A Model for the Coordination of 20-foot and 40-foot Container Movements in the Hinterland of a Container Terminal - Computational Logistics - page 120

Selection of Locations for Loading and Unloading

z +

CONT _ LOC ( k ) k ≥

y rk ∀ k ∈C (1)

rinREQS

z +

ik ≥ y rk

∀ k ∈C ,r ∈ REQS

(2)

i ∈N

z ik ≥ y rk

∀ k ∈C ,r ∈ REQS (3)

i ∈N

z +

ik ≤ 1

∀ i ∈N (4)

k ∈C

z ik ≤

1 ∀ i ∈N (5)

k ∈C

The start node for each container is known (1). If request r is assigned to con-
tainer k then a start node must be selected for container k (2). Similarly, a stop
node is selected for container k assigned to request r (3). A node can become
the starting point of at most one container (4). Similarly, it is not allowed that
two or more containers are delivered to a node (5).

z + ∀ r ∈ REQS EXP ,k ∈C

REQSTART ( r ) k ≥ y rk

(6)

z REQSTOP ( r ) k ≥ y rk ∀ r ∈ REQS EXP ,k ∈C (7)

z + ∀ r ∈ REQS IMP ,k ∈C

REQSTART ( r ) k ≥ y rk

(8)

z REQSTOP ( r ) k ≥ y rk ∀ r ∈ REQS IMP ,k ∈C (9)

z + ∀ r ∈ REQS STOR ,k ∈C

REQSTART ( r ) k ≥ y rk

(10)

z REQSTOP ( r ) k ≥ y rk ∀ r ∈ REQS PROV ,k ∈C

(11)

The constraint (6) ((7)) assigns the pickup (delivery) node of the export request r
to container k . For each import request, the two constraints (8) and (9) determine
the corresponding container pickup and the container delivery location. The start
node for each container being assigned to a storage request is known (10) but
for each provision request only the destination node is known (11).

z ik ≥ y rk ∀ r ∈ REQS STOR ,k ∈C (12)

i ∈N | REQUI ( k,i ) > 0

z + ∀ r ∈ REQS PROV ,k ∈C

ik ≥ y rk

(13)

i ∈N | AV AIL ( k,i ) > 0

z ik ≤ REQU I ( k, i )

∀ i ∈N ,k ∈C (14)

z +

ik ≤ AV AIL ( k, i )

∀ i ∈N ,k ∈C (15)

z +
ik

+ z ik ≤

1 ∀ i ∈N ,k ∈C (16)

Constraint (12) ensures that only a node that needs a container becomes the
terminating node of a storage request. Constraint (13) ensures that only a node