Recall that the factor-2 approximation algorithm for makespan minimization on identical machines is the Longest Processing Time (LPT) algorithm, which sorts jobs in descending order and assigns each job to the machine with the current smallest load.

To analyze the approximation ratio, consider the optimal makespan (OPT) and compare it to the makespan produced by LPT. Start by proving that OPT is at least the maximum of the largest job and the average machine load.

Prove that the makespan of LPT is at most (3/2) times the optimal makespan by analyzing the worst-case scenario where the last job assigned causes the makespan to exceed OPT by the maximum possible margin.