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NETWORK AND GRAPH PROBLEMS
- 1. NETWORK AND GRAPH PROBLEMS Dispatching of small containers via coastal freight liners: The case of the Aegean Sea BY : KURTULUŞ ÖZTÜRK S.OZAN ÖZCAN ARTICLE FROM: European Journal of Operational Research 152 (2004) 365–381
- 2. 1. INTRODUCTION Transportation of goods is an important problem in Aegean Sea for Greece. Because Greece possesses 14 854 km of coasts, 3500 islands and 750 ports and anchorages. By effect of this geographic discontinuity there are a lot of small and remote markets formed. A new approach is considered which includes transportation of goods with small containers, an important new technology, in an effort to reengineer coastal freight shipping. The problem, hereby referred to as Coastal Freight Shipping Problem (CFSP). For the planning case, a pilot network of 13 ports and 25 sea links were taken into consideration. Strategic planning will be analyzed by using an LP formulation for the determination of vessel traffic. Supply and demand constraints are known and total fuel costs and port dues are wanted to minimized.
- 3. Standart containers exhibit advantages particularly in the case of large islands, that have high demand for many goods. But these containers is not suitable for small islands which have small ports. So use of small containers with standardized dimensions, could be a rational solution for the transportation of goods to small islands since: Small containers may be easily loaded on passenger vessels without the use of special port cranes. Liner ships can carry small containers Small containers can be easily carried by smaller vessels that will be able to moor in islands with small ports. The capacity issue will be solved since small containers will serve island markets more efficiently than the existing standard ones. • There will be no need for additional infrastructure in the islands since small containers may be easily transported by medium-sized trucks within island hinterlands. • Small containers may remain on the islands, be loaded with new cargo and return to their origin (low connectivity cost). • Small containers may be easily used for door to door transport.
- 4. 2. PROBLEM DESCRIPTION Transportation network contains; nodes corresponding to ports and links corresponding to sea route between two ports . Nodes (ports) have a demand for certain types of goods (in tons) and supply of certain types of goods (in tons); and it is assumed that ports can accept any kind and number of ships. As the results of our analysis, if there must be a very large port at the present location of a small port or even a non-existent port, this will mean that new port infrastructure will have to be constructed for optimal functioning of cargo transport. On the other hand, links (sea routes) are bi-directional and both direction to be equal to actual distances in nautical miles. To simplify things, it is assumed that with small containers the only type of cargo transported.
- 5. The following considerations can be define and delimit the problem: • A planning horizon of one calendar year is selected so that seasonal fluctuations may be disregarded. • Since it is assumed that all goods are carried in small containers, cargo is measured not in tons but in number of small containers. Demand and supply numbers for ports are similarly expressed in terms of small containers. • Costs are include fuel consumption costs and port fees. The objective function is equal to the sum of fuel consumption costs and port dues as ships carry small containers along the routes. • According to node balance constraints incoming minus outgoing cargo be equal to or greater than the demand of the node and total supply not be exceeded. Also, cargo stored in a ship may not exceed ship capacity.
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- 7. 3. APPLICATION TO AEGEAN MARINE TRANSPORT Different goods types are actually transported between the nodes. These are usually categorized in three main categories which include fuels, raw materials and industrialized goods. In this work different vessel types are ignored and there is no limit on the fleet size. All vessels are assumed to have a capacity of 300 small containers or 1500 tons.
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- 9. Planned LP formulation is applied to a pilot network of 13 Aegean islands (in relatively close proximity to Piraeus) and their most ordinary links. The pilot network is shown in Fig. 2. Numbers on the links represent distance in nautical miles ;
- 10. * Fuel consumption is assumed to be €10 per nautical mile, corresponding to a market price of $200 per ton for marine diesel. * Therefore, in this problem, it is assumed that port dues amount to €20 per day. Demands and supplies of islands ;
- 11. OUR OBJECTIVE FUNCTION IS: Wij, of containers transported fromnode i to node j. Supposing that nij is the number of ships traveling from node i to node j. Lij is the length of link ij (miles) cF is the cost of fuel consumed per mile (EUR) cPi is the fee of port i per ship (EUR) lingo
- 12. CONSTRAINTS: (balance of incoming and outgoing containers at node i (demand must be satisfied at all nodes) 1
- 13. CONSTRAINTS: 2 Non-negativity constraints
- 14. MODEL: SETS: PORT/1..13/:DEMAND,SUPPLY; ROUTES(PORT,PORT):DIST,POSS,VESSEL; ENDSETS DATA: FUELCOST=10; DELAYCOST=20; DEMAND=360055 8002 1684 2992 6805 15875 1847 26495 29477 48805 23116 20251 5066; SUPPLY=331368 2293 723 568 924 171211 0 2429 21672 5008 28465 8457 1520; Q=300; table2
- 15. DIST=0 45 54 76 80 85 0 0 0 0 0 0 0 0 0 22 0 0 0 27 0 0 0 0 0 0 0 0 0 29 0 0 0 0 41 0 49 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0 21 0 0 36 0 31 0 37 0 0 0 0 0 0 0 0 0 0 0 0 48 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 13 11 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 26 22 0 0 0 0 0 0 0 0 0 0 0 0 18 27 0 0 0 0 0 0 0 0 0 0 0 0 28 0 0 0 0 0 0 0 0 0 0 0 0 0; network
- 16. POSS=0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0; network
- 17. MIN=((@SUM(ROUTES:DIST*VESSEL)*FUELCOST)+(@SUM(ROUTES:VESSEL)*DELAYCOST)); @FOR(PORT(I):@SUM(PORT(J)|J#LT#I: @SUM(PORT(K)|I#LT#K:VESSEL(J,I)*POSS(J,I)*Q-VESSEL(I,K)*POSS(I,K)*Q+ SUPPLY(I)-DEMAND(I)))=0); @FOR(ROUTES(I,J)|I#LT#J:VESSEL*POSS*Q>=0); @FOR(ROUTES(I,J)|I#LT#J:VESSEL(I,J)>=0); @GIN(ROUTES:VESSEL); END obj
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