Scheduling on identical parallel machines to minimize total completion time with deadline and machine eligibility constraints

This study addresses the identical parallel machine scheduling problem with job deadlines and machine eligibility constraints to minimize total job completion time. Jobs must be completed before or at a deadline and preemptions are not allowed. Every job is allowed to be processed on a specified subset of machines. This problem is NP-hard. A heuristic and a branch and bound algorithm are developed to solve the problem. For the branch and bound algorithm, a lower bound based on the dual solution of the assignment problem is proposed and the heuristic serves as the initial upper bound. Many dominance rules are developed to curtail the branching nodes during the search procedure. Computational results indicate that the lower bound improves the performance of those in the literature in terms of execution time, and heuristic consistently generates a good quality schedule.