The LNG Inventory Routing Problem with Pick-Up Contracts Henrik Andersson Marielle Christiansen Roar Grønhaug Henrik Andersson
Agenda • The Liquefied Natural Gas Supply Chain • Problem characteristics – Regasification terminals – Ship movements – Liquefaction plants – Contracts • Model summary • Solution approach Henrik Andersson
The LNG Supply Chain Exploitation Liquefaction Shipping Regasification End users & Production & Storage & Storage • Exploitation & Production • Liquefaction / Storage • Shipping • Regasification / Storage • End users Henrik Andersson
The LNG Supply Chain Exploitation Liquefaction Shipping Regasification End users & Production & Storage & Storage • Exploitation & Production • Liquefaction / Storage • Shipping • Regasification / Storage • End users Henrik Andersson
Problem characteristics Liquefaction Shipping Regasification & Storage & Storage • Liquefaction plants • Regasification terminals – Contracts – Inventories – Port availability – Sales – Port availability • Ship movements – Paths – Boil-off Henrik Andersson
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 Henrik Andersson
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 Henrik Andersson
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) Henrik Andersson
Ship movements; Quantities • Boil-off – Can be used as fuel for the ship 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 Q 1 + Q 2 = Q v ·(1-B)·(7-1) Q 3 = Q v ·(1-B)·(10-7) Henrik Andersson
Liquefaction plants • One of many actors at the liquefaction plants • Contracts instead of inventories • Berth constraints Berth capacity • Inter-arrival gaps Time ≤ 1 1 ≤ 1 ≤ Henrik Andersson
Contract characteristics Q • Upper and lower limits on quantities Q U 1 Q L 1 • Start date and end T date T S T E 1 1 [Q U , Q L ] 1 1 • Partitions to [Q U , Q L ] [Q U , Q L ] regulate the 11 11 12 12 quantity loaded [Q U , Q L ] [Q U , Q L ] 13 13 14 14 Henrik Andersson
Contract characteristics • Connected to one D 1 liquefaction plant Q i D 2 • Designated P 1 regasification D 3 terminals D 4 • Destination restrictions Q 1 + Q 2 W(Q 1 + Q 2 + Q 3 + Q 4 ) ≥ Henrik Andersson
Contract characteristics • Destination and time dependent Q t1 prices P j – Contract – Quantity loaded Q t2 – Unloading time – Destination D i q t3 Cost : C Di t2 ·Q t1 Revenue : R Di t3 ·q t3 Henrik Andersson
Loading and unloading • Due to boil-off, we do not use quantities to connect the loading and unloading • Instead we use shares Share loaded at P 1 : 1 Share unloaded at D 1 : 2/3 Q:48 T:14 Share unloaded at D 2 : 1/3 D 2 Q:150 T:3 P 1 D 1 Q:96 T:10 Henrik Andersson
Loading and unloading; Contracts • Assume 2 contracts, both connected to P1 The share used for contact c when loading in time period t a CP ct The share used for contact c when unloading at regasification terminal i in time a CD ict period t Share loaded at P 1 : 1 Share unloaded at D 1 : 2/3 Q:48 T:14 Share unloaded at D 2 : 1/3 D 2 Q:150 T:3 = 1 a CP + a CP P 1 1 3 2 3 D 1 = 2/3 a CD + a CD D1 1 10 D1 2 10 Q:96 T:10 = 1/3 a CD + a CD D2 1 14 D2 2 14 Henrik Andersson
Connecting loading and unloading ⎛ ⎞ t ∑ ∑ Q:48 ⎜ ⎟ − ≥ ∈ ∈ 0, , CP CD a a c C t T τ τ ⎜ ⎟ T:14 c ic ⎝ ⎠ τ = ∈ D 2 S D T i N c Q:150 ⇓ T:3 P 1 ≥ = = CP 0 1, 3 a c t 13 D 1 − ≥ = = 0 1, 10 CP CD a a c t Q:96 13 1110 D T:10 − − ≥ = = CP CD CD 0 1, 14 a a a c t 13 1110 2114 D D ≥ = = CP 0 2 , 3 a c t = 1 23 a CP + a CP 1 3 2 3 − ≥ = = 0 2 , 10 CP CD a a c t 23 1210 D = 2/3 a CD + a CD D1 1 10 D1 2 10 − − ≥ = = CP CD CD 0 2 , 14 a a a c t 23 1210 2214 D D = 1/3 a CD + a CD D2 1 14 D2 2 14 Henrik Andersson
Model summary; Constraints • Regasification terminals • Contracts – Inventory balance constraints – Limits on quantity loaded on each contract – Limits on inventory levels and sales – Destination restrictions – Berth constraints • General • Ship movement – Connection constraints – Convexity constraints • Contracts • Loading – Implicit feasibility through the • Unloading path information • Path information • Liquefaction plants – Berth constraints – Inter-arrival gaps Henrik Andersson
Model summary; Objective + - - Liquefaction Shipping Regasification & Storage & Storage • Maximize Revenue from selling gas − Cost of purchasing gas − Ship operating costs Henrik Andersson
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 Henrik Andersson
Solution approach • Master problem – All of the above constraints – Implicit path feasibility Master problem Dual information Feasible paths Subproblem • Subproblem – Explicit path feasibility – Boil-off and quantity calculations Henrik Andersson
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 Henrik Andersson
Questions Henrik Andersson
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