Online scheduling with multi‐state machines

In this paper, we propose a general framework for online scheduling problems in which each machine has multiple states that lead to different processing times. For these problems, in addition to deciding how to assign jobs to machines, we also need to set the states of the machines each time they are assigned jobs. For a wide range of machine environments, job processing characteristics and constraints, and cost functions, we develop a 5.14-competitive deterministic online algorithm and a 3.65-competitive randomized online algorithm. The online weighted traveling repairman problem belongs to this general framework, and both our deterministic and randomized online algorithms lead to lower competitive ratios than the current existing ones in the literature. In addition, we include a complete proof that the online algorithm ReOpt (re-optimizing the route of the repairman whenever a new request is released) is almost surely asymptotically optimal for a probabilistic version of this problem.

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