A Multi-Period Optimization Model for the Design of New LNG Supply Chains

A multi-period optimization model for the design of new LNG supply chains Alice Bittante Henrik Saxén Frank Pettersson Åbo Akademi University, Turku, Finland, {alice.bittante,henrik.saxen, frank.pettersson}@abo.fi Abstract The rising interest in LNG and the lack of infrastructures have served to activate several LNG- This paper presents a mathematical model developed to related projects worldwide. Among these, a new market aid decision making in the design of a supply chain for segment of small-scale LNG supply chains has become liquefied natural gas (LNG). The supply problem increasingly important, promoting LNG utilization for considers the delivery of LNG from a number of supply middle- to small-scale applications and in sparsely ports to a set of consumers by maritime transportation to distributed areas. Traditionally, the LNG supply chains satellite terminals and by land-based truck transports have been designed for large volumes transported over from the terminals to consumers on or off the coast. The long distances with LNG cargo capacities between model addresses both tactical and strategic aspects in the 125,000 m3 and 140,000 m3 (but with tanker sizes up to design of a new supply chain, optimizing maritime 265,000 m3 currently available), in what is called liner routing of a heterogeneous fleet, truck connections and shipping networks. Small-scale supply chains present the strategic locations of the satellite terminals. The specific characteristics and features, which differ objective is to minimize the overall cost for the selected substantially from larger chains. Vessels capacities vary time horizon, considering both operation and investment from some thousand cubic meters to 30,000-40,000 m3 costs. By contrast to an earlier effort by the authors, the and the ship loads can be split on consecutive receiving present work also addresses storage sizes and inventory ports. Demands are small and distributed over short at the satellite terminals by applying a multi-period distances, from hundred to a few thousand kilometers. formulation. The performance of the model is illustrated Satellite terminals are equipped with small storage tanks by a case study, where the optimal LNG supply chain (<50,000 m3) to be refilled once or a few times a month. for a coastal region at a gulf was designed. The model Given the high investment cost involved in both was found to be a flexible tool for an initial design and infrastructure and operation of such supply networks, feasibility analysis of small-scale LNG supply chains. the optimization of the supply chain design can have a Keywords: Energy Systems; MILP; Optimization; Small very significant effect on the overall economics of an Scale LNG; Supply Chain LNG project. The model presented in this paper is partially based 1 Introduction on previous work by the authors (Bittante et al. 2016), where a single-period model was introduced to aid Liquefied natural gas (LNG) is produced by cooling decision making on crucial aspects in the design of natural gas (NG) below -162 °C (at atmospheric small-scale LNG supply chains. The work focused on pressure), which reduces the volume to approximately both strategic and tactic decisions, simultaneously one six-hundredth of the original. It is the cleanest form optimizing location of the satellite terminals, size of the of fossil fuels since it has undergone purification during fleet and vehicle routing to solve the overall logistic the liquefaction process, and it has a high H/C ratio as it problem. The contribution of the current paper lies in the is primarily composed of methane. The lower carbon consideration of storage size and inventory level intensity is the key of its recent growth of popularity: optimization, achieved through the adoption of a multi- LNG is a perfect bridge fuel on the way to a world using period formulation. 100 % renewable energy, providing grid stability and In general, the problem studied can be considered reliability during fluctuations in the electricity part of the broad research area of vehicle routing generation of intermittent renewable sources. Further- problems (VRP), for which the literature is rich and more, the recent regulations against pollution in the many variants and classes have been established maritime transportation within identified emission (Braekers et al. 2015). However, classical VRP control areas imposed by the International Maritime problems do not consider all aspects tackled by the Organization (IMO) have also increased the popularity proposed model. The subproblem defining the number of LNG, making it the most suitable fuel for maritime and size of vessels needed to solve the maritime vessels propulsion. DOI: 10.3384/ecp17138332 Proceedings of the 58th SIMS 332 September 25th - 27th, Reykjavik, Iceland transportation represents a fleet-size and mix-vehicle routes being predefined, the path-flow formulations do routing problem (FSMVRP), while the strategic not include constraints related to routing feasibility, but subproblem of locating