Minimising total weighted completion time on batch and unary machines with incompatible job families

Zewen Huang, Zhongshun Shi and Leyuan Shi

International Journal of Production Research, 2019, vol. 57, issue 2, 567-581

Abstract: This paper addresses the problem of scheduling on batch and unary machines with incompatible job families such that the total weighted completion time is minimised. A mixed-integer linear programming model is proposed to solve the problem to optimality for small instances. Tight lower bounds and a 4-approximation algorithm are developed. A constraint programming-based method is also proposed. Numerical results demonstrate that the proposed algorithms can obtain high quality solutions and have a competitive performance. Sensitivity analysis indicates that the performance of the proposed algorithms is also robust on different problem structures.

Date: 2019
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DOI: 10.1080/00207543.2018.1470341

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