Optimizing Location, Routing and Scheduling Decisions ... - gerad

Simple Valid Inequalities
Introduction
Problem Definition and Formulation
Solution Methodology
Conclusion
References
Problem Definition
Set Partitioning Formulation
X
a ipz p ≤ t j ∀i ∈ I, ∀j ∈ J (σ ji ), (6)
p∈P j
X
t j ≥ N F , (7)
j∈J
X
z p = v j ∀j ∈ J (ν j ), (8)
p∈P j
v j ≥ t j ∀j ∈ J, (9)
v j ∈ Z + ∀j ∈ J. (10)
N F is the minimum number of facilities required to be open:
N F = argmin {l=1..|J|}
lX
Cj F t
≥ X !
D i
t=1 i∈I
s.t. Cj F 1
≥ Cj F 2
≥ ... ≥ Cj F n
Akça, Ralphs, Berger
LRS PROBLEM