The LNG Inventory Routing Problem with Pick-Up Contracts

Transcription

1 The LNG Inventory Routing Problem with Pick-Up Contracts Marielle Christiansen Roar Grønhaug

2 Agenda The Liquefied Natural Gas Supply Chain Problem characteristics Regasification terminals Ship movements Liquefaction plants Contracts Model summary Solution approach

3 The LNG Supply Chain Exploitation & Production Liquefaction & Storage Shipping Regasification & Storage End users Exploitation & Production Liquefaction / Storage Shipping Regasification / Storage End users

4 The LNG Supply Chain Exploitation & Production Liquefaction & Storage Shipping Regasification & Storage End users Exploitation & Production Liquefaction / Storage Shipping Regasification / Storage End users

5 Problem characteristics Liquefaction & Storage Shipping Regasification & Storage Liquefaction plants Contracts Port availability Regasification terminals Inventories Sales Port availability Ship movements Paths Boil-off

6 Regasification terminals Assuming full control at the regasification terminals I L Inventory I U Q S L Sales S U Inventory balance Berth constraints T

7 Ship movements Information about the ship movements is contained in paths consisting of: Geographical route Visits and sequence Schedule Times for loading and unloading Quantity Loaded and unloaded

8 Ship movements; Network The ship movements can be represented in a time-space network D 2 D 1 P 2 P 1 D 2,4,Q 1 D 1,6,Q 2 D 1,8,Q 3 P 1,1,Q v P 2,7,Q v P 1,10,Q v Each path in the network corresponds to at least one set of (route, schedule, quantities)

9 Ship movements; Quantities Boil-off Can be used as fuel for the ship D 2 D 1 P 2 P 1 P 1,1,Q v D 2,4,Q 1 D 1,6,Q 2 P 2,7,Q v D 1,8,Q 3 P 1,10,Q v Q 1 + Q 2 =Q v (1-B) (7-1) Q 3 = Q v (1-B) (10-7)

10 Liquefaction plants One of many actors at the liquefaction plants Contracts instead of inventories Berth constraints Berth capacity Inter-arrival gaps 1 Time 1 1

11 Contract characteristics Upper and lower limits on quantities Q Q U 1 Q L 1 Start date and end date T S 1 T E 1 T Partitions to regulate the quantity loaded [Q U 1, QL 1 ] [Q U 11, QL 11 ] [QU 12, QL 12 ] [QU 13, QL 13 ] [Q U 14, QL 14 ]

12 Contract characteristics Connected to one liquefaction plant Q i D 1 Designated regasification terminals P 1 D 2 D 3 Destination restrictions Q 1 + Q 2 W(Q 1 + Q 2 + Q 3 + Q 4 ) D 4

13 Contract characteristics Destination and time dependent prices Contract Quantity loaded Unloading time Destination P j Q t1 D i Q t2 q t3 Cost : Revenue : C Di t2 Q t1 R Di t3 q t3

14 Loading and unloading Due to boil-off, we do not use quantities to connect the loading and unloading Instead we use shares Q:150 T:3 Q:48 T:14 D 2 Share loaded at P 1 : 1 Share unloaded at D 1 : 2/3 Share unloaded at D 2 : 1/3 P 1 D 1 Q:96 T:10

15 Loading and unloading; Contracts Assume 2 contracts, both connected to P1 a CP ct a CD ict The share used for contact c when loading in time period t The share used for contact c when unloading at regasification terminal i in time period t Q:48 T:14 Share loaded at P 1 : 1 Share unloaded at D 1 : 2/3 Share unloaded at D 2 : 1/3 P 1 Q:150 T:3 D 2 a CP 13 + acp 23 = 1 D 1 Q:96 T:10 a CD D acd D1210 = 2/3 a CD D acd D2214 = 1/3

16 Connecting loading and unloading t τ = T CP 13 CP CD 13 D1110 CP CD CD 13 D1110 D2114 CP 23 S c CP CD acτ aicτ 0, c C, t T D i N a 0 c = 1, t = 3 a a 0 c = 1, t = 10 a a a 0 c = 1, t = 14 a 0 c = 2, t = 3 CP CD 23 D1210 a a 0 c = 2, t = 10 CP CD CD 23 D1210 D2214 a a a 0 c = 2, t = 14 P 1 Q:150 T:3 a CP 13 + acp 23 = 1 Q:48 T:14 D 2 D 1 a CD D acd D1210 = 2/3 a CD D acd D2214 = 1/3 Q:96 T:10

17 Model summary; Constraints Regasification terminals Inventory balance constraints Limits on inventory levels and sales Berth constraints Ship movement Convexity constraints Implicit feasibility through the path information Liquefaction plants Berth constraints Inter-arrival gaps Contracts Limits on quantity loaded on each contract Destination restrictions General Connection constraints Contracts Loading Unloading Path information

18 Model summary; Objective Liquefaction & Storage Shipping Regasification & Storage Maximize Revenue from selling gas Cost of purchasing gas Ship operating costs

19 Solution approach; Branch and price Branch-and-price Solve the model with a restricted number of paths using branch-and-bound Each node in the branch-and-bound tree is solved using column generation

20 Solution approach Master problem All of the above constraints Implicit path feasibility Master problem Dual information Feasible paths Subproblem Explicit path feasibility Boil-off and quantity calculations Subproblem

21 Summary An important part of the LNG supply chain has been modeled Pick-up contracts with destination restrictions Path-based model Separates path assignment and path feasibility Branch-and-price Works well for similar problems

22 Questions