Bounding Strategies for the Parallel Processors Scheduling Problem With No-Idle Time Constraint, Release Date, and Delivery Time

The identical parallel processors scheduling problem with no-idle time, release date, and delivery time is addressed in this paper. The problem considers a family of tasks that has to be processed by identical parallel processors without idle time. Each task is ready for processing from a release date (arrival time) in an available processor. After completing the processing, a task is delivered during a delivery time. There is no-idle time in each processor from the first treated task until the last one. This is the no-idle processor time constraint, which is faced in real life problems. In these problems, minimizing the consumed energy during the processing of tasks is a crucial issue. Building a feasible schedule satisfying all the already mentioned constraints and minimizing the makespan (maximum completion time) is the objective. The studied scheduling problem is proofed to be NP-Hard in the strong sense. Therefore, a family of efficient heuristics solving the addressed problem are proposed. These heuristics are composed of two phases: Phase 1 and Phase 2. The building of a feasible schedule is performed during phase 1, while in the second phase (phase 2) an improvement procedure is proposed. In order to evaluate the quality of the proposed heuristics, a tight lower bound is developed. The optimal solution of the parallel processors scheduling problem with release date and delivery time is the basic used algorithm while developing the proposed procedures (heuristics and lower bound). In order to assess the performance and the efficiency of the proposed procedures, an extensive experimental study is carried out. During this experimental study the relative mean gap is not exceeding 0.7%, which provides strong evidence of the performance of the developed procedures.