisions on grouping jobs into batches and scheduling batches on parallel machines are jointly made. To address the problem, we model it as two-stage set-partitioning (TSSP) type formulation with exponential number of rows and columns. To find solutions, we propose a row-and-column generation method. The proposed method starts with a restricted version of the linear relaxation of (TSSP), and enlarges the model through iteratively generating needed rows and columns. The integer solution is obtained by solving the final integer programming with generated rows and columns. Experimental results show the efficiency of the proposed method.