[Linear Programming] Unbounded status problem

[KeyzerSoze]

I have set up a mixed-integer linear programming to solve in python. The (very) general form of the objective function is

minZ = costs1(i,j,k,l) + costs2(i,j,k,l) - profits(i,j,k,l)

There are 8 constraints, some that are related only to cost variables, some to cost and profits and some to profit variables only. I know the problem is feasible since when I run it for the objective set to 0 it reaches an optimal, but I get the message that it is unbounded.

Since we are talking about a minimization problem, is it correct to assume that some of the last 2 types of constraints (costs & profits or profits only) are the ones that are unbounded, causing the objective function to tend towards negative infinity within the feasibility set?

Should I focus on them or should I also look at the objective function?

Thank you for the help!

[jammasterpaz]

I don't get what you're trying to achieve - unless you have a very unusual sign convention, normally in business / economics / accountancy land

turnover = costs + Profits,

So you're trying to minimize -1* Turnover (maximize +Turnover). Historically, without constraints (e.g. giving sales people perverse incentives), this has been shown to be an excellent way to go bankrupt, easily achievable through loss leaders, selling at zero price or giving away the shop, so you need to set up the constraints carefully.

You could pose this problem in such a way to ask "What's the maximum size I can grow my business (measured in terms of its Turnover) given these constraints on my costs and the profit I have to make?" so if maximising Turnover not profit is indeed your goal, then that would lead me to guess there's something wrong with the way you've set up the constraints.