SLIDE 6 Complete Optimization Problem
Danilo Ardagna
min
x,ν,s,R
X
i∈C
(στisi + πτiRi) (P1a) subject to: X
j∈V
xij = 1, ∀i ∈ C (P1b) Pi,τi = X
j∈V
Pijxij, ∀i ∈ C (P1c) στi = X
j∈V
σjxij, ∀i ∈ C (P1d) πτi = X
j∈V
πjxij, ∀i ∈ C (P1e) xij ∈ {0, 1} , ∀i ∈ C, ∀j ∈ V (P1f) (ν, s, R) ∈ arg min X
i∈C
(στisi + πτiRi) (P1g) subject to: si ≤ ηi 1 − ηi Ri, ∀i ∈ C (P1h) νi = Ri + si, ∀i ∈ C (P1i) T (Pi,τi, νi; Hi, Zi) ≤ Di, ∀i ∈ C (P1j) νi ∈ N, ∀i ∈ C (P1k) Ri ∈ N, ∀i ∈ C (P1l) si ∈ N, ∀i ∈ C (P1m)
- Many integer variables and constraints make the problem
intractable with exact methods
- We split the problem in two layers