Linear Programming: 2 problems with "alternative variables"

[bruegae]

Hi everyone,
I am struggling with a problem I created myself to get more familiar with linear programming. Unfortunately the complete problem is hard to describe. So I will just describe the mathematical sub-problems were I was unable to find a satisfying solution (set of equations) so far:
Every sub-problem shall operate with the variables x1, x2, x3, x4.
- Problem 1: It shall be only allowed to assign the following values to each of the variables: 0, 1, 2, 4 or 8 (basically this seems to be non-linear, but maybe its not!?)
- Problem 2: Only two of the variables are allowed to get a value assigned other than 0 (which will be non-zero will be decided by other already existing equations)

Has someone solutions, ideas or thoughts concerning my problems?

 

[Ishuda]

Hi everyone,
I am struggling with a problem I created myself to get more familiar with linear programming. Unfortunately the complete problem is hard to describe. So I will just describe the mathematical sub-problems were I was unable to find a satisfying solution (set of equations) so far:
Every sub-problem shall operate with the variables x1, x2, x3, x4.
- Problem 1: It shall be only allowed to assign the following values to each of the variables: 0, 1, 2, 4 or 8 (basically this seems to be non-linear, but maybe its not!?)
- Problem 2: Only two of the variables are allowed to get a value assigned other than 0 (which will be non-zero will be decided by other already existing equations)

Has someone solutions, ideas or thoughts concerning my problems?

Without knowing the complete problem, it is difficult, at least for me, to answer your question because I really don't know what the problems is. You have given a set of constraints which might make sense for any number of problems.

So, can you make a clear statement of the problem and tell us what are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

 

[bruegae]

Ah sorry i thought i'll get an email when someone replys here.
Meanwhile i found out that the problem i have thought about actually has a name: undirected multicommodity flow problem. For the multicommodity flow problem there is a nice LP formulation on wikipedia. Till now i was not able to find such a nice LP formualtion for the undirected version. So I tried so solve it myself:
In the directed version, one has an arc1 from nodeA to nodeB. To get the undirected version i just added an (reverse-)arc2 from nodeB to nodeA. This nearly doubles the amount of variables which is not satisfying to me
"Problem 1" in my initial post is no problem here anymore. The only thing which is needed is (problem 2) a bunch of constraints that restricts each node (except the sink and source nodes) to 1 in- and 1 out-flow or none of both for each commodity.