1 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

2 Outline 1.Problem Description 2.Construction and Improvement Heuristic (CIH) 3.Computational Results 4.Future research

3 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 ShippingRegasification & Storage Gas Utilities ResidentialElectric Utilities Industries

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6 A Large Problem LNG tankers 8-20 long-term contracts 1 year planning horizon deliveries Two gas types: RLNG and LLNG Heterogeneous fleet Some contract specific ships

7 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

8 Constraints Routing constraints Inventory constraints (supply side) Berth constraints (loading port) Ship-Contract compatibility Maintenance constraints on ships

9 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

10 Mathematical Model Berth constraints Inventory constraints Soft Demand constraints Routing constraints Maintenance constraints

11 Construction & Improvement Heuristic (CIH)

12 Construction & Improvement Heuristic (CIH)

13 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

14 Construction Heuristic

15 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

16 Ship rankings Ships are prioritized in the following way 1.By how many contracts it may serve (few contracts prioritized) 2.By capacity to cost ratio (high ratio prioritized)

17 Lookahead parameter Best lookahead parameter seems to be linked to the inventory to production ratio of each gas type. K g = floor( Inventory * days/total production) + σ Where σ is an integer

18 Construction & Improvement Heuristic (CIH)

19 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)

20 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

21 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

22 Swapping ships between two SR Remove a pair (v 1,c 1,t 1 ) and (v 2,c 2,t 2 ) from S, add pair (v 2,c 1,t 1 ) and (v 1,c 2,t 2 ) to S –Limited by inventory constraints –Limited by routing constraints –Both ships must be allowed to serve both contracts

23 Swapping contracts between two SR Remove a pair (v 1,c 1,t 1 ) and (v 2, c 2, t 2 ) from S, add a pair (v 1,c 2,t 1 ) and (v 2,c 1,t 2 ) 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

24 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)

25 Construction & Improvement Heuristic (CIH)

26 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

27 Mathematical Programming Heuristic Variable generation: New constraints:

28 Computational Results (1:4) CIH-LS

29 Computational Results (2:4)

30 Computational Results (3:4)

31 Computational Results (4:4) 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

32 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

33 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

34 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

35 LNG Inventory Routing Problem - Introduction Jørgen Glomvik Rakke, Magnus Stålhane, Christian Rørholt Moe, Marielle Christiansen, Kjetil Fagerholt and Henrik Andersson Department of Industrial Economics and Technology Management, NTNU

36 Mathematical Model MIP model with scheduled routes as binary variables –A scheduled route consists of: Ship Destination (Contract) Departure day Based on pre-generation of all scheduled routes The main decision is which combination of ships should deliver LNG to which contracts, and when the deliveries are to be made. Problem DescriptionMathematical ModelResults

37 Objective Function Maximize revenue from selling LNG in the spot market Minimize transportation costs Penalize over- and under-delivery( and ) Problem DescriptionMathematical ModelResults

38 Constraints (1 / 3) Contractual constraints: –The contracts either outline: the monthly demand that is to be delivered, or that the LNG is to be delivered “fairly evenly spread” throughout the year. –Implemented as soft demand constraint with a hierarchy of penalty costs based on the length of the time partition. Ship inventory constraints: –All cargoes have to be full shiploads. –A cargo may only contain one type of LNG. Problem DescriptionMathematical ModelResults Constraints (1 / 3)

39 Constraints (2 / 3) Inventory constraints: –The amount of LNG in the storage tanks at the producer’s facility have to be between an upper and lower bound at all times during the planning horizon. –The production rates limits the number of possible shiploads in any given time interval. Berth constraints: –There are a limited number of berths available for loading each type of gas. Problem DescriptionMathematical ModelResults

40 Constraints (3 / 3) Routing constraints: –A ship may become available to lift its first cargo after the planning horizon has started. –Some ships are dedicated to only serve certain customers. –Due to vessel acceptance policies at some regasification terminals, not all ships can serve all customers. –The number of ships operated by the producer is limited. –Only Conventional ships may be chartered. –Pre-allocated activities for the ships may limit their availability during the planning horizon. Problem DescriptionMathematical ModelResults

41 Exact Solution Method Implemented in Mosel using Xpress IVT ver and solved by using Xpress Optimizer ver on a Pentium 4, 2.4 GHz. Could not solve the given real-world problem –~ binary variables for the tested problem instance –Flat objective function –Many (near) symmetric solutions –Large solution space The inability to solve the problem with an exact solution method motivates heuristic approaches. Problem DescriptionMathematical ModelResults

42 Sets (1 of 3)

43 Sets (2 of 3)

44 Sets (3 of 3)

45 Constants Problem DescriptionESMRHHCIHGAResultsF R

46 Variables Binary decision variables Continuous slack variables for over and under delivery

47 Objective function Minimize transportation cost Penalize over- and under-delivery Revenue from selling LNG in the spot market

48 Volume of LNG in the tank time Max capacity Safety-level ProductionShip loading

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