A Constructive Algorithm to Minimise the Makespan on Identical Parallel Machines

In this paper we present constructive algorithms for the classical deterministic scheduling problem of minimising the makespan on identical parallel machines. Since the problem is known to be NP-hard in the strong sense, the approximate algorithms play a relevant role when solving this problem. The proposed algorithms are based on list scheduling procedures. The algorithms consist in not taking into consideration all the machines at the beginning, but taking into account subsets of machines, step by step, until the full set of machines are employed. Computational results show that the proposed algorithms perform very well, taking less time to run than the seminal Longest Processing Time First Algorithm.