Abstract
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 Li. Open image in new windowOpen image in new window-hardness proofs or polynomial algorithms were given for all cases except for the one where ai=a, bi=b and Li=L. In this paper we present an exact algorithm for this problem with time complexity O(nr2L) where Open image in new window holds. Therefore the algorithm is linear in the number of jobs for fixed L.
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