İşlerin zamana bağlı bozulduğu durumlar için özdeş olmayan paralel makinelerde çizelgeleme

We consider scheduling of deteriorating jobs on nonidentical parallel machines where the objective is to minimize mean flow time while ensuring the average value (i.e., quality) of processed jobs on machines exceeds a threshold. Deterioration is considered to be time-dependent and has a two-fold effect on jobs. The processing time of jobs as well as their values are deteriorating with time. We analyze the scheduling problem where the processing time and the value functions take linear (piece-wise linear) forms. We first formulate the problem as a mixed integer linear program and obtain optimal solutions for limited problem sizes. We then develop a heuristic algorithm to solve the problem and several ideas to sort jobs in the system. Linear and poisson regression models are trained to predict position of jobs on machines and also used in rank aggregation with simple sorting lists to provide better sorting approaches.