Scheduling of Jobs on Identical Parallel Machines to Minimize Total Flow Time Subject to Optimal Makespan

Abstract

Algorithms based on Simulated Annealing and Tabu search has been proposed and implemented on scheduling a problem of parallel machines. The identical parallel machine scheduling problem has been considered to minimize the total flow-time subject to optimal makespan. The proposed algorithms have two phases. In the first phase, an initial solution has been obtained using Longest Processing Time (LPT) dispatching rule and in the second phase, simulated annealing and tabu search have been applied to reach a near optimal solution. The performance of the both proposed algorithms have been evaluated by comparing their results for different number of jobs and processing times. The computational results indicate that the proposed Tabu Search algorithm is capable of obtaining better solutions for the given scheduling problem as compared to the Simulated Annealing algorithm. Although both of these algorithms provide the best solutions as compared to the other heuristic algorithms but in comparison of these two; Tabu Search provides the better solutions for the given problem.