Modelling tricks

Question 1

Disjunctive expressions: How can they be implemented for 2 or 3 products, of which either of the products has to go above a certain minimum production threshold?

Answer 1

x1 >= x1_min * delta
x2 >= x2_min* (1-delta)

delta ist binary und 1, wenn x1 >= x_min und 0, wenn x2 >= x2_min

für 3 Items:

x(i) >= delta(i)*x(i)_min
sum(i,delta(i)) =e= 1;

Question 2

Choice between two machines (either one of the capacity restraints has to “fire”)

Answer 2

6x1 + 9x2 - BigMdelta <= 700
4x1 + 12x2 - BigM(1-delta) <= 800

delta ist 1, wenn Maschine 2 benutzt wird und 0, wenn Maschine 1 benutzt wird.

Question 3

conditional expression (e.g., if one particular item x1 is produced, another item x2 has to be produced as well)

Answer 3

x1 <= BigMpsi
x2 >= psiepsilon

with BigM being sufficiently large and epsilon being sufficiently small