Linear Programming, max function (if statement)

Question

I have a value x, which is a combination of decision variables.

I need to calculate a cost, which only triggers if x > 100. So cost = MAX(x - 100, 0) * 20.

Is there any way to do this in linear programming?

I've tried creating two binary variables (y1 & y2), in which y1 = 1 when x <= 100 & y2 = 1 when x > 100 & y1 + y2 = 1, from this website - https://uk.mathworks.com/matlabcentral/answers/693740-linear-programming-with-conditional-constraints. However, my excel solver is still giving non-linearity complaints...

Any advice on how I can fix this?

if anyone else is stuck on similar problem: math.stackexchange.com/questions/2446606/… this could be useful — tcotts
– tcotts, Commented Dec 4, 2022 at 15:14

Erwin Kalvelagen · Accepted Answer · 2022-12-05 10:39:21Z

2

The objective

 min cost = max(x-100,0)*20

can be implemented in an LP as:

 min cost = y*20
     y >= x - 100 
     x >= 0, y >= 0

There is no need for binary variables.

answered Dec 5, 2022 at 10:30

Erwin Kalvelagen

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