Scheduling of step-improving jobs with an identical improving rate

Job processing times change over time in real-life production and manufacturing systems due to various factors including machine or worker learning, machine deterioration, production system upgrades or technological shocks. For step-improving processing times, job processing times are reduced by a certain rate if they start to process at, or after, a common critical date, which has wide applicability in real-world settings, such as data gathering networks and production systems with part-time workers. This paper considers single machine scheduling of minimizing total weighted completion time with step-improving jobs. The problem is shown to be intractable. Both exact and heuristic algorithms are developed, and the approximability of the heuristic algorithm is shown for a special case of the problem. Finally, computational experiments show that the proposed algorithms provide very effective and efficient solutions.