Job shop scheduling with unit length tasks

In this paper, we consider a class of scheduling problems that are among the fundamental optimization problems in operations research. More specifically, we deal with a particular version called job shop scheduling with unit length tasks . Using the results of Hromkovic, Momke, Steinhofel, and Widmayer presented in their work Job Shop Scheduling with Unit Length Tasks: Bounds and Algorithms , we analyze the problem setting for 2 jobs with an unequal number of tasks. We contribute a deterministic algorithm which achieves a vanishing delay in certain cases and a randomized algorithm with a competitive ratio tending to 1. Furthermore, we investigate the problem with 3 jobs and we construct a randomized online algorithm which also has a competitive ratio tending to 1.