Homework #1 solutions / IEOR4405
1
1. Problem 2.3
(a) The optimal schedule has Σ
U
j
= 2. The following schedules are optimal
{
1
,
3
,
2
,
4
}
,
{
1
,
3
,
4
,
2
}
,
{
3
,
4
,
1
,
2
}
,
{
3
,
4
,
2
,
1
}
,
{
2
,
3
,
1
,
4
}
,
{
2
,
3
,
4
,
1
}
,
{
2
,
4
,
3
,
1
}
,
{
2
,
4
,
1
,
3
}
Direct computation reveals that
all the above schedules have Σ
U
j
= 2.
(b) The optimal schedule is discussed in Algorithm 3.3.1 in chapter 3. It will be discussed in the
following week during lecture hours.
2. Problem 2.5
The total processing time of 11 jobs is 75. Since there are 5 machines working in parallel. We
need at least 15 time units to process all the jobs. That is
C
*
max
≥
15. Now, consider the
following schedule, The schedule has a completion time of 15. This is exactly the lower bound
that we computed. Since a feasible solution equals the lower bound, it is the optimal solution.
3. If we have a preemptive policy with all the jobs having the same release date. Then it is no dif-
ferent from the problem without a preemptive policy