Exact and Heuristic Procedures for the Two-Center Hybrid Flow Shop Scheduling Problem With Transportation Times

This paper addresses the two centers hybrid flow shop scheduling problem with transportation times. This problem is faced in several real-world applications. The considered objective function to be minimized in this problem is the maximum completion time. This scheduling problem is NP-hard, and most presented research in this scheduling area ignore the transportation times. In order to solve the considered scheduling problem, several lower bounds are developed. In addition, a two phase's heuristic is presented. This heuristic is based on the optimal solution of the parallel machine scheduling problem with release date and delivery time. Furthermore, a branch and bound exact procedure is developed. Finally, extensive numerical experiments are presented in order to asses the performance and the effectiveness of the proposed procedures. Computational results provide evidence that the proposed procedures are very effective in term of producing optimal solutions in a short computational time for large size problems.