A benders decomposition algorithm for multi-factory scheduling problem with batch delivery

The multi-factory supply chain problem is investigated to determine the production and transportation scheduling of jobs, which are allowed to be transported by batches. This is a mixed-integer optimization problem, which could be challenging to solve. The problem incorporates two parts: (1) assigning jobs to the appropriate batch, and (2) scheduling jobs of batches for production and transportation. Based on the problem structure and because of its NP-hardness characteristics, Benders decomposition is recognized as a suitable approach. This approach decomposes the problem into assignment master problem and scheduling sub-problem. This would facilitate the solution procedure. By comparing performance of the proposed algorithm with an exact approach, i.e. Branch and Bound, it is demonstrated that it is able to find the near-optimal solution in low computational times in comparison with the Branch and Bound.