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**Solving a two-agent single-machine scheduling problem considering learning effect.**
*(English)*
Zbl 1251.90165

Summary: Scheduling with multiple agents and learning effect has drawn much attention. We investigate the job scheduling problem of two agents competing for the usage of a common single machine with learning effect. The objective is to minimize the total weighted completion time of both agents with the restriction that the makespan of either agent cannot exceed an upper bound. In order to solve this problem we develop several dominance properties and a lower bound based on a branch-and-bound to find the optimal algorithm, and derive genetic algorithm based procedures for finding near-optimal solutions. The performances of the proposed algorithms are evaluated and compared via computational experiments.

### MSC:

90B35 | Deterministic scheduling theory in operations research |

90C59 | Approximation methods and heuristics in mathematical programming |

68T05 | Learning and adaptive systems in artificial intelligence |

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\textit{D.-C. Li} and \textit{P.-H. Hsu}, Comput. Oper. Res. 39, No. 7, 1644--1651 (2012; Zbl 1251.90165)

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