Section: New Results

Production scheduling

Together with Shunji Tanaka, from Kyoto University, we developed Lagrangian relaxation-based methods for solving min-sum shop scheduling problems. In our studies, large scale network flow formulations of the problems are suggested together with strong Lagrangian bounds based on these formulations.

In [23] , we consider the flow-shop problem on two machines with sequence-independent setup times to minimize total completion time. To cope with the size of the network, filtering procedures are developed. To solve the problem to optimality, we embed the Lagrangian bounds into two branch-and-bound algorithms. The best algorithm is able to solve all 100-jobs instances of our testbed with and without setup times, thus significantly outperforming the best algorithms in the literature, which were limited to instances with 30 and 45 jobs respectively.

In [25] , we propose a new dual bound for the job-shop problem with the objective of minimizing the sum of completion costs of the operations. The bound is obtained by a Lagrangian relaxation that decomposes the problem into two types of large network flow problems: one dealing with the precedence constraints among operations of a same job, and the other one satisfying the disjunctive constraints related to the machines. Numerical experiments on the just-in-time job-shop problem show that the method is able to improve the existing lower bounds significantly.