1 A construction and improvement heuristic for a large scale liquefied natural gas inventory routing problem Magnus Stålhane, Jørgen Glomvik Rakke, Christian.

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A construction and improvement heuristic for a large scale liquefied natural gas

inventory routing problem

Magnus Stålhane, Jørgen Glomvik Rakke, Christian Rørholt Moe, Marielle Christiansen, Kjetil Fagerholt and Henrik Andersson

Department of Industrial Economics and Technology Management, NTNU

22.09.2009

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Outline

1. Problem Description

2. Construction and Improvement Heuristic (CIH)

3. Computational Results

4. Future research

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Problem Description

• A combined large-scale route scheduling and inventory management problem for a producer and distributor of LNG

• The goal is to create an annual delivery program (ADP) that:– Minimize cost of fulfilling the producers long-term contracts– Maximize profit from spot-contracts

Exploitation& Production

Liquefaction& Storage

Shipping Regasification& Storage

Gas Utilities

ResidentialElectric Utilities

Industries

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5

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A Large Problem

• 30-50 LNG tankers• 8-20 long-term contracts• 1 year planning horizon • 300-600 deliveries• Two gas types: RLNG and LLNG• Heterogeneous fleet• Some contract specific ships

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Assumptions

• Unlimited number of spot ships available for chartering

• Inventory management only on supply side• Discrete time (days)• Always spot-demand for LNG• Maintenance can be performed ”en-route”• A ship will only visit one regasification terminal on

each voyage, and all loads have to be full ship loads

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Objective Function

Maximize revenue from selling LNG in the spot market

Minimize transportation costs

Penalize under-delivery

LNG

Add value of LNG in tank at end of year

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Mathematical Model

Berth constraints

Inventory constraints

Soft Demand constraints

Routing constraints

Maintenance constraints

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Construction & Improvement Heuristic (CIH)

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Definition of a Scheduled Route

• A feasible solution to the ADP planning problem consists of a set S of Scheduled Routes (SR),

with SR = (v,c,t) – v is the ship sailing

– c is the contract (destination)

– t is the day loading starts at the loading port

– The three parameters above implicitly give the day of delivery and the return day to the loading port

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Construction Heuristic

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Contract rankings

• Two principal ideas:– Rank by volume left to be delivered– Rank by percentage of demand left to be delivered

• Solution:– A combination of the two above.– If the difference in percentage is greater than some value α, rank by percentage– Otherwise, rank by volume

• Spot contracts are given artificial demand equal to β times the excess production in a month

• At the end of each month, deviations from contractual demands for long-term contracts are transferred to the next month

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Ship rankings

• Ships are prioritized in the following way1. By how many contracts it may serve (few contracts prioritized)

2. By capacity to cost ratio (high ratio prioritized)

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Lookahead parameter

• Best lookahead parameter seems to be linked to the inventory to production ratio of each gas type.

• Kg = floor( Inventory * days/total production) + σ

• Where σ is an integer

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Local Search

• Improves the ADP created by the construction heuristic

• Neighborhood search by replacing/swapping ships v and contracts c in the Scheduled Routes (v,c,t)

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Changing contract (destination) of a SR

• Re-routing the destination of a Scheduled route from one contract to another– Replace (v,c,t) with (v,c*,t) where c ≠ c*

– Limited by the restrictions on which contracts the ship may serve

– Limited by the routing constraints

– c and c* must have demand for same type of LNG

Ship

Potential route Contract 7

0 10 20 30

Contract 2Contract 1 Contract 5Ship

Potential route Contract 7

0 10 20 30

Contract 1 Contract 5 Contract 2Ship Contract 7

Potential route

0 10 20 30

Contract 5 Contract 2Ship

Potential route

0 10 20 30

Contract 1 Contract 5 Contract 2

Contract 6

Ship

Potential route

0 10 20 30

Contract 6

Contract 1 Contract 5 Contract 2Ship

Potential route

0 10 20 30

Contract 6Contract 1 Contract 2

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Changing ship used on a SR

• Replacing the ship used on a scheduled route– Replace (v,c,t) with (v*,c,t) where v ≠ v*

– Limited by the restrictions on which contracts the ship may serve

– Limited by the Inventory contraints

– Limited by the routing contraints

Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 1

Contract 1

Contract 4

Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 1Contract 4

Contract 1Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 4

Contract 1

Contract 1

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Swapping ships between two SR

