Fixed cost in a linear problem

[Nandi Moksnes]

Hi,

I have a problem where I would like to impose an initial "penalty" or fixed cost in case there is a shipment. If not then the cost should remain 0. My problem is a minimization problem and I have tried adding piecewise constraints. However, as the costs are declining I have not been able to solve the problem in such a way.

The model is very large, so using an Integer program is not possible.

Is there any other way to approach this without making it an integer program?

Thank you,

Nandi

[AMPL Google Group]

Fixed costs cause the cost function to jump suddenly when a shipment moves from 0 to a positive value. As a result, the cost function is not continuous, and it cannot be modeled by linear functions in continuous variables. It is possible to model the discontinuous cost function using nonlinear functions in continuous variables, but the resulting formulations are just as hard -- or even harder -- than the ones that use integer variables.

You say that, "The model is very large, so using an Integer program is not possible." Do you mean that you tried to formulate your optimization problem as an integer program, and you were unable to get a usable solution? If you can explain what solver you used and what happened when you tried to use that solver, perhaps you can get some help with it. Many large integer programs do prove to be solvable.

--
Robert Fourer
am...@googlegroups.com

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