Assigned:
Thursday, February 24, 2005
Due:
Thursday, March 3, 2005, in class
General Instructions
- Please review the
course information.
- You must write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
- Numbered problems are all from the textbook Scheduling:
Theory, Algorithms and Systems.
Problems
- Problem 5.8.
- In the book and in class, we saw a linear program for
P|pmtn|Cmax. In this linear program the variable
xij only
described which machine a job should run on. Suppose we wanted to
write a linear program in which we actually assign each job to
particular time period(s) on each machine.
- Write an integer program for
P|pmtn|Cmax in which the variables are xijs,
where xijs is 1 if job j runs on machine i during the time
interval (s,s+1), and 0 otherwise.
- Write an integer program for
P|pmtn|Cmax in which the variables are xijst,
where xijst is 1 if job j begins running on machine i at
time s and finishes running on machine i at time t.
- What are the advantages and disadvantages of each integer
program (You should consider issues such as number of variables and
number of constraints in the formulation and the number of nonzero
variables in the solution. Express your answers in terms of n, m
and Cmax.)?
- Consider the following instance of R|pmtn|Cmax.
|
j1
|
j2
|
j3
|
j4
|
j5
|
m1
|
4
|
2
|
6
|
4
|
6
|
m2
|
5
|
9
|
3
|
4
|
4
|
m3
|
6
|
4
|
1
|
5
|
6
|
Find the optimal schedule, any way you can. Be sure to explain why the schedule you found is optimal.
- Being working on your project proposal (due 3/8)
Switch to:
cliff@ieor.columbia.edu