1. Presented By
M.Sangeetha
Pondicherry University

2. CONTAINER ROUTING IN LINER SHIPPING
Conventional methods in container routing had 2
deficiencies
1) Satisfy level of service
2) Maritime cabotage.
To overcome we use a operational network
representation of a liner shipping network.

3. LINER SHIPPING NETWORK

4. Xiamen
Chennai (XM)
(CN)
Hong Kong
(HK)
Colombo
(CB)
Cochin
(CC)
Singapore
(SG)
SHIP ROUTE 1 (SR1) Jakarta
HK(1) -> JK(2) -> SG(3) -> HK (JK)
SHIP ROUTE 2 (SR2)
HK(1) -> XM(2) -> SG(3) -> CB(4) -> SG(5) -> HK
SHIP ROUTE 3 (SR3)
CB(1) -> CN(2) -> CC(3) -> CB

5. CONVENTIONS USED
 (O-D) – Origin Destination pair
 SR - Service Routes (Ship Routes)
P - Ports
R - Set of routes
 Nr - No. of portcalls (port)
 Pri - i th portcall (port) on route r .
 Ir - (1,2,3,…Nr}

6. REPRESENTATION
 A possible container path can be given as
+XM - SR2(2,4) + CB - SR3(1,2) + CN
+XM - Loading at Xiamen.
-SR2 – On ship route2 delivered at Colombo.
+CB – Loading at Colombo.
-SR3 – On ship route3 delivered at Chennai.
+CN – Loading at Chennai.

7. OPERATIONAL NETWORK

8. OPERATIONAL NETWORK
 (N,A) for O-D pairs where
N - Node Set (set of all nodes + source + sink)
A – Arc Set
 Arc Set A := Av U At U Asource U Asink
Av – Voyage Arcs
At – Transshipment Arcs
Asource – Arcs from source node
Asink – Arcs from sink node

9. VOYAGE ARCS
 a Є Av can be represented by (r,i)
 Voyage arcs are edges between adjacent nodes.
 Eg: a voyage arc connecting (r,i) and (r,i+1)
 Voyage arcs (r,Nr) is the voyage from node (r,Nr) to
node (r,1) because each ship route forms a loop.

10. VOYAGE ARCS Chennai
(CN) (2) SHIP ROUTE 3 (SR3)
CB(1) -> CN(2) -> CC(3) -> CB
Cochin Colombo
(CC) (3) (CB) (1)
Voyage : Colombo -> Chennai -> Cochin -> Colombo
(r,i) : (3,1) -> (3,2) -> (3,3) -> (3,1)
(r,i) -> (r,i+1) ->(r,i+2) / (r,N) -> (r,i)

11. TRANSSHIPMENT ARCS
 Transshipment nodes are those belonging to two ship
routes.
 A Transshipment arc a Є At can be represented by
((r,i),(s,j)) where pri = psj
 Containers are transshipped at a port that is present in
two routes.

12. TRANSSHIPMENT ARCS
Hong Kong
Colombo (HK) Xiamen
(CB) (Xm)
Singapore Jakarta
(SG) (JK)
SHIP ROUTE 1 (SR1) SHIP ROUTE 2 (SR2)
HK(1) -> JK(2) -> SG(3) -> HK HK(1) -> XM(2) -> SG(3) -> CB(4) -> SG(5) -> HK
Colombo (CB) to Jakarta (JK) : CB -> SG -> HK -> JK
Transshipment : Hong Kong (HK) ( SR2(1) and SR1(1) )
Hong Kong : P 11 = P21 ie Pri = psj

13. TIME AND COST
 Each arc a has time duration denoted by ta .
 For voyage time is calculated by ,
ta = t r2 – tr1
 For transshipment time is calculated by considering
the dwell time in a particular port.
 Similarly each arc a has a associated cost given by ca

14. OBJECTIVE
 Xa Є {0,1}, a Є A.
 Xa is 1 only if there exist a path in the network
 OBJECTIVE : Minimize the total cost
minxa ∑ aЄA CaXa
where Xa represent a container path
Ca represent the cost

15. CONSTRAINTS
 All paths from the source and sink are considered to be 1 .
 Flow conservation:
∑aЄAsource xa = 1
∑aЄAsink xa = 1

16. Cont’d...
 Containers never visit their origin port from other ports.
X(r,i-1) = 0 rЄR , I Є Ir , pri = origin
 Containers never go from their destination to other ports.
X(r,i) = 0 rЄR , I Є Ir , pri = destination
 Containers are never transshipped at origin or
destination port.
X((r,i),(s,j)) = 0 ((r,i),(s,j)) Є Aot U Adt

17. Cont’d…
 If the liner shipping company is subject to the maritime
cabotage restriction in the country of the origin port, then it
cannot transship the containers at that port.
X((r,i),(s,j)) = 0 , p Є PѲo ,((r,i),(s,j)) Є Apt
 Similarly, if there is restriction in the country of the
destination port,
X((r,i),(s,j)) = 0 , p Є PѲd ,((r,i),(s,j)) Є Apt

18. Cont’d...
 The transit time cannot exceed maximum allowable transit
time Tod
∑aЄAvU At taxa ≤ Tod
 The total cost cannot be larger than maximum allowable
cost.
∑aЄA Caxa ≤ Cod

19. SUMMARY
 The above model is an integer(binary) linear
programming model.
 This model can easily capture the various container
paths and obtain all paths that satisfy the constraints.