and-spoke routing on a maritime container network

Transcription

1 Direct versus hub-and and-spoke routing on a maritime container network Chaug-Ing Hsu and Yu-Ping Hsieh Department of Transportation Technology & Management National Chiao Tung University, Taiwan 7 th Maritime Transportation System R&T Coordination Conference, Nov , 2004, Washington D.C.

2 Introduction-Motivation Container carriers operate in an increasing competitive and market-driven environment. Most of them continuously provide their services using hub-and-spoke networks. Under a hub-and-spoke networks, economies of flow can be realized by consolidating freight through a hub and using large ships. Routing all freight through a hub is not appropriate in any situations. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.2

3 Introduction-Motivation Although the average shipping cost per TEU decreases on main-line of hub-and-spoke networks, Freight originated in feeder ports must be transshipped through a hub, and incur extra shipping distance, shipping time, port charges and loading/unloading charges. Container carriers must decide whether to route a shipment through a hub or directly to its destination. This study constructs an analytical model on exploring this issue. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.3

4 Introduction-Literature Review Previous studies were focused on general networks, while studies about hub-and-spoke networks were few. Some proposed employing constraints to deal with the characteristic of transshipment. Some introduced cost discount on main-line shipping to deal with flow economics. Differing from previous studies, this study formulates flowdependent cost functions and constructs a two-objective model to deal with this two characteristics, respectively. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.4

5 Introduction-Methodology Based on that ocean carriers consider not only lowering their shipping costs, but also enhancing their service, thereby attracting more shippers. The inventory costs usually are the main considerations of shippers. A two-objective model by individually minimizing shipping costs and inventory costs is constructed. This model not only provides flexibility for ocean carriers in routing, ship size decision-making, but also provides a tool to analyze the trade-off between these two costs. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.5

6 Introduction-Objective Formulate both shipping and inventory cost functions by analyzing a multi-port calling route. Determine the Pareto optimal solutions of the two-objective model. Show the optimal routing, ship size and sailing frequency with respect to each level of inventory cost. Present an example that demonstrates the usefulness of the proposed model. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.6

7 Cost Functions Shipping Cost Function, TC1 m Shipping costs can be divided into three main categories: Capital and operating cost, fuel cost, and port charge. Capital and operating cost m m Di TC 1 = fs t ( Wi + ) + St V f f i i α i m ( F D + B )+ it t + i i j it t β it Ri + G i m Qij + Q R i j i m m ( Q + Q ) ij ji m ji + Fuel cost Port charge 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.7

8 Cost Functions (Cont.) Inventory cost function, TC2 m Inventory costs represents opportunity cost or loss of value that cargo cannot be used or sold in the shipping process. Only inventory costs related to container shipping process are taken into account, involving the waiting time cost and the shipping time cost. TC2 m 91H = 2 f H i j Q m ij + W D m m m k Qij δijk k + i j k Vt Waiting time cost + H f i j k l Q m ij R δ k m ijk m m ( Q + Q ) kl lk Shipping time cost 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.8

9 Ship Size and Sailings Frequency Decision For any type of ship, there is a trade-off between shipping costs and inventory costs. The relationship is a hyperbolic function: TC1 m Shipping costs(tc1 m ) decrease as inventory costs(tc2 m ) increase (TC2 m t,tc1m t ) TC2 m A complete optimal solution does not exist due to these two costs conflict with each other. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.9

10 Ship Size and Sailings Frequency Decision Instead of a complete optimal solution, the Pareto optimality concept introduced herein. The Pareto optimality is the solution where no objective can be reached without simultaneously worsening at leasing one of the remaining objectives. The hyperbolic function indicates not only trade-off between two costs, but also solutions for the two-objective model. Consider the capacity constraint, then the feasible solutions can be determined. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.10

11 Routing Decision Whether shipping through a hub or directly to its destination can be determined by comparing Pareto optimal solutions for the two types of shipping routes. Since Pareto optimal solutions for one feeder line won t be affected by all other feeder lines, only costs on three lines are considered. hub Main line, q h -q d hub hub Main line, q h hub Feeder line, q s -q d spoke Direct line, q d Feeder line, q s spoke Shipping directly to its destination Shipping through a hub 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.11

