A fuzzy LPT algorithm for scheduling

Scheduling is an important process widely used in the fields of manufacturing, production, management, computer science, and so on. It mainly concerns the allocation of resources to tasks over time, under some necessary constraints. In the past, the processing time of each job was usually assigned or estimated as a fixed value. In many real-world applications, however, the processing time of each job may dynamically vary with the situations. In this paper, the fuzzy concept is utilized in the longest processing time first (LPT) algorithm for managing uncertain scheduling. Given a set of tasks, each with its membership function for the processing time, the fuzzy LPT algorithm can get a scheduling result with a membership function for the final completion time. Also, the traditional LPT scheduling algorithm is shown as a special case of the fuzzy LPT scheduling algorithm with special membership functions being assigned. The fuzzy LPT scheduling algorithm is then a feasible solution for both the deterministic and uncertain scheduling.