Hub-and-Spoke Liner Shipping Network Design with Demand Uncertainty. 03/Jun/2013

Transcription

1 Hub-and-Spoke Liner Shipping etwork Design with Demand Uncertainty Speaker: Wang Tingsong 03/Jun/2013

2 Outline Introduction Literature Review Problem Statement Model Development Solution Algorithm umerical Example Conclusion 2

3 Introduction Liner Shipping Regular service Fixed schedule Fixed route Liner Operator A liner container shipping company typically operates a fleet of heterogeneous ships on a set of liner trade routes at a regular schedule in order to pick up and delivery cargoes for shippers 3

4 Introduction (cont d) Hub-and-Spoke (H&S) Main line: hub ports allocation line: feeder ports allocation Fleet deployment: ship assignment to main line and feeder line to provide pickup and delivery liner shipping service for shipper Uncertainty Uncontrollable and unpredicted factors Container shipment demand of a port pair 4

5 Introduction (cont d) Objectives How to design main line and feeder line? How to deal with uncertainty of container shipment demand? Model and solution algorithm Evaluation by implementing a numerical example 5

6 Literature Review Representative literature Author (s) Year Model Problem Statement Maurao et al 2001 IP Assign ships with hub and spoke constraints Aversa et al 2005 MIP Imai et al 2006 IP Konings 2006 Hsu and Hsieh 2007 MIP Takano and Arai 2008 MIP Locate a hub port in the East coast of South America Analyze mega ship viability and propose a model to deploy mega ship onto H&S shipping network Analyze the cost, service and geographical characteristics of H&S networks A two-objective model to design a shipping network by minimizing shipping cost and inventory cost Containerized cargo transport problem with H&S network Imai et al 2009 MIP Compare multi-ports liner shipping network and H&S network 6/26

7 Problem Statement Given a set of ports which can be divided into two groups: hub and spoke, and given a set of ships which can be divided into two groups: mega ship and feeder ship, it intends to make an optimal hub-and-spoke shipping network design to minimize the total cost over a given short-term planning horizon while satisfies a predetermined service-level. How to design main line? How to allocate the feeder ships to each feeder line? 7

8 Problem Statement (cont d) Assumption The planning horizon is 6 months Containers are homogeneous, all refer to TEUs The liner operators are required to maintain a weekly shipping frequency only on main line The time of ships travelling between any two pots are known and fixed o direct link between any two spokes Containers can be transferred via at most two hub ports 8

9 Model Development A typical hub-and-spoke liner shipping network feeder line spoke hub main line mega ships feeder ships 9

10 Model Development(cont d) Decision Variables 10

11 Model Development (cont d) Objective Function Z = min c khs zk + c vhj zv + s S h H h, j k v V H V intrinsic cost transporting cost transshiping cost ckhs xkhs + cvhj xvhj + s S h H h, j k V H v V c y + c y trans trans h khs h vhs s S h H s h k S H v V V 11

12 Model Development (cont d) Constraints x z C, k V, h H, s S khs k k vhj v v V x z C, v, h, j H y x, k V, h H, s S khs khs yvhs xvhj, v V, h, j H s S k khs kh k khs max ( ) ( ˆ max ) δ, z t + tˆ t δ, k V, h, H s S z t + t t v V v vhj vj vhj v h, j H s S k V v V δ1,, h H k V khs δ1,, h H s S khs δδ7, t,, v V h j H vhj vhj vhj h, j H Prξ, zk, Ck 1 hs h H s S α k V Prξ,, zv Cv 1 hj h j H α capacity constraints Transshipment constraints Time constraints Ship constraints Chance constraints 12

13 Solution Algorithm Difficulties of Solving the Model onlinear ( ˆ max ) δ, z t + t t v V v vhj vj vhj v h, j H Probabilistic form Prξ, zk, Ck 1 hs h H s S α k V Prξ,, zv Cv 1 hj h j H α v V 13

14 Solution Algorithm (cont d) Linearization It is noticed that if decision variables is removed, then the problem is reduced to a mixed integer linear programming (MILP) model with chance constraints. If the mega ship v serves only two ports and does not visit any other port enroute, it makes the maximum number of trips; if it serves all ports enroute, it makes the minimum number of trips z v For example, if 2 5, then has 4 values: 2,3,4,5. For each problem with a corresponding value of MILP model with chance constraints. z v z v z v, it is a 14

15 Solution Algorithm (cont d) Sample Average Approximation (SAA) Let ( zξ, ξ ) = max h H, s S FL hs k k k V ( zξ, ξ) = max h, j H ( ) ( ) FL We then define ( z ξ ) ( z ) ML p ( z ξ ) = ( z ) > ML hj v v v V Rewrite the chance constraints p : = Pr, > 0 : Pr, 0 z z C C Prξ, zk, Ck 1 hs h H s S α k V Prξ,, zv Cv 1 hj h j H α v V p p ( z ) ( z ) α α 15

16 Solution Algorithm (cont d) SAA(Atlason et al., 2008; Luedtke and Ahmed, 2008) FL n Let p ( z ξ ) = 11( 0, ) ( z, ) p n= 1 ( ) ( z ξ ) = 11 ( ) ( 0, ) z, n= 1 ( ) FL n 11 ( )( y 0, ) 1, if y > 0, : = 0, if y 0. Law of Large umber Theory Then p ( z ) p ( z ) α α p p ( z ) ( z ) β β β can be different with α 16

17 Solution Algorithm (cont d) MILP { } Z β = min intrinsic cost + transporting cost + transshiping cost s.t. capacity constraints + Transshipment constraints + Time constraints + Ship constraints + Chance constraints p p ( z ) ( z ) β equivalent β equivalent n n ϑ ξξ, + 1, z, ; C, n = h H s S n hs k k hs k V ϑn β n= 1 n n ϑ ξξ, + 1, z, C;, n = h j H n hj v v hj v V ϑn β n= 1 ϑn ϑn { }, 0,1 17

18 Solution Algorithm (cont d) Solution quality(luedtke and Ahemd, 2008) Lower bound L Let βα >, L is a lower bound of Z with a significance level ε Z β Upper bound Z β U Let βα <, U is a upper bound of Z with a significance level ε 18

19 umerical Example 19

20 Results Sensitivity Analysis of SAA Parameters 20

21 Results(cont d) Xingang Dalian Qingdao Shanghai Shekou Hong Kong Penang Port Kelang Singapore 21

22 Results(cont d) 22

23 Conclusion A H&S shipping network design problem Demand uncertainty Linearization SAA 23

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