Question

I am writing a linear program in LINGO to balance a drum using a minimum number of weights. My question is how do I limit a variable to a set of values? For example, if I wanted a variable called Weight to be limited to the values (0, 1, 2, 4, 5, or 10) how could I achieve this?

Answer 1

The usual way to achieve this is by introducing several binary (0,1) indicator variables into the formulation.

Let’s say that X is the variable of interest and it can take discrete values {0,1,2,4,5, 10}
Introduce six indicator variables (Y_0, Y_1, … Y_10)
We only want one of these Y’s to take on the value of 1, everything else to be 0.

Y_0 + Y_1 + Y_2 + Y_4 + Y_5 + Y_10 = 1 (Mutual exclusivity constraint)

Now tie the indicator variables with the Original variable.

X = 0 Y_0 + 1 Y_1 + 2 Y_2 + 4 Y_4 + 5 Y_5 + 10 Y_10
(X will take on the appropriate value depending on which indicator variable is 1.)

Now use X in the rest of your formulation.