12 Routing Decision Costs for shipping through a hub The total shipping costs(ttc1 t ) and inventory costs(ttc2 t ) for shipping through a hub can be expressed as ( h ) s ( s q TC q ) t h TTC1 = TC1 * + 1 t ( h ) s ( s q TC q ) t h TTC2 = TC2 * + 2 t Costs for the main line Costs for the feeder line Constant Trade-off Since a hub has the advantage of cargo-consolidation, the study assumes cargo flow in main line is very large. Then, the main line can be served with the minimum shipping cost. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.12

13 Routing Decision Since there is a trade-off between shipping and inventory costs of the feeder line. The Pareto optimal solutions for the feeder line can be determined. Consequently, the Pareto optimal solutions for shipping through a hub can be determined. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.13

14 Routing Decision Costs for shipping directly to its destination The total shipping costs(ttc1 d ) and inventory costs(ttc2 d ) for shipping directly to its destination can be expressed as h d s s d d d ( q q ) + TC1 ( q q ) TC ( q ) d h TTC1 = TC1 * + 1 t h d s s d d d ( q q ) + TC2 ( q q ) TC ( q ) d h TTC2 = TC2 * + 2 t Costs for the main line Costs for the feeder line Costs for the direct line Constant Trade-off Trade-off 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.14

15 Routing Decision Since there are trade-offs between shipping costs and inventory costs of feeder line and directly line. The Pareto optimal solutions for these two line can be determined by the cost functions formulated. Consequently, the Pareto optimal solutions for shipping directly to its destination can be determined. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.15

16 Example A Transpacific containership service from Far East to US West Coast is considered herein to demonstrate the application of the proposed models. The objective of the example attempts to a make analysis about routing decision whether shipping container from Manila to US West Coast through hub port Kaohsiung or directly to US West Coast. Busan 5230 Los Angeles Busan 5230 Los Angeles Kaohsiung Kaohsiung 342 Hong Kong 543 Malia 342 Hong Kong 543 Malia Shipping directly to its destination Shipping through a hub 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.16

17 Example Suppose five types of ships are used. Port relative parameters are estimated from data of Kaohsiung Harbor. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.17

18 Example-Shipping through a hub The Pareto optimal solutions for shipping through a hub are determined: The optimal ship size of feeder line is T4, T2 and T1 for three cases. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.18

19 Example-Shipping directly to its destination The Pareto optimal solution for shipping directly to its destination are shown: The optimal ship size is shown in Table: The inventory costs for direct shipping Optimal ship size TTC2 d Direct line Feeder line TTC2 d < 7.36*10 7 T4 T4 7.36*10 7 < TTC2 d < 8.43*10 7 T4 T1 8.43*10 7 < TTC2 d < 8.66*10 7 T4 T2 8.66*10 7 < TTC2 d < 8.69*10 7 T5 T1 8.69*10 7 < TTC2 d < 8.92*10 7 T5 T2 8.92*10 7 < TTC2 d < 10.92*10 7 T5 T4 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.19

20 Example-Routing Decision The figure shows both Pareto optimal solutions for shipping through hub port and directly to its destination. For the range of inventory cost between 7.358*10 7 and 8.015*10 7 USD, transshipment is preferred, while for others direct shipping is preferred. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.20

21 Example-Flow increases This figure shows that as container flow between origin and destination port raises five times, no matter what the inventory cost are, the shipping directly is always the optimal routing decision. The result shows that the routing decision tends to shipping directly as container flow between origin and destination ports increases. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.21

22 Conclusions This study developed a two-objective model by individually minimizing shipping costs and inventory costs to decide ship size and routing strategies for container carriers. Shipping and inventory cost function are formulated for a multi-port calling route. Based on a trade-off between two costs for two types of shipping routes, Pareto optimal solutions of the two-objective model are determined. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.22

23 Conclusions(Cont.) A routing decision can be illustrated and made in objective value space. The optimal routing, ship size and sailings frequency with respect to each level of inventory cost is shown. The optimal decision tends to be direct shipping as container flow between origin and destination ports increases. 7 th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.23

24 Thank You! Chaug-Ing Hsu Yu-Ping Hsieh Department of Transportation Technology and Management National Chiao Tung University 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, R.O.C. Fax: , Tel: th MTS R&T Coordination Conference, Nov , 2004, Washington D.C., P.24