The LNG Inventory Routing Problem with Pick-Up Contracts

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

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

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

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

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

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

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)

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)

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

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 ]

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

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

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

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 D1110 + acd D1210 = 2/3 a CD D2114 + acd D2214 = 1/3

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 D1110 + acd D1210 = 2/3 a CD D2114 + acd D2214 = 1/3 Q:96 T:10

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

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

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

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

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

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