the satellite terminals and the focus on the set of ports or customers to serve. This is linked routing belongs to the class of location-routing usually beneficial when the size of the problem problems (LRP). Finally, the sizing of storage tanks and increases. Often, the solution time is anyhow the associated inventory include aspects attributable to unacceptably long and pure heuristics or early the class of inventory routing problems (IRP). For more terminations in exact methods are preferred. This is detailed information on these classes of problems we mainly due to the intrinsic complexity of VRP in refer to Hoff et al. (2010) for a review paper on general. Usually only very small problems, not relevant FSMVRP with both maritime and land transport, Drexl for real-life studies, can be solved in reasonable and Schneider (2015) for a recent survey and computation time with a deterministic approach. To classification on LRP, and Andersson et al. (2010) for a overcome this limitation still applying an exact comprehensive review on IRP. method we neglected some operational aspects that Most of the approaches proposed in the literature were not considered essential at the first level of focus on heuristics solutions and very few papers planning: We do not consider scheduling, supply present exact methods. Baldacci et al. (2009) designed a availability according to production rate or inventory, mixed integer linear programming (MILP) model to boil-off loss, time windows at the ports, or load solve a FSMVRP problem similar to the one considered dependent fuel consumption for the ships. With these in this paper, but where each customer is associated with simplifications, a mixed integer linear programming a single route as in the classic VRP. By contrast, in our (MILP) model was formulated that can solve realistic approach we allow for multiple visits at the customers problems within a few hours of computation time. Both by multiple vehicles. This feature also occurs in the strategic infrastructure decisions and tactical planning formulation of the LRP subproblem. While most of the are simultaneously optimized. The multi-period variables used for describing the activation of satellite formulation allows for a more detailed evaluation of the terminal and their associated routes and delivery are the storage tank sizes and inventory, offering the possibility same as those used in the literature (Gonzalez-Feliu for a more efficient routing. The multi-period 2009), the set of binary variables to activate the routes formulation is illustrated by comparison to the single- associated with an activated satellite terminal has been period solution of a case study based on the emerging changed into integer variables to allow for multiple LNG market in the Gulf of Bothnia. voyages to the same port. According to the classification given in the review paper by Andersson et al. (2010), 2 Problem description our approach falls into the finite time class, featuring deterministic demand, many-to-many topology, In this paper we present a multi-period formulation as multiple routing, fixed inventory, and heterogeneous an extension of the model presented in Bittante et al. fleet composition. A contribution listed in the reviewed (2016). The problem tackled is a regional supply of literature presenting similar features and where a LNG from a set of potential supply ports to inland end deterministic approach is used is the work by Al- customers through a set of potential satellite terminals. Khayyal and Hwang (2007) for an IRP for a multi- At the supply ports LNG is loaded to specially designed commodity liquid bulk. Their problem is a classic IRP vessels and transported to the satellite terminals. LNG problem, where storage sizes are given as well as the can also be transported by truck from the ports to inland fleet of ships. The model focuses on the key aspects of customers. Satellite terminals have potential locations a multi-product pickup-delivery problem and the and can be activated or not according to the overall authors solve a small illustrative example for detecting objective. Potential satellite terminals and inland the central parameters to be used in developing a customers have given fixed demands for the time strategy for solving larger instances. A recent paper by horizon considered, which must be satisfied either by Koza et al. (2017) presents many characteristics similar transported LNG or by an alternative fuel. This generic to our problem, including the focus on LNG market and fuel is merely used to allow the model to partly or fully infrastructure. Our contribution differs by the market- exclude customers from the LNG supply chain; segment it is directed to (i.e., small-scale logistics versus therefore we do not consider the transportation costs of liner networks), the feature of locating the satellite the alternative fuel. It should be noted that the demand terminals and the multi-period formulation for sites represent cluster of consumers, which justifies the optimized storage sizing and inventory.

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