Single machine scheduling problem of minimising weighted sum of maximum weighted earliness and weighted number of tardy jobs
by Parvaneh Eghbalpor; Mohammad Reisi-Nafchi; Ghasem Moslehi
International Journal of Manufacturing Research (IJMR), Vol. 16, No. 2, 2021

Abstract: Due to the intense competition in the markets, manufacturers are trying to deliver their customers' orders in a timely manner. Therefore, taking into account just-in-time production criteria in scheduling problems is of great importance. In this article, two criteria of maximum weighted earliness and weighted number of tardy jobs are simultaneously considered in a single machine environment for the first time. An optimal algorithm is proposed to minimise maximum weighted earliness in a single machine scheduling. Then a mixed integer programming model is presented for the bi-criteria problem. In addition, a branch-and-bound, with upper and lower bounds and dominance rules are presented to optimally solve the bi-criteria problem. To evaluate the performance of proposed methods a set of instances was generated and solved. The computational results showed that the mixed integer programming model and the branch-and-bound were capable of solving instances up to 26 and 34 jobs in size, respectively. [Submitted 1 November 2018; Accepted 1 September 2019]

Online publication date: Wed, 09-Jun-2021

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