Pulp Add Constraint That At Least One Lpaffineexpression Is Equal To One

Say I have a PuLP model defined as thus: model = pulp.LpProblem('',pulp.LpMaximize) And I have added an objective function (it does not matter) Now I have a list of LpAffineExpress

Solution 1:

There is no "OR" in linear or integer programming. However, you can use binary variables to simulate such an OR construct. (Or SOS1 variables if big-M's are undesirable; I am not sure to what extend Pulp supports SOS1 variables).

The idea is:

1 - M * (1-δ(i)) <= L(i) <= 1 + M * (1-δ(i)) 
sum(i, δ(i)) >= 1 
δ(i) ∈ {0,1}

• Obviously the L(i) are your l1,l2,l3,...
• δ(i) is a binary variable indicating if L(i)=1. We have δ(i)=1 ⇒ L(i)=1.
• The constants M can be set to lower and upper bounds of L(i).