This paper presents heuristic algorithms for scheduling independent tasks on nonidentical processors. The authors analyze the worst-case performance of several heuristic algorithms, including A, B, C, D, and E, in terms of their finishing time relative to the optimal finishing time. They show that the worst-case ratio of finishing time for these algorithms is at most m, where m is the number of processors. However, for Algorithm D, the worst-case ratio can approach 2 for m = 2. The paper then introduces a new heuristic algorithm, Algorithm F, for scheduling on two nonidentical processors. This algorithm has a better worst-case performance than the previous algorithms, with a finishing time ratio of at most (sqrt(5)+1)/2, which is approximately 1.618. This bound is proven to be the best possible for two processors. The paper also considers the case of identical processors, where all processors have the same processing speed. It shows that the LPT (Longest Processing Time first) scheduling algorithm produces schedules that are near optimal for large n. Furthermore, the paper proves that the simplified problem of scheduling on identical processors with processing times that do not vary "too much" is P-complete, meaning it is computationally as difficult as other known P-complete problems. Finally, the paper shows that the LPT schedule for the ρ-PT (processing time) problem is near optimal for large n. The ratio of the finishing time of the LPT schedule to the optimal finishing time is bounded by 1 + 2(m-1)/n when n ≥ 2(m-1)ρ. This indicates that the LPT schedule becomes increasingly optimal as n increases.This paper presents heuristic algorithms for scheduling independent tasks on nonidentical processors. The authors analyze the worst-case performance of several heuristic algorithms, including A, B, C, D, and E, in terms of their finishing time relative to the optimal finishing time. They show that the worst-case ratio of finishing time for these algorithms is at most m, where m is the number of processors. However, for Algorithm D, the worst-case ratio can approach 2 for m = 2. The paper then introduces a new heuristic algorithm, Algorithm F, for scheduling on two nonidentical processors. This algorithm has a better worst-case performance than the previous algorithms, with a finishing time ratio of at most (sqrt(5)+1)/2, which is approximately 1.618. This bound is proven to be the best possible for two processors. The paper also considers the case of identical processors, where all processors have the same processing speed. It shows that the LPT (Longest Processing Time first) scheduling algorithm produces schedules that are near optimal for large n. Furthermore, the paper proves that the simplified problem of scheduling on identical processors with processing times that do not vary "too much" is P-complete, meaning it is computationally as difficult as other known P-complete problems. Finally, the paper shows that the LPT schedule for the ρ-PT (processing time) problem is near optimal for large n. The ratio of the finishing time of the LPT schedule to the optimal finishing time is bounded by 1 + 2(m-1)/n when n ≥ 2(m-1)ρ. This indicates that the LPT schedule becomes increasingly optimal as n increases.