A GRASP for a Multi-depot Multi-commodity Pickup and Delivery Problem with Time Windows and Heterogeneous Fleet in the Bottled Beverage Industry - Computational Logistics - page 147

l k − M T (1 − z k ) ≤ OT k ≤ u k + M T (1 − z k ) k ∈ K

(16)

s ik
60 ≤

hy ikh ≤ ( h +1) y ikh k ∈ K,i ∈ V \{ σ ( k ) } (17)

h∈H h∈H

OT k
60 ≤

hy σ ( k ) kh ≤ ( h +1) y σ ( k ) kh k ∈ K (18)

h∈H h∈H

y ikh ≤ 1 i ∈ V,k ∈ K (19)

h∈H

y ikh ≤ f ih i ∈ V,h ∈ H (20)

k∈K

s ik + S + s ij 1

+ s ij v type

v type
k

− k ∈ K,

k

− M T (1 − x ijk ) ≤ s jk ( i,j ) ∈ E | j = σ ( k ) (21)

s ik + S + s iσ ( k ) 1

+ s iσ ( k ) v type

v type
k

−

k

− M T (1 − x iσ ( k ) k ) ≤ OT k i ∈ V,k ∈ K (22)

g ikp ≤ n ip

i ∈ V,p ∈ P (23)

k∈K

g ikp ≥ n ip i ∈ V,p ∈ P (24)

k∈K

n ip
j :( j,i )

g ikp ≤ x jik i ∈ V,k ∈ K,p ∈ P (25)

∈ E

n ip
j :( j,i ) ∈E

g ikp ≤ x jik i ∈ V,k ∈ K,p ∈ P (26)

q ikp + g jkp − g jkp i ∈ V,k ∈ K,p ∈ P,

− M L (1 − x ijk ) ≤ q jkp j ∈ V \{ σ ( k ) } (27)

q ikp + g jkp − g jkp i ∈ V,k ∈ K,p ∈ P,

+ M L (1 − x ijk ) ≥ q jkp j ∈ V \{ σ ( k ) } (28)

q ikp
o p ≤

v top
k

+ v bel
k

i ∈ V,k ∈ K (29)

p ∈ P

v be k +
t∈T σ ( k ) ∩T e

q ikp
o p ≤

c to t w kt i ∈ V,k ∈ K (30)

p∈P N

c ik + c ij 1

+ c ij v type

v type
k

−

k

− M C (1 − x ijk ) ≤ c jk i ∈ V,k ∈ K,j ∈ V \{ σ ( k ) (31)

c ik + c iσ ( k ) 1

+ c iσ ( k ) v type

v type
k

−

k

− M C (1 − x iσ ( k ) k ) ≤ c jk i ∈ V,k ∈ K (32)

w kt =0 k,t | σ ( k ) = σ ( t ) (33)

g σ ( k ) kp =0

k ∈ K,p ∈ P (34)