An exact algorithm for scheduling identical coupled tasks

摘要

The coupled task problem is to schedule n jobs on one machine where each job consists of two subtasks with required delay time between them. The objective is to minimize the makespan. This problem was analyzed in depth by Orman and Potts [3]. They investigated the complexity of different cases depending on the lengths ai and bi of the two subtasks and the delay time L_i. NP-hardness proofs or polynomial algorithms were given for all cases except for the one where a_i = a, b_i = b and L_i = L. In this paper we present an exact algorithm for this problem with time complexity O(nr~(2L)) where r ≤ a~(1/a-1) holds. Therefore the algorithm is linear in the number of jobs for fixed L.