An improved MIP-based approach to minimise total earliness and tardiness in unrelated parallel machines scheduling with machine idle time

This paper proposes an effective and efficient mixed integer linear programming (MIP) formulation of the unrelated parallel machine scheduling problem with the objective of minimising total earliness and tardiness (ET) and explores how scheduling performance can be improved by allowing machine idle time. In addition, four simple dispatching rules are utilised to improve solution efficiency. From the results of experiments, it is found that: 1) the improved MIP formulation fixes a potential problem of existing models in literature; 2) the ET value can be significantly reduced if machine idle time is properly allowed before jobs; 3) the utilised dispatching rules yield comparable efficient and quality solutions.

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