A Heuristic to Minimize Makespan in Proportional Parallel Flow Shops

This paper addresses the problem of minimizing the makespan on a two-stage parallel flow shops with proportional processing times. The problem of scheduling n independent jobs on m proportional parallel flow shops to minimize makespan is known to be NP-hard and hence too difficult to solve in polynomial time. A multiphase heuristic algorithm to minimize the makespan on two proportional parallel flow shops is proposed. A simulation study is conducted to examine the effectiveness of the proposed heuristic algorithm for small and large problems. The results and analysis of quite extensive computational experiments for small size problems show that the proposed algorithm can yield solutions within a few percent of optimal solutions. The computational results for large size problems show that the performance of the proposed algorithm is relatively more effective than the existing SKV algorithm.