A distributed scheduling methodology for a two-machine flowshop using cooperative interaction via multiple coupling agents

This paper presents a distributed scheduling methodology for a two-machine flowshop problem. It is assumed that the decision authorities and information are distributed in multiple subproduction systems that must share two machines to satisfy their demands. The associated scheduling problems are modeled using 0/1 integer formulations, and the problem is solved using Lagrangian relaxation techniques modified to work in an environment where very limited information sharing is allowed. Specifically, no global upper-bound is known, no single decision entity has complete view of all the constraints that couple the participating subproduction systems, and there is no disclosure of local objectives and constraints. The main objective of the proposed algorithm is to find a compromise state where all coupling constraints and local constraints are satisfied, and the total sum of weighted completion time of jobs is minimized. The proposed methodology showed promising experimental results when compared to the traditional Lagrangian relaxation with subgradient method.