Uncertain Single-Machine Scheduling with Deterioration and Learning Effect

A single-machine scheduling problem with deterioration and learning effect is studied in the present paper. The processing time and due date are considered uncertain variables due to lack of historical data. The aim is to minimize the makespan, total completion time, total weight completion time, and maximum lateness under an uncertain environment. To address the problem in an uncertain environment, the expected value model and pessimistic value model are developed. These models can be converted into equivalent models based on the inverse distribution method. It is proved that the corresponding dispatching rules can solve the problem optimally under different objective criteria. Finally, sensitivity analysis is used to illustrate the effectiveness of these rules.