Inventory Ship Routing and Cargo Stowage Planning on Chemical Tankers

Chemical tankers are a type of ocean carrier with multi-compartments to simultaneously carry various liquid chemicals in bulk and prevent their mixing. This paper discusses the difficulties chemical tanker managers experience when planning vessel routes and scheduling inventory maintenance because of chemical tankers’ unique characteristics and operational constraints. To date, no models have addressed chemical tankers’ inventory routing and scheduling needs while accounting for these challenges. Bridging the research gap, we propose a novel, integrated, mathematical model of inventory ship routing and stowage planning problem (ISRSPP) for chemical tankers. We seek to combine stowage planning, which is an operational problem, with inventory ship routing, which is a tactical problem, through integrated tactical planning. Our objective is to propose a solution with minimal total voyage costs. For this purpose, we formulate our problem in a mixed integer linear program. We build two scenarios to analyze the models applicability and performance, and we solve both of them using a commercial solver. Our results confirm that the stowage planning problem cannot be separated from the inventory ship routing problem for chemical tankers because such a separation could lead to fleet routes for which no feasible stowage plan is possible.

Chemical tankers; Integrated planning model; Inventory ship routing; Mixed-integer linear programming; Stowage planning

     Maritime transport, an important pillar of world trade and globalization, is critical for economic growth and sustainable development (Akbulaev & Bayramli, 2020; Bagoulla and Guillotreau, 2020; Dui et al., 2021). Disruption due to the coronavirus disease 2019 (COVID-19) pandemic, such as a short-term decrease in the volume of global maritime trade by 4.1% in 2020 (UNCTAD, 2020), presents challenges and opportunities to build resilience and sustainability in the maritime transport sector (Dulebenets, 2019; Dui et al., 2021; Berawi et al., 2020). This turmoil has also influenced the US$5.7 trillion global chemical industry, which has been an integral part of the global economic landscape for many years. Nevertheless, reaching over US$2.9 trillion in 2019, the global chemical trade has realized moderate average annualized growth of 4.54% over the last decade (World Trade Organization, 2020). As a result, the global demand for commercial shipping fleets—including chemical tankers—has remained strong. In 2019–2020, chemical tankers’ dead-weight capacity tonnage grew by 2.9% (UNCTAD, 2020).
      In this paper, we present an integrated, mathematical model of chemical tankers’ inventory ship routing and stowage planning problem (ISRSPP). Chemical tankers can be distinguished from other ocean bulk carriers by their multiple compartments to simultaneously store various liquid chemicals in bulk and prevent their mixing. Parcel tankers’ compartments are equipped with separate cargo pumping systems. Each cargo pumping system features one hydraulically driven, submerged cargo pump with independent piping, which enables the simultaneous handling of multiple cargoes without mixing.
    Chemical tanker managers must address two compatibility constraints for safety concerns regulated by the International Maritime Organization (Oh & Karimi, 2008). According to the International Bulk Chemical (IBC) Code, first, both the construction and coating materials of a compartment determine the chemical cargoes that can be loaded. Typically, chemical tankers with stainless steel compartments can carry a wider range of chemical cargoes than those with compartments lined with organic, epoxy-based and inorganic, zinc silicate-based coating materials (Neo et al., 2006; Oh & Karimi, 2008). Second, the cargoes loaded into chemical tankers’ adjacent compartments must be non-reactive. If the common bulkhead of neighboring compartments is cracked, incompatible cargoes can create a disastrous chemical reaction. The US Coast Guard Compatibility Chart specifies a related regulatory stowage restriction.
        To ensure vessel stability, two requirements must be fulfilled. First, vessels must comply with intact (Marine Safety Committee, 2008a) and damage stability (Marine Safety Committee, 2008b) requirements. Operationally, these requirements are met by determining how high a vessel’s center of gravity is in loading conditions, which is a function of the vessel’s draft and accounts for the free-surface effect (Øvstebø et al., 2011). Second, a vessel must ensure its stability during a voyage by properly distributing cargoes’ weight across compartments so that it does not trim excessively. Trim by either the bow or the stern must be limited, depending on the vessel’s design. Additionally, the allocation of ballast water into ballast tanks is also important to maintain a vessel’s stability (Zeng et al., 2010; Braidotti et al., 2018). However, this problem must be addressed by tanker operators anticipating uncertainty in a dynamic operational environment.
    Next, during loading and unloading activities, a vessel’s structure must be strong enough to withstand unevenly distributed weight. At a given draft and trim in still water, buoyant force is also non-uniformly distributed along a vessel’s length, though in a fixed fashion since each unit length of the vessel experiences a downward force equal to the weight of water displaced by a transverse section of the corresponding unit length (Eyres & Bruce, 2012). Therefore, either an excess of weight or an excess of buoyant force can occur at each vessel’s section along its length. Excessive load concentration at the front and rear ends of the vessel creates a hogging deformation. Meanwhile, excessive load concentration in the middle of the vessel creates a sagging deformation. In the long run, the uneven distribution of cargo weight across a chemical tanker’s compartments may result in the cracking of the vessel’s structure (Nugroho et al., 2018).
    An inventory ship routing problem generally is experienced in industrial shipping when an owner is responsible for both managing inventory and transporting cargoes. This problem can be categorized as tactical in maritime transportation planning (Christiansen et al., 2007). Meanwhile, a stowage planning problem can be classified as operational, and operational problems are generally resolved after tactical problems have been solved. However, due to the aforementioned characteristics and key operational constraints of chemical tankers, separating these two planning problems can lead to fleet routes for which no feasible stowage plan is possible.
    The first model for a routing and scheduling problem facing a single chemical tanker, as well as a fleet of heterogeneous chemical tankers transporting multiple liquid chemical products, is proposed by Jetlund and Karimi (2004). Although they address the cargo routing problem for chemical tankers, they overlook chemical tankers’ uniqueness. Neo et al. (2006) formulate an extended version of the single chemical tanker cargo routing and scheduling model discussed in the previous paper by including additional constraints on cargo compatibility and vessel stability in their mixed-integer linear programming (MILP) model. This model is solved using commercial software considerably fast. A similar MILP model to the two in the previously mentioned papers is formulated by Cóccola and Méndez (2013), but it does not account for product compatibility and vessel stability. Oh & Karimi (2008) introduce what they call a “novel solution approach” to solve an industrial-scale chemical tanker routing and scheduling problem that accounts for product compatibility. They assume that vessel stability can be maintained within limits by filling a ballast tank adequately. All the above-mentioned routing and scheduling problems can be categorized as cargo routing problems (Al-Khayyal & Hwang, 2007).
        Inventory ship routing and scheduling solutions for maritime chemical transport companies’ heterogeneous vessels transporting multiple liquid bulk products is proposed by Al-Khayyal and Hwang (2007) and Siswanto et al. (2011). Al-Khayyal and Hwang (2007) consider an MILP model to plan routes and schedules for multiple vessels carrying liquid bulk products in their multi-dedicated compartments, where each compartment is dedicated for a certain product. Siswanto et al. (2011) relax the previous problem by substituting multi-dedicated compartments with multi-undedicated compartments. They formulate the problem as an MILP and develop a multi-heuristics-based approach to solve it. Neither of these papers considers product compatibility and vessel stability constraints in their models.
       Hvattum et al. (2009) introduce the problem of allocating bulk cargoes to compartments in a planned route maritime shipping, which is called the tank allocation problem (TAP). They consider product-compartment compatibility, compartment sloshing, stability, and hazmat regulation constraints in their MILP formulation and solve the problem using a commercial solver. Vilhelmsen et al. (2016) modify an optimality-based method presented in the previous paper. In contrast to the previous paper, they approach the TAP from a tactical viewpoint. Instead of identifying an optimal compartment allocation, their main objective is to swiftly determine feasible cargo allocations for a planned vessel route.
      Decisions resulting from separate solution approaches to interrelated decision problems may not be compatible with each other. In this case, an integrated solution approach is needed that can solve problems simultaneously (Pasha et al., 2020). To our knowledge, no inventory ship routing problem has been formulated for chemical tankers that considers the stowage planning problem through integrated tactical planning. To bridge this research gap, we introduce a new mathematical model that integrates stowage planning, considering product compatibility, vessel stability, and durability as part of chemical tankers’ inventory routing when shipping multiple liquid chemicals.
        The remainder of this paper is organized as follows. Section 2 describes the specific problem that we address. Our ISRSPP mathematical model is presented in Section 3. Section 4 discusses a case study. The results of our numerical experiments are presented and discussed in Section 5. Finally, Section 6 concludes this paper.

