The LNG Inventory Routing Problem with Pick-Up Contracts Henrik - - PowerPoint PPT Presentation

Henrik Andersson

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 & Production

Exploitation & Production Liquefaction & Storage Shipping Regasification & Storage End users

• Liquefaction / Storage
• End users
• Shipping
• Regasification / Storage

Henrik Andersson

The LNG Supply Chain

• Exploitation & Production

Exploitation & Production Liquefaction & Storage Shipping Regasification & Storage End users

• Liquefaction / Storage
• End users
• Shipping
• Regasification / Storage

Henrik Andersson

Problem characteristics

• Liquefaction plants

– Contracts – Port availability

• Regasification

terminals

– Inventories – Sales – Port availability

• Ship movements

– Paths – Boil-off

Liquefaction & Storage Shipping Regasification & Storage

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Regasification terminals

• Assuming full control at the regasification

terminals

– IL ≤ Inventory ≤ IU – SL ≤ Sales ≤ SU – Inventory balance – Berth constraints

Q T

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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

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Ship movements; Network

• The ship movements can be represented in

a time-space network

– Each path in the network corresponds to at least one set of (route, schedule, quantities)

P1 ,1,Qv D2 ,4,Q1 D1 ,6,Q2 P2 ,7,Qv D1 ,8,Q3 P1 ,10,Qv

P2 D1 P1 D2

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Ship movements; Quantities

• Boil-off

– Can be used as fuel for the ship Q3 = Qv ·(1-B)·(10-7) Q1 + Q2 = Qv ·(1-B)·(7-1)

P1 ,1,Qv D2 ,4,Q1 D1 ,6,Q2 P2 ,7,Qv D1 ,8,Q3 P1 ,10,Qv

P2 D1 P1 D2

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Liquefaction plants

• One of many actors at the liquefaction

plants

• Contracts instead of inventories
• Berth constraints
• Inter-arrival gaps

Berth capacity Time ≤ 1 ≤ 1 ≤ 1

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Contract characteristics

• Upper and lower

limits on quantities

• Start date and end

date

• Partitions to

regulate the quantity loaded

TE

1

TS

1

QL

1

QU

1

Q T [QU

1

, QL

1

] [QU

11

, QL

11

] [QU

12

, QL

12

] [QU

14

, QL

14

] [QU

13

, QL

13

]

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Contract characteristics

• Connected to one

liquefaction plant

• Designated

regasification terminals

• Destination

restrictions

Q1 + Q2 ≥ W(Q1 + Q2 + Q3 + Q4 ) D3 D4 D2 D1 P1 Qi

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Contract characteristics

• Destination and

time dependent prices

– Contract – Quantity loaded – Unloading time – Destination

Cost : CDi

t2·Qt1

Revenue : RDi

t3·qt3

Qt1 Pj Qt2 qt3 Di

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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 Q:96 T:10 P1 D2 D1

Share loaded at P1 : 1 Share unloaded at D1 : 2/3 Share unloaded at D2 : 1/3

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Loading and unloading; Contracts

• Assume 2 contracts, both connected to P1

aCP

ct

The share used for contact c when loading in time period t

aCD

ict

The share used for contact c when unloading at regasification terminal i in time period t

Q:150 T:3 Q:48 T:14 Q:96 T:10 P1 D2 D1

Share loaded at P1 : 1 Share unloaded at D1 : 2/3 Share unloaded at D2 : 1/3

aCP

13

+ aCP

23

= 1 aCD

D1110

+ aCD

D1210

= 2/3 aCD

D2114

+ aCD

D2214

= 1/3

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Connecting loading and unloading

Q:150 T:3 Q:48 T:14 Q:96 T:10 P1 D2 D1

aCP

13

+ aCP

23

= 1 aCD

D1110

+ aCD

D1210

= 2/3 aCD

D2114

+ aCD

D2214

= 1/3

13 13 1110 13 1110 2114 23 23 1210 23 1210 2214

0, , 1, 3 1, 10 1, 14 2 , 3 2 , 10 2 , 14

S D c

t CP CD c ic T i N CP CP CD D CP CD CD D D CP CP CD D CP CD CD D D

a a c C t T a c t a a c t a a a c t a c t a a c t a a a c t

τ τ τ = ∈

⎛ ⎞ ⎜ ⎟ − ≥ ∈ ∈ ⎜ ⎟ ⎝ ⎠ ⇓ ≥ = = − ≥ = = − − ≥ = = ≥ = = − ≥ = = − − ≥ = =

∑ ∑

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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

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Model summary; Objective

• Maximize

Revenue from selling gas − Cost of purchasing gas − Ship operating costs

Liquefaction & Storage Shipping Regasification & Storage

+

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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

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Solution approach

• Master problem

– All of the above constraints – Implicit path feasibility

• Subproblem

– Explicit path feasibility – Boil-off and quantity calculations Master problem

Dual information Feasible paths

Subproblem

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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