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