    In this paper, we developed a novel mathematical model ISRSPP that integrates our stowage planning problem and accommodates cargo compatibility, ship stability, and ship durability into the inventory routing and scheduling problem facing heterogeneous chemical tankers transporting multiple liquid chemicals. Integrating stowage planning from a tactical perspective, this model aims to suggest feasible vessel routes and schedules, rather than an optimal stowage plan. This model minimizes total voyage costs—including traveling costs, anchoring costs, port dues, and cargo dues—while satisfying constraints for routing, loading and unloading, scheduling, inventory, and stowage planning during the planning horizon. To the best of our knowledge, the literature has not presented a mathematical model that integrates inventory ship routing and stowage planning for chemical tankers.
    We applied this MILP model to a small-case study solved in two scenarios using the LINGO 18 solver. Our results imply that cargo stowage planning cannot be separated from inventory ship routing and scheduling, particularly for chemical tankers, because such exclusion could create fleet routes for which no feasible stowage plan is possible. However, our model faces limitations, mainly due to considerable computation time, as our case study has shown. Obviously, this limitation must be addressed by developing specialized algorithms to exploit this model’s inherent structure before the model can be further developed so that it can solve more decision problems, such as ballast allocation, speed selection, fuel consumption, and weather routing. Such development would further expand the maritime transport sector’s resilience and sustainability.

    The commercial solver used in this work was fully supported by LINDO Systems Inc., whose support is gratefully acknowledged.

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