Geometric and harmonic means based priority dispatching rules for single machine scheduling problems

Abstract

This work proposes two new prority dispatching rules (PDRs) for solving single machine scheduling problems. These rules are based on the geometric mean (GM) and harmonic mean (HM) of the processing time (PT) and the due date (DD) and they are referred to as GMPD and HMPD respectively. Performance of the proposed PDRs is evaluated on the basis of five measures/criteria i.e. Total Flow Time (TFT), Total Lateness (TL), Number of Late Jobs (TNL), Total Earliness (TE) and Number of Early Parts (TNE). It is found that GMPD performs better than other PDRs in achieving optimal values of multiple performance measures. Further, effect of variation in the weight assigned to PT and DD on the combined performance of TFT and TL is also examined which reveals that for deriving optimal values of TFT and TL, weighted harmonic mean (WHMPD) rule with a weight of 0.105 outperforms other PDRs. The weighted geometric mean (WGMPD) rule with a weight of 0.37 is found to be the next after WHMPD followed by the weighted PDT i.e. WPDT rule with a weight of 0.76.

Keywords

• job sequencing
• priority dispatching rule
• single machine scheduling
• geometric mean of the processing time and due date (gmpd)
• harmonic mean of the processing time and due date (hmpd)