Single-Machine Rework Rescheduling to Minimize Total Waiting Time With Fixed Sequence of Jobs and Release Times

Motivated by energy-saving efforts in the quartz manufacturing industry, this study investigates a single-machine rescheduling problem for a set of newly arrived rework jobs. The original jobs have release times, and the rework jobs need to be separated in a schedule already in progress. The objective is to achieve energy savings by minimizing the total waiting time. A mixed-integer linear programming model is formulated and its NP-hardness is proved. Properties of the optimal solution are derived and used to design the subsequent algorithms. A pseudo-polynomial optimal algorithm for a special case, a heuristic algorithm and a genetic algorithm with an adaptive local search mechanism for general problems are developed and tested. Numerical simulations show that the genetic algorithm yields high-quality solutions under various conditions. A case study suggests that significant energy savings can be achieved with the proposed rescheduling methodology.