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 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: Branch and Bound, It is achieved that it is able to find the near optimal solution in smaller computational times than the Branch and Bound.