• Remove a pair (v1,c1,t1) and (v2,c2,t2) from S,

add pair (v2,c1,t1) and (v1,c2,t2) to S

– Limited by inventory constraints

– Limited by routing constraints

– Both ships must be allowed to serve both contracts

Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 1

Contract 4 Contract 1


Ship 2 Contract 2

0 10 20 30



Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 1

Contract 1

Contract 4

Contract 5

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Swapping contracts between two SR

• Remove a pair (v1,c1,t1) and (v2, c2, t2) from S,

add a pair (v1,c2,t1) and (v2,c1,t2) to S

– Limited by routing constraints

– Both ships must be allowed to serve both contracts

– Both contracts must have demand for same type of LNG

Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 1

Contract 4

Contract 5

Contract 2

Ship 1 Contract 3

Ship 2 Contract 2

0 10 20 30

Contract 1

Contract 4Contract 2


Ship 2 Contract 2

0 10 20 30



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Additional search moves

• Adding a SR to the ADP, S = S U (v,c,t)• Deleting a SR from the ADP, S = S\ (v,c,t)

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Mathematical Programming Heuristic

• Uses mathematical model with parts of solution fixed• Uses one feasible ADP as starting point• For each SR = (v,c,t)

– If it is going to a long-term contract, we fix c and t

– If it is going to a spot-contract, we fix t

– If it is going to maintenance, we do nothing

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Mathematical Programming Heuristic

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Variable generation:

New constraints:

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Computational Results (1:4)

Case (ships-contracts-days) Opt. Gap UB - LB34-8-365 48.79 % 2243534-8-242 14.32 % 1475734-8-181 40.36 % 1372934-8-120 13.67 % 901134-8-91 15.67 % 11434

16-4-365 18.92 % 435616-4-242 8.84 % 454116-4-181 18.25 % 374416-4-120 14.54 % 313416-4-91 11.94 % 2013

46-17-365 2.21 % 3185846-17-241 2.57 % 2613846-17-181 2.20 % 1792446-17-120 2.39 % 1309546-17-91 1.79 % 7207

30-8-365 2.47 % 2134530-8-241 2.99 % 1896530-8-181 5.06 % 2510730-8-120 3.51 % 1152630-8-91 1.11 % 2655

CIH-LS

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Computational Results (2:4)CIH-Con-MIP CIH-LS-MIP

case (ships-contracts-days) Opt. Gap Opt. Gap34-8-365 192.44% 51.91%34-8-241 16.07% 19.41%34-8-181 166.14% 37.70%34-8-120 42.74% 9.35%34-8-90 19.27% 10.52%

16-4-365 47.20% 18.92%16-4-241 11.24% 7.82%16-4-181 19.28% 16.64%16-4-120 33.23% 17.73%16-4-90 27.13% 11.65%

46-17-365 2.03% 1.84%46-17-241 2.98% 2.56%46-17-181 3.74% 2.82%46-17-120 4.09% 2.40%46-17-90 2.18% 0.39%

30-8-365 3.67% 1.59%30-8-241 1.82% 2.99%30-8-181 5.40% 5.20%30-8-120 1.08% 0.81%30-8-90 1.10% 1.10%

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Case (ships-contracts-days) CPU(s) MP<CIH34-8-365 1587 >8640034-8-242 642 >8640034-8-181 318 193034-8-120 157 181334-8-91 87 180

16-4-365 152 960516-4-242 76 141816-4-181 42 15916-4-120 23 7616-4-91 15 130

46-17-365 1788 >8640046-17-241 729 >8640046-17-181 410 1434846-17-120 218 33746-17-91 206 215

30-8-365 530 >8640030-8-241 226 >8640030-8-181 134 5430-8-120 66 22330-8-91 44 31309

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• Provides very good solutions in a short period of time– Creates a feasible, low-cost ADP in less than a second.– Algorithm creates an ADP for ”all” combinations of parameters (α, β, σ) and

selects the best – Total running time less than 30 minutes

• Local search does improve the constructed ADP significantly

• Mathematical programming may be used to improve ADP further

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Concluding remarks and Future Research

• Presented a heuristic solution approach to a large scale inventory routing problem.

• CIH provides good solutions to the problem in short time• CIH is well suited for a Decision support system:

– is flexible in time used– Deterministic

• Look at Robustness and disruption management• Exact and other heuristic solution approaches• Improve lower bound

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22.09.2009

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22.09.2009

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1 A construction and improvement heuristic for a large scale liquefied natural gas inventory routing problem Magnus Stålhane, Jørgen Glomvik Rakke, Christian.

Documents

month slide

construction heuristic

loading port slide

end of year slide

future research slide

inventory management

volume spot contracts

lng maintenance