Single machine scheduling problem of minimising weighted sum of maximum weighted earliness and weighted number of tardy jobs

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]