روش های بهینه سازی مصرف سوخت رسان در کشتیرانی: بررسی انتقادی و الحاقات

It is crucial nowadays for shipping companies to reduce bunker consumption while maintaining a certain level of shipping service in view of the high bunker price and concerned shipping emissions. After introducing the three bunker consumption optimization contexts: minimization of total operating cost, minimization of emission and collaborative mechanisms between port operators and shipping companies, this paper presents a critical and timely literature review on mathematical solution methods for bunker consumption optimization problems. Several novel bunker consumption optimization methods are subsequently proposed. The applicability, optimality, and efficiency of the existing and newly proposed methods are also analyzed. This paper provides technical guidelines and insights for researchers and practitioners dealing with the bunker consumption issues.

Maritime transportation is the backbone of world trade, and world seaborne trade was estimated at 8.4 billion tons in terms of the total goods loaded in 2011 (UNCTAD, 2011). In recent years, increased competition and global shipping downturn have been putting downward pressure on the revenues of shipping companies; at the same time, increased security regulations and fuel prices continued to increase their operating costs. The bunker cost constitutes a large proportion of the operating cost of a shipping company (Notteboom, 2006). For example, Ronen (2011) estimated that when bunker fuel price is around 500 USD per ton the bunker cost constitutes about three quarters of the operating cost of a large containership. The amount of bunker consumed by ships also determines the amount of gas emission, including Green House Gas (GHG) such as carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O), Non-Green House Gases such as sulfur oxides (SOx) and nitrogen oxides (NOx), and various other pollutants, such as particulate matter, volatile organic compounds, and black carbon (Psaraftis and Kontovas, 2013). The above gases have negative effect on global climate. For example, GHGs contribute to global warming, SOx causes acid rain and deforestation, and NOx causes undesirable health effects. According to the 2009 GHG study by the International Maritime Organization (IMO, 2009), international shipping contributes 2.7% of the CO2 emitted globally. IMO is currently considering many measures to reduce GHGs (Psaraftis, 2012). For instance, the IMO Marpol 73/78 Annex VI regulations aim to reduce nitrogen oxide (NOx) emissions and prevent sulfur oxide (SOx) and particulate matter emissions from ships. In view of strict regulations on CO2 emission, tradable CO2 emission schemes have been developed and applied, and the current average contract price is about 8 Euros per ton of CO2 emitted (ICE-ECX, 2012). To meet future regulation on emission, shipping companies must either reduce bunker consumption or use cleaner but more expensive bunker fuel, or purchase emission quota from other companies. 1.1. Impact of sailing speed on shipping capacity, inventory cost and bunker consumption The bunker consumption of a ship on one hand depends on the design and structure of the ship, and it is on the other hand very sensitive to the sailing speed. This study focuses on the impact analysis of sailing speed on bunker consumption. Fig. 1 plots the relations between sailing speed and bunker consumption for four types of ships: ships with a capacity of 3000 twenty-foot equivalent units (3000-TEU ships for short), 5000-TEU ships, 8000-TEU ships and 10000-TEU ships. Clearly, when the speed increases, the bunker consumption increases more than linearly. Ronen (1982) mentioned that daily bunker consumption is approximately proportional to the sailing speed cubed, and Wang and Meng (2012a) further calibrated the relation using historical operating data of containerships and found that the exponent is between 2.7 and 3.3, which supports the third power approximation. Du et al. (2011) used the exponent of 3.5 for feeder containerships, 4 for medium-sized containerships, and 4.5 for jumbo containerships according to suggestions of a ship engine manufacturing company. Kontovas and Psaraftis (2011) suggested using an exponent of four or greater when the speed is greater than 20 knots. In general, a higher sailing speed has both advantages and disadvantages. The first advantage is that the amount of cargo that can be shipped annually is larger. For example, consider a ship with a capacity of 10,000 tons that sails between two ports (A and B) whose distance is 10,000 n miles, and suppose that the total time for discharging and then loading a full ship load is 3 days at each port, as shown in Fig. 2. If the ship sails at 15 knots, it needs 3 + 10,000/(24 × 15) ≈ 30.8 days to transport 10,000 tons of cargo from port A to port B (or from port B to port A). Therefore in 1 year it can transport 365/30.8 × 10,000 = 1.19 × 106 tons of cargo. If the ship sails at 20 knots, it needs only 23.8 days to ship cargo from A to B and hence would be able to transport 1.53 × 106 tons of cargo annually. The second advantage is that the inventory cost associated with shipping is lower. In the above example, the cargo needs a total of 30.8 days for maritime transportation and handling if the ship sails at 15 knots, and needs only 23.8 days at the speed of 20 knots. The inventory cost of containerized cargos is high because of the high value of the cargos. For instance, Notteboom (2006) estimated that one day delay of a 4000-TEU ship implies a total cost of 57,000 Euros associated with the cargos in the containers; Bakshi and Gans (2010) estimated the inventory cost of containerized cargo at 0.5% the value of a container per day. The disadvantage of a higher sailing speed is that the amount of bunker burned is much higher. Suppose that the daily bunker consumption is proportional to the sailing speed cubed. As a result, the bunker consumption for accomplishing a trip from port A to port B in Fig. 2 is proportional to the sailing speed squared (the daily bunker consumption is proportional to the sailing speed cubed, but the number of days required is inversely proportional to the sailing speed). Therefore, the amount of bunker consumed annually at the speed of 20 knots (proportional to 202 × (365/23.8) ≈ 6134) is 130% higher than that at the speed of 15 knots (proportional to 152 × (365/30.8) ≈ 2666), and the amount of cargo carried is only (1.53–1.19)/1.19 ≈ 29% higher. Consequently, the optimal sailing speed is desirable to balance the tradeoffs between cargo shipping capability, inventory cost, and bunker cost. 1.2. Contexts of bunker consumption optimization In literature, bunker consumption optimization is cast into three application contexts. The first one is minimizing the operating cost of a shipping company by optimizing the sailing speed. For example, in shipping network design (Alvarez, 2009), ship fleet deployment (Gelareh and Meng, 2010), ship schedule construction (Qi and Song, 2012 and Wang and Meng, 2012b), sailing speed optimization (Norstad et al., 2011, Ronen, 2011 and Wang and Meng, 2012a), and selection of bunkering port and volume (Yao et al., 2012). As aforementioned, a lower speed means larger inventory cost. However, the inventory cost is borne by shippers and hence is not directly related to the shipping companies. Therefore, inventory cost is not considered in most of the studies in this category. Some studies explicitly incorporate the inventory cost (e.g., Wang and Meng, 2011 for schedule design), or impose a certain level of service in terms of the maximum allowable origin-to-destination (OD) transit time (Meng and Wang, 2011). In the second category, the amount of emission (usually converted to CO2 equivalent) is formulated in the model (Corbett et al., 2009 and Kontovas and Psaraftis, 2011). From the government’s viewpoint, imposing a fuel tax would effectively lower down the sailing speed of ships, thereby reducing the emissions at least in the short term (Corbett et al., 2009). From the shipping company’s viewpoint, taking the minimization of bunker consumption (which is proportional to emission) as an objective has two implications: one is to fulfill the international or local regulations on ship emission; the other is to build an image of social responsibility. To account for emission in modeling, one approach is to minimize the weighted sum of operating cost and emission. Mathematically, this approach is equivalent to an increase of bunker price. Another possible approach aims to minimize the operating cost while ensuring that the emission cannot exceed a certain upper limit. This approach can be adopted to find Pareto-optimal solutions that minimize the operating cost and emission, as shown in Fig. 3. In the third category, port operators take into account the bunker cost of the shipping companies (Golias et al., 2010, Lang and Veenstra, 2010, Du et al., 2011 and Wang et al., 2013), which contrasts conventional planning approaches where port operators maximize their own efficiency in berth allocation. In such a setting, port operators prioritize the berthing of incoming ships while accounting for the bunker cost of incoming ships. After that, port operators inform each ship captain a suggested arrival time, and as a result the ship could slow down to save bunker if the port is already very congested. For example, suppose that the ship is 200 n miles away from the port, and it has to wait for 5 h for a berth if it sails at its current speed 20 knots. If the port operator informs the ship captain that a berth is available only 200/20 + 5 = 15 h later, then the captain could slow down to a speed of 200/15 = 13.3 knots, resulting in a significant reduction in bunker consumption. We give another example with more than one ship. Suppose that there are two identical ships approaching one port. One ship is sailing at the speed of 20 knots from 1000 n miles away, and the other is sailing at 25 knots from 1250 n miles away. Both ships need 10 h’ time for container handling at berth and both ships desire to be berthed in 60 h. Only one berth is available for these two ships. If all other conditions are the same (identical ships sailing under the same condition and requiring the same container handing operations at the port), the port operators should let the ship at 20 knots be berthed first, and inform the ship at 25 knots to slow down to the speed of 1250/(1000/20 + 10) = 20.8 knots. Note that if the ship at 25 knots is berthed first, the resulting bunker cost reduction is smaller, because the bunker consumption is more sensitive to speed when the speed is higher. 1.3. Objectives and contributions Investigations on the solution methods are of considerable difficulty/significance for the bunker consumption optimization problems, due to the nonlinearity of bunker consumption relation with sailing speed and existence of discrete decision variables (the number of ships to deploy or berth allocation decisions). As a consequence, the objective of this paper is to critically review the solution methods proposed in the literature and then design efficient solution methods that supplement the existing methods. Contributions of this paper are threefold. First, we provide a complete framework on tailored ε-optimal solution methods, and this framework enables us to design six new tailored ε-optimal solution methods. Second, based on Du et al. (2011), we introduce an auto-conduction second-order cone programming (SOCP)-transformation procedure that provides the optimal solution. Third, we review the existing methods in the literature and methods proposed by this paper and then analyze the advantages and disadvantages of each method. Hopefully, this review could provide guidelines for researchers and practitioners for optimizing bunker consumption to minimize operating cost and emission from the viewpoints of both shipping companies and port operators. Moreover, the approaches may also be applied to optimize sailing speed in settings with fixed speed ( Christiansen et al., 2004, Shintani et al., 2007, Karlaftis et al., 2009, Gelareh et al., 2010, Bell et al., 2011, Brouer et al., 2011 and Reinhardt and Pisinger, 2012). The remainder of this paper is organized as follows. Section 2 gives a simple bunker consumption example for us to demonstrate the solution approaches. Section 3 presents two basic solution methods: enumeration and dynamic programming. Section 4 introduces a discretization approach. Section 5 proposes a complete framework on tailored ε-optimal solution methods. Section 6 is dedicated to an exact SOCP approach. A summary of these methods are provided in Section 7.

This study has reviewed and extended a number of bunker consumption optimization methods. The enumeration method is supplemented by proving that the sailing speed is constant in a round-trip. The dynamic programming method is borrowed from tramp shipping speed optimization to solve the liner ship speed optimization problem. The scheme of the discretization method is introduced in detail. A complete framework on tailored ε-optimal solution methods that take advantage of the convexity of the problem is proposed based on the existing studies. This framework enables us to design six new tailored ε-optimal solution methods. Finally, an auto-conduction second-order cone programming (SOCP)-transformation procedure is introduced. These methods could be used to optimize the sailing speed of ships, minimize emissions, and plan jointly for port operations and shipping operations. The properties of these approaches are summarized in Table 2.