A flexible dispatching rule for minimizing tardiness in job shop scheduling

In this paper, a dispatching rule called the Weight Biased Modified RRrule is developed that minimizes the mean tardiness of weighted jobs in an m‐machine job shop, i.e. $J_m|r_i,\mathit{recrc}|{\Sigma }_i{T}_{\mathit{ik}}$ where T ik denotes the tardiness of those jobs with weight greater than a specified threshold level k. It is a significant extension of the RRrule in that it has linear complexity and considers weighted jobs. In addition, the WBMR rule allows for biasing of the schedule towards meeting the deadline of high priority jobs through the tuning of a single parameter, where such an effect is quantified by evaluating tardiness at different truncation thresholds. Numerical testing demonstrates the ability of the WBMR to outperform other traditional rules at various congestion and due‐date tightness levels.