Minimizing the total weighted completion time of fully parallel jobs with integer parallel units

Abstract

Fully parallel jobs model was proposed to analyze a kind of parallel computers which schedule jobs with preemption, but unlike the traditional parallel computers, jobs executed in a fully parallel jobs machine are paused instead of being terminated when interrupted by another job, which is to say, once the job resumes its execution, it would not lose its previous progress. Also, in this scheduling model, one resource cannot be shared by two or more jobs in a single time unit, and a job is finished as soon as it accumulates a given number of resources. Fully parallel jobs model was first researched by Zhang et al. in 2012. While we are not sure whether a computer using this model really exists, the model can be used to simulate one kind of real-life problems. Think of a box factory which produces a fixed number of boxes every day, and the boxes can either be exported at the end of the day or stored in the factory. A number of orders have been made to the factory, each with a certain number of boxes and is weighted by the importance, urgency, impact of the customer, and so on. Now we want to minimize the total weighted cost of all the orders. This project is subjected to study the same problem, and can be treated as a sequel to that made by Zhang et al.