Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Abstract In this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. particular, actual processing time a job assumed be step function its starting deteriorating threshold. When later than threshold, faces two choices: (1) maintaining status in holding equipment being processed base (2) consuming penalty finish processing. The work patterns need different amounts consumption. To implement energy-efficient scheduling, selection pre-processing must carefully considered. mixed integer linear programming (MILP) model proposed total Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating studied into master some independent sub-problems. relaxed only making assignment decisions. sub-problems find optimal schedules job-to-machine assignments given problem. Moreover, MILP heuristic Tabu search used solve evaluate performance our methods, three groups test instances were generated inspired both real-world applications benchmarks from literature. computational results demonstrate that can compute competitive for medium- large-size problems terms solution quality. LBBD performs best among suggested